Nelson Math Sampler K-6
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NELSON MATHS Australian Curriculum NSW
AUSTRALIAN CURRICULUM
NSW
K– 6
o o k B a t n n e d d u t S her ’s Resour c c e a Te SAMPLER
STUDENT BOOK AND TEACHER’S RESOURCE SAMPLER
Written for the NSW Mathematics K–6 Syllabus for the Australian Curriculum Glenda Bradley, Pauline Rogers, Yale Mercieca, Lauren White & Aaron Tait PRI 8368 NMAC NSW Sampler Cover.indd 3
15/05/14 11:28 AM
Nelson Maths: Australian Curriculum NSW Sampler
Text: Glenda Bradley, Pauline Rogers and Brian Murray Series consultant and co-author: Jay Dale Series consultant (NSW): Brian Murray Editor: Sarah Russell Designers: Mark Sanders and Stella Vassiliou Cover designer: Ivana Tendean Cover illustration: Ned Culic Text illustrations: Mary Ann Furness, Colby Heppell, Rob Mancini, Joe Sciglitano Production controller: Renee Cusmano Acknowledgements The authors and publisher would like to acknowledge permission to reproduce material from the following source: NSW Mathematics K–10 Syllabus © Board of Studies, NSW for and on behalf of the Crown in right of the state of New South Wales, 2013 The Board of Studies takes no responsibility for errors in the reproduction of the Material supplied by the Board of Studies to the Publisher.
ACARA Copyright Notice All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2014.
For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum. Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors. Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au. This material is reproduced with the permission of ACARA.
Every effort has been made to trace and acknowledge copyright. However, if any infringement has occurred, the publishers tender their apologies and invite the copyright holders to contact them.
Text © 2014 Cengage Learning Australia Pty Limited Illustrations © 2014 Cengage Learning Australia Pty Limited
Copyright Notice This Work is copyright. No part of this Work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without prior written permission of the Publisher. Except as permitted under the Copyright Act 1968, for example any fair dealing for the purposes of private study, research, criticism or review, subject to certain limitations. These limitations include: Restricting the copying to a maximum of one chapter or 10% of this book, whichever is greater; Providing an appropriate notice and warning with the copies of the Work disseminated; Taking all reasonable steps to limit access to these copies to people authorised to receive these copies; Ensuring you hold the appropriate Licences issued by the Copyright Agency Limited (“CAL”), supply a remuneration notice to CAL and pay any required fees.
Cengage Learning Australia Level 7, 80 Dorcas Street South Melbourne, Victoria Australia 3205 Phone: 1300 790 853 Cengage Learning New Zealand Unit 4B Rosedale Office Park 331 Rosedale Road, Albany, North Shore NZ 0632 Phone: 0800 449 725 For learning solutions, visit cengage.com.au Printed in Australia by RR Donnelley Asia Printing Solutions Limited 1 2 3 4 5 6 7 18 17 16 15 14
PRI 8368 NMAC NSW Sampler Cover.indd 4
210 x 297
15/05/14 11:28 AM
K– 6
o o k B a t n n e d d u t S her ’s Resour c c e a Te SAMPLER Glenda Bradley, Pauline Rogers, Yale Mercieca, Lauren White & Aaron Tait
Marketing Sampler.indb 1
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Contents Introduction Kindergarten
3
Lesson Plan BLM 8 ‘Blank Cards’ BLM 15 ‘Dot Patterns to 6’ BLM 16 ‘Make a Dice’ BLM 17 ‘Number Fan: Numerals’ BLM 20 ‘In the Pond’ BLM 21 ‘Speckled Frogs’ Assessment Task Card Student Book
6 6 10 11 12 13 14 15 16 18
Lesson Plan Student Book
22 22 26
Year 1 Lesson Plan BLM 6 ‘Blank Number Line’ BLM 14 ‘100 Chart’ BLM 15 ‘Make Your Own 100 Chart’ Assessment Task Card Student Book
30 30 34 35 36 37 38
Lesson Plan Student Book
Statistics and Probability Unit 20 Chance Lesson Plan Student Book
Number and Algebra Unit 18 Decimals to 2 Decimal Places Lesson Plan BLM 34 ‘Decimal Numbers and Words 2’ BLM 42 ‘Symbols’ Assessment Task Card Student Book
Unit 8 Shape Lesson Plan Student Book
42 42 46
Unit 1 Place Value Lesson Plan BLM 2 ‘5-digit Number Expander’ Assessment Task Card
Student Book
Number and Algebra
Unit 14 Perimeter
BLM 1 ‘Number Cards’ BLM 2 ‘Arrow Cards 1’ BLM 3 ‘Arrow Cards 2’ BLM 4 ‘Number Stairs’ Assessment Task Card Student Book
50 50 54 55 56 57 58 60
Measurement and Geometry Unit 10 Position Lesson Plan Student Book
Year 3 Lesson Plan BLM 1 ‘Number Cards 1’
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Student Book
114 114 118 119 120 122 126 126 130
Year 6 Number and Algebra Unit 3 Integers Lesson Plan BLM 1 ‘Integer Cards 1’ BLM 2 ‘Number Line’ BLM 4 ‘Plotting Points’ BLM 5 ‘1 cm Grid Paper’ Assessment Task Card Student Book
134 134 138 139 140 141 142 143 144
Number and Algebra
Number and Algebra Unit 1 Numbers, Numbers, Numbers
Lesson Plan
BLM 3 ‘Integer Cards 2’
64 64 68
106 106 110
Number and Algebra
Measurement and Geometry
Lesson Plan
94 94 98 99 100 101 102
Year 5
Year 2 Unit 4 Numbers Up to 1000
86 86 90
Year 4
BLM 1 ‘Place-Value Chart’
Measurement and Geometry Unit 10 Length and Area
Student Book
77 78 79 80 82
Measurement and Geometry
Number and Algebra Unit 8 Numbers Beyond 20
Assessment Task Card
BLM 33 ‘Decimal Numbers and Words 1’
Measurement and Geometry Unit 12 2D Shapes
BLM 3 ‘Blank Chart’ BLM 4 ‘Blank Cards’
Number and Algebra Unit 6 Dot Patterns
BLM 2 ‘Number Cards 2’
72 72 76
Unit 11 Cartesian System Lesson Plan Student Book
Scope and Sequence
148 148 152 156
07/05/14 3:23 PM
Introduction This Sampler presents units from the new primary mathematics program – Nelson Maths: Australian Curriculum NSW – available for implementation in 2015. This exciting new mathematics program supports the Australian Curriculum content strands of Number and Algebra, Measurement and Geometry, and Statistics and Probability from Kindergarten to Year 6. The program also integrates the Working Mathematically outcomes of Communicating, Problem Solving and Reasoning throughout the activities and tasks for each year level. Assessment is an essential part of Nelson Maths: Australian Curriculum NSW, providing teachers with a variety of opportunities to assess their students’ learning for future planning.
6
Two units from each year level from Kindergarten to Year 6 are included in this Sampler. One of the units for each year level is from the strand of Number and Algebra, to showcase the sequential development of this content throughout the year levels.
6
Teachers can be assured that Nelson Maths: Australian Curriculum NSW NSW continues the tradition of offering teachers choice when selecting tasks to suit the needs of their students. AUSTRALIAN CURRICULUM
AUSTRALIAN CURRICULUM
General Overview
NSW
er’ Teacrhce Bs
Nelson Maths: Australian Curriculum NSW supports the implementation of the NSW Syllabus for the Australian Curriculum: Mathematics K-10. The units cover the content strands of Number and Algebra, Measurement and Geometry and Statistics and Probability K–6, and integrate the Working Mathematically strands of Communicating, Problem Solving and Reasoning throughout the activities and tasks.
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This edition of Nelson Maths provides: • up to 33 units of work, specifically written to match the Australian Curriculum • extensive assessment opportunities including 30+ Assessment Task Cards, Student Assessment pages and Mid- and End-of-Year Tests • numerous hands-on tasks and investigative activities where teachers have the opportunity to choose tasks that best suit the needs of their students
• interactive activities in every unit, incorporating ICT and utilising classroom computers and interactive whiteboards
Nelson Maths: Australian Curriculum NSW is based on between 30 and 35 units of work for each year level. Each unit of work is divided into three 6 teaching 2 Lesson Plans. A Lesson Plan can be taught over one or more 5 sessions depending on the needs of students. While the Lessons Plans% 8 5.. 6 are sequential and should be taught in the order they appear in7the63 unit, teachers have the flexibility to complete a number of activities from a Lesson Plan over a number of days – to cater for the learning requirements of their class.
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• an extensive range of interactive Nelson Teaching Objects and reference to Learning Objects from Education Services Australia • specific recommendations for future learning experiences, including both scaffolded and extension activities • over 50 unit, resource, assessment and planning BLMs.
YEAR 6
NSW
NELSON MATHS Australian Curriculum
AUSTRALIAN CURRICULUM
NSW
6
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Nelson Maths: Australian Curriculum NSW supports the implementation of the NSW Syllabus for the Australian Curriculum: Mathematics K-10. The units cover the content strands of Number and Algebra, Measurement and Geometry and Statistics and Probability K–6, and integrates the Working Mathematically strands of Communicating, Problem Solving and Reasoning throughout the activities and tasks.
The Nelson Maths: Australian Curriculum NSW Edition Student Books feature: • engaging tasks that students can complete independently or in groups • three Student Book pages per unit • one Student Assessment page per unit • the linking NSW Syllabus for the Australian Curriculum - Mathematics K-10 content sub-strand, outcome and code for each unit • a Glossary of mathematical terms.
Nelson Maths Facts CVR.indd 1
For learning solutions, visit cengage.com.au
21/01/09 10:16 AM
9 780170 352925
If you experience difficulties using this product, email: [email protected]
Unit
6
1 to 6, using small paper plates and dot stickers. Get them to arrange the plates in a random order in front, and using NTO K.20 ‘Dice’ roll a number and get them to point to a plate with the same number of dots. Repeat, gradually rolling the dice more quickly.
Dot Patterns
Whole numbers: MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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LESSON PLAN
TUNING IN HOW MANY CAN YOU SEE?
1
FIVE LITTLE SPECKLED FROGS
Give the student a set of cards made from BLM 15 ‘Dot Patterns to 6’. Present NTO K.4 ‘Numbers’ and randomly generate a number from 0 to 6. Have them read the number and find the matching number card.
3
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is more than the dot pattern displayed.
4
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is less than the dot pattern displayed.
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, a large number fan and one for each student made from BLM 17 ‘Number Fan: Numerals’ Ask students how many speckled frogs were sitting on the log. Show students large cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns and invite a student to find a dot plate that shows five. Show students the enlarged number fan made from BLM 17 ‘Number Fan: Numerals’ and all the numbers that are on it. Tell students that you will hold up each number, and when you get to the number that matches the plate, students put up their hand. Select another dot plate and then ask a student to find the corresponding number on the number fan. Give a number fan to each student, and hold up various dot plates, getting students to find the matching number on their number fan.
Note: Choose from Tasks 1, 2 or 3. You will need: NTO K.20 ‘Dice’ or a large dice, BLM 16 ‘Make a Dice’, counters, NTO K.19 ‘How Many Dots?’, Student Book p. 18 ‘Dot Plates’
6
You will need: BLM 20 ‘In the Pond’, counters, a dice, NTO K.22 ‘What Number Is This?’, Student Book p. 19 ‘Glub! Glub!’
IN THE POND
Give a copy of BLM 20 ‘In the Pond’ to pairs of students. Each student will need about 20 counters that are the same colour but different from their partner’s. Students take it in turns to roll a dice and then place one counter on a lily pad that matches the dice. The counter can be placed on a word, numeral or dot pattern that matches the dice. If they cannot find a lily pad to match the dice, they miss that turn. The student who places the most counters on the board is the winner.
INTERACTIVE TASK
Have students use NTO K.19 ‘How Many Dots?’.
STUDENT BOOK p. 18 ‘Dot Plates’
TASK 2:
TEACHING GROUP
DOT PATTERNS
TARGETED ASSESSMENT
If the student is experiencing difficulty:
Note: Choose from Tasks 1, 2 or 3.
TASK 1:
K.6
Kindergarten: Assessment Task Card Unit
INDEPENDENT TASKS
SAME, SAME
Ask students what they can see on the sides of a dot dice on NTO K.20 ‘Dice’ or a large dice. Explain that they are going to make their own dice using BLM 16 ‘Make a Dice’. In one of the squares students draw one dot. In the next square they draw two dots and so on until each side has been filled with dots for each number from 1 to 6. Students cut out the dice net and assemble. Note: students may need teacher, older peer or parent support to assemble. Have students play ‘Same, Same’ with a partner. Students roll their dice, and when the numbers rolled are the same, they collect a counter. The first pair to collect six counters is the winner.
Q1
Have the student practise reading dot patterns by playing board games, e.g. ‘Number Game Board’ in Nelson Maths Building Mental Strategies Big Book 1, pp. 12–13.
Q2
Have the student use NTO K.19 ‘How Many Dots?’ set to numbers from 0 to 6 and randomly generate either dot patterns or numerals for recognisation.
Q3
Give the student the set of cards made from BLM 15. Using NTO K.19 to generate a number between 0 and 6, have the student find a card with the same dot pattern. Then have them find the cards that show more and show less.
Q4
Select a card from BLM 15, and have the student guess the card by asking ‘Is it less?’ questions, e.g. ‘Is it less than 3?’
INTERACTIVE TASK
Have students use NTO K.22 ‘What Number Is This?’. Vary the range of numbers to suit the abilities of students.
You will need: a set of paper plates with dot patterns or a set of enlarged cards made from BLM 15 ‘Dot Patterns to 6’, round counters, paper plates, stickers, NTO K.20 ‘Dice’, poster paper
TASK 3:
MAKING DOT PLATES • For students who require support, you may need to allow more time for them to view dot patterns and provide many experiences to view common arrangements of dots. Show students a paper plate or card, and ask them how many dots they can see. Get them to select that many counters and then make the arrangement on a paper plate. Continue showing them a plate or card and they select that amount of counters to make the same arrangement. Students can make their own set of dot plates for numbers
Teacher’s Resource
2
DOTS AND NUMBERS
INDEPENDENT TASKS
Nelson Maths Australian Curriculum NSW
Present NTO K.19 ‘How Many Dots?’ and check if the student can automatically recognise how many dots.
WHOLE-CLASS INTRODUCTION
You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, paper plates, round counters Hold up a card made from BLM 15 ‘Dot Patterns to 6’ or a plate for a few seconds and ask, ‘What did you see?’ Hold up the card or plate again to check. Repeat. When students are comfortable identifying the number of dots, give each student a paper plate and counters. Hold up a card or plate with three dots for a few seconds. Ask students how many dots they can see and have them make the arrangement of dots with their counters. Ask, ‘Can you make three another way?’ Explore different arrangements. Repeat for other numbers.
6
K.6
DOT PATTERNS
Resources: NTO K.19 ‘How Many Dots?’, BLM 15 ‘Dot Patterns to 6’, NTO K.4 ‘Numbers’
1
2
You will need: NTO K.21 ‘Five Little Speckled Frogs’, enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Present NTO K.21 ‘Five Little Speckled Frogs’, and while singing, hold up fingers matching the number of frogs in each verse. Next, display dot plates with the numbers 1 to 5 represented. This time, as students sing, invite a student to hold up a dot plate to match the number of frogs.
DOT PATTERNS
TASK 3:
LESSON PLAN
TUNING IN
WHOLE-CLASS INTRODUCTION
TASK 2:
6
Select from the following to suit your class and their learning outcomes: • Ask students to show all the different ways they made five on Student Book p. 17. Make a ‘Fabulous Five’ poster recording the different ways students found to represent five. • Ask students how they were able to recognise the numbers quickly. Discuss what they see when they look at arrangements for five and six. Ask which numbers are easy to recognise and discuss why.
You will need: NTO K.7 ‘Can You Count?’ Present NTO K.7 ‘Can You Count?’ showing a collection of objects, and ask, ‘How many can you see?’. Invite a student to point to each item while counting aloud to check if the response is correct. Repeat. This is a good time to identify students who may still be having difficulty counting collections.
TASK 1:
Unit
REFLECTION
five, four, less, more, one, same, six, three, two, zero
9 780170 353007
Kindergarten: Assessment Task Card
DOT PATTERN POSTER • For students who require a challenge, have them work with a greater range of numbers. Get them to choose a number, and using a paper plate and counters, have them explore different ways they can represent the number. Students can record their findings by making a poster.
NUMBER AND ALGEBRA
CD-ROMs inside
ISBN: 978-0170353007
For learning solutions, visit cengage.com.au
STUDENT BOOK p. 19 ‘Glub! Glub!’
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
TEACHING GROUP You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, BLM 21 ‘Speckled Frogs’, scissors, BLM 8 ‘Blank Cards’ © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution.
Unit 6
Kindergarten
Nelson Maths Australian Curriculum NSW
7
Dot Patterns
16
Teacher’s Resource
Kindergarten
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Dot Plates
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Glub! Glub!
DATE:
*
Show 5 in different ways. Use a paper plate and some counters.
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DATE:
BLM
15
Draw dots on each frog to match the number of bugs it will eat. One has been done for you.
BLM
20
Dot Patterns to 6
In the Pond
Draw some of the ways you found.
4
5
3
the lily pad, write the matching number word. * On One has been done for you.
2
*
three
1
two
five
Play a game.
six
Draw a line matching each frog to a lily pad and a bug. One has been done for you.
You will need:
• a partner
one
five
6
• a dice
How to play:
four
• In turn, roll a dice. • Each time you roll 5, cover one of the paper plates above with a piece of paper.
five
• The first player to cover all their plates wins.
six
one
two © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution.
18
Unit
6
Unit
Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
Marketing Sampler.indb 18
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
19 06/05/14 2:06 PM
Unit
Unit
6 16
Whole numbers MAe-4NA
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
Teacher’s Note: Patterns can be made on paper plates or printed, laminated and made into sets of cards.
6
Unit
9
Whole numbers MAe-4NA
11
Marketing Sampler.indb 11
Teacher’s Note: This BLM can be printed and laminated to use for other number activities.
14
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Units in the Sampler For each Number and Algebra unit in this Sampler, there are: • three Lesson Plans, which include Tuning In, Whole-Class Introduction, Independent Tasks, Teaching Group tasks, Reflection, Home Tasks, Assessment and Recommendations for Future Learning • accompanying unit and resource BLMs • an Assessment Task Card • three Student Book pages and one Student Assessment page that accompanies each unit. Also included in this Sampler are the Lesson Plans, Student Book and Student Assessment pages from an additional unit for each year level.
Components The following components are available in 2015 for each year level from Kindergarten to Year 6.
Teacher’s Resource The Teacher’s Resource Book provides: • three Lesson Plans for each unit • an Assessment Task Card with a linking Targeted Assessment Task Card • Tests A and B • assessment and planning BLMs • a CD-ROM containing all Nelson Teaching Objects (NTOs) • a CD-ROM containing all BLMs, tests, answers and Assessment Task Cards as printable PDFs.
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ISBN: 978-0170352987
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Student Book and Teacher’s Resource Sampler
07/05/14 3:23 PM
Nelson Teaching Objects and Learning Objects Nelson Maths: Australian Curriculum NSW is committed to integrating Information and Communication Technology (ICT) into the classroom. The program provides a large number of Nelson Teaching Objects (NTOs) available for use on interactive whiteboards (IWBs) and individual computers. The NTOs: • illustrate mathematical concepts explicitly • engage students actively in their learning • scaffold student learning • require students to use their mathematical understandings in an engaging and meaningful context. Also available are pedagogically sound, interactive Learning Objects (LOs) from Education Services Australia.
An example of a Nelson Teaching Object DATE:
Unit
6
STUDENT ASSESSMENT
Tommy Turtle get to the letter box. * Help Colour in the stepping stones that show 5.
Assessment Resources The assessment for each unit consists of: • one Student Assessment page per unit that links to Recommendations for Future Learning in the Teacher’s Resource Book
5
3
4
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* more dots than Tommy.
Draw a friend for Tommy Turtle who has
a friend for Tommy Turtle who has * Draw less dots than Tommy.
• one Assessment Task Card that has been designed to be used with individual students, small groups or as a whole-class assessment task. Each Assessment Task Card has a linking Targeting Assessment Task Card with specific recommendations for future learning • two pen-and-paper tests (Test A and Test B) for mid- and end-of-year assessment and report writing.
Draw a friend with the same number of dots as Tommy Turtle. Use a different pattern.
Unit
6
Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
Marketing Sampler.indb 21
21 06/05/14 2:06 PM
We hope you and your class enjoy and benefit from the sample units provided in this Sampler. We feel proud to say that Nelson Maths: Australian Curriculum NSW continues to provide teachers with choice by featuring an array of hands-on tasks and investigative activities. Teachers have the opportunity to tailor a program for their students based on their different learning styles and their diverse needs. Each unit provides ideas on how to scaffold students’ learning and also provides learning tasks to extend more able students.
Introduction
Marketing Sampler.indb 5
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07/05/14 3:23 PM
Unit
6
Dot Patterns
NUMBER AND ALGEBRA Whole numbers: MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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five, four, less, more, one, same, six, three, two, zero
LESSON PLAN
TUNING IN HOW MANY CAN YOU SEE?
1
You will need: NTO K.7 ‘Can You Count?’ Present NTO K.7 ‘Can You Count?’ showing a collection of objects, and ask, ‘How many can you see?’. Invite a student to point to each item while counting aloud to check if the response is correct. Repeat. This is a good time to identify students who may still be having difficulty counting collections.
WHOLE-CLASS INTRODUCTION DOT PATTERNS You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, paper plates, round counters Hold up a card made from BLM 15 ‘Dot Patterns to 6’ or a plate for a few seconds and ask, ‘What did you see?’ Hold up the card or plate again to check. Repeat. When students are comfortable identifying the number of dots, give each student a paper plate and counters. Hold up a card or plate with three dots for a few seconds. Ask students how many dots they can see and have them make the arrangement of dots with their counters. Ask, ‘Can you make three another way?’ Explore different arrangements. Repeat for other numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: NTO K.20 ‘Dice’ or a large dice, BLM 16 ‘Make a Dice’, counters, NTO K.19 ‘How Many Dots?’, Student Book p. 18 ‘Dot Plates’
TASK 1:
SAME, SAME
Ask students what they can see on the sides of a dot dice on NTO K.20 ‘Dice’ or a large dice. Explain that they are going to make their own dice using BLM 16 ‘Make a Dice’. In one of the squares students draw one dot. In the next square they draw two dots and so on until each side has been filled with dots for each number from 1 to 6. Students cut out the dice net and assemble. Note: students may need teacher, older peer or parent support to assemble. Have students play ‘Same, Same’ with a partner. Students roll their dice, and when the numbers rolled are the same, they collect a counter. The first pair to collect six counters is the winner.
TASK 2:
INTERACTIVE TASK
Have students use NTO K.19 ‘How Many Dots?’.
TASK 3:
STUDENT BOOK p. 18 ‘Dot Plates’
TEACHING GROUP You will need: a set of paper plates with dot patterns or a set of enlarged cards made from BLM 15 ‘Dot Patterns to 6’, round counters, paper plates, stickers, NTO K.20 ‘Dice’, poster paper MAKING DOT PLATES • For students who require support, you may need to allow more time for them to view dot patterns and provide many experiences to view common arrangements of dots. Show students a paper plate or card, and ask them how many dots they can see. Get them to select that many counters and then make the arrangement on a paper plate. Continue showing them a plate or card and they select that amount of counters to make the same arrangement. Students can make their own set of dot plates for numbers
6
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1 to 6, using small paper plates and dot stickers. Get them to arrange the plates in a random order in front, and using NTO K.20 ‘Dice’ roll a number and get them to point to a plate with the same number of dots. Repeat, gradually rolling the dice more quickly. DOT PATTERN POSTER • For students who require a challenge, have them work with a greater range of numbers. Get them to choose a number, and using a paper plate and counters, have them explore different ways they can represent the number. Students can record their findings by making a poster.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask students to show all the different ways they made five on Student Book p. 17. Make a ‘Fabulous Five’ poster recording the different ways students found to represent five. • Ask students how they were able to recognise the numbers quickly. Discuss what they see when they look at arrangements for five and six. Ask which numbers are easy to recognise and discuss why.
LESSON PLAN
TUNING IN FIVE LITTLE SPECKLED FROGS
2
You will need: NTO K.21 ‘Five Little Speckled Frogs’, enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Present NTO K.21 ‘Five Little Speckled Frogs’, and while singing, hold up fingers matching the number of frogs in each verse. Next, display dot plates with the numbers 1 to 5 represented. This time, as students sing, invite a student to hold up a dot plate to match the number of frogs.
WHOLE-CLASS INTRODUCTION DOTS AND NUMBERS You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, a large number fan and one for each student made from BLM 17 ‘Number Fan: Numerals’ Ask students how many speckled frogs were sitting on the log. Show students large cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns and invite a student to find a dot plate that shows five. Show students the enlarged number fan made from BLM 17 ‘Number Fan: Numerals’ and all the numbers that are on it. Tell students that you will hold up each number, and when you get to the number that matches the plate, students put up their hand. Select another dot plate and then ask a student to find the corresponding number on the number fan. Give a number fan to each student, and hold up various dot plates, getting students to find the matching number on their number fan.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 20 ‘In the Pond’, counters, a dice, NTO K.22 ‘What Number Is This?’, Student Book p. 19 ‘Glub! Glub!’
TASK 1:
IN THE POND
Give a copy of BLM 20 ‘In the Pond’ to pairs of students. Each student will need about 20 counters that are the same colour but different from their partner’s. Students take it in turns to roll a dice and then place one counter on a lily pad that matches the dice. The counter can be placed on a word, numeral or dot pattern that matches the dice. If they cannot find a lily pad to match the dice, they miss that turn. The student who places the most counters on the board is the winner.
TASK 2:
INTERACTIVE TASK
Have students use NTO K.22 ‘What Number Is This?’. Vary the range of numbers to suit the abilities of students.
TASK 3:
STUDENT BOOK p. 19 ‘Glub! Glub!’
TEACHING GROUP You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, BLM 21 ‘Speckled Frogs’, scissors, BLM 8 ‘Blank Cards’
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Dot Patterns
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FROG JUMP • For students who require support, practise identifying the dot patterns by making a trail of cards from BLM 15 ‘Dot Patterns to 6’ and getting students to jump onto the first card, call out the number, and if correct, jump to the next and so on. Then give pairs of students a copy of BLM 21 ‘Speckled Frogs’ and have them cut out each item (these could be prepared before the lesson). Get students to match the frogs, lily pads and bugs. Then get students to place the items face-down and take it in turns to turn over a frog, a lily pad and a bug to see if they get a match. MORE DOT CARDS • For students who require a challenge, they can work with greater range of numbers. Give them a copy of BLM 8 ‘Blank Cards’ and have them make a set of cards by the writing the numerals for the numbers they want to work with. Then they can make matching cards with the words for the numbers and also a set of dot pattern cards. Students can play ‘Snap’ or ‘Memory’ with a partner.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘When you played “In the Pond” (Independent Tasks, Task 1), what did you cover first? Was it the numeral, word or dot pattern?’ Also ask, ‘Was it difficult to find a match to the dice all of the time? Why?’ • Ask, ‘When you look at dot patterns, do you recognise the number instantly? Which patterns are easiest to recognise? Why?’
LESSON PLAN
TUNING IN PUT THE PLATES IN ORDER
3
You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Revisit the dot patterns by holding up a dot pattern card made from BLM 15 ‘Dot Patterns to 6’ (or a paper plate with dot patterns) for a few seconds and have students call out how many. Place all of the dot pattern cards on the floor and ask a student to find a card or plate that has three dots. When the student has identified the card or plate, ask, ‘Can you find another plate/card that shows the same number?’ Repeat for a few other numbers. Tell students that you would like their help to pack the plates (or cards) up in order starting from zero. Make sure all of the plates showing the same number are picked up.
WHOLE-CLASS INTRODUCTION MORE OR LESS DOTS You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Hold up a dot pattern card (or plate) that shows three dots and ask students how many dots they can see. Invite a student to come and find a card or plate that has less dots. Ask, ‘How do you know it has less dots?’ Then ask if anyone can find a card that has more dots. Again ask, ‘How do you know that the dot pattern has more dots?’ Repeat for other number patterns. Next, hold a card in each hand and ask students to indicate which has more by holding out the same arm. Repeat for other numbers. Give out number fans and hold up a dot plate (or dot card) and ask students to show a number on their fan that is more and less. Repeat.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: a set of cards for each student made from BLM 15 ‘Dot Patterns to 6’, NTO K.20 ‘Dice’, Student Book p. 20 ‘Hungry Frogs’
TASK 1:
MORE DOTS
From their set of cards made from BLM 15 ‘Dot Patterns to 6’, each student turns over a card. Students compare cards and the student who has the card that shows more takes both cards and adds them to the bottom of their pile of cards. The game continues until one student has won all of the cards.
TASK 2:
INTERACTIVE TASK
In pairs with their sets of cards made from BLM 15, students take it in turns to generate a number using NTO K.20 ‘Dice’. However, before they select a card, they predict if the number on their card will be more, less or the same than the number generated. If they are correct, they keep the card. The student with the most cards wins.
TASK 3:
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TEACHING GROUP You will need: paper plates with dot patterns as in BLM 15 ‘Dot Patterns to 6’, paper plates, counters MAKE MORE OR LESS • For students who require support, give them a dot paper plate with a number of dots on it that they can identify, e.g. 3. Have them place the plate in front, and in front of their dot pattern plate, have them place an empty plate and another empty plate after it. On the first plate they make a dot pattern that is less and on the last plate they make a dot pattern that is more. Ask them how they know that the number is less or more. Repeat with other number dot plates. MORE OR LESS CHALLENGE • For students who require a challenge, have them use the dot pattern cards made from BLM 15 that they made in Lesson Plan 2. In pairs, one student puts down one of their cards. Their partner turns over one of their cards, but before they do, they must say if their number will be more, less or the same. If their choice is correct, then they keep the pair of cards, but if not, their partner wins the cards. The students then take it in turns deciding if the card they turn over is more, less or the same. The student with the most cards at the end wins.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘How did you recognise the patterns that were more or less?’ Discuss if it was easy to tell which numbers were more or less and why. • Hold up a dot pattern plate and ask, ‘If I were to show another plate, do you think it would be a number that is more, less or the same?’ Ask students to explain their choice.
Assessment • Have students complete Student Assessment p. 21. • Review with students Assessment Task Card K.6. During the three lessons: • Observe which students were able to quickly recognise dot patterns during Lesson Plan 1, Independent Tasks, Task 2 and Lesson Plan 2, Independent Tasks, Task 1, and mark on a class list. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty. • Make a note of students’ responses to reflection questions.
Recommendations for Future Learning Specific to Student Assessment p. 21; if the student is experiencing difficulty: Continue working with recognition of dot patterns beginning with patterns for 1, 2 and 3 and then Q 1 gradually increasing. Q 2–3 Use NTO K.20 ‘Dice’ to randomly generate numbers and have the student copy and then add or subtract one counter to make more or less. Provide the student with paper plates and counters to explore different possible arrangements for each Q 4 number from 2 to 6. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card K.6 for specific recommendations. 2. Give more exposure to dot patterns by playing games, e.g. ‘Snap’ and ‘Concentration’. 3. Continue to work with dot patterns in the context of other number work. 4. Review Nelson Maths Building Mental Strategies Big Book 1, p. 6. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 1 Unit xx, pp. xx–xx. 2. Extending the student in any of the listed activities or tasks by using larger numbers.
Unit 6
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Dot Patterns
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BLM
8
Blank Cards
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit Unit
Unit
26 3
Unit
6
Unit
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Unit
Unit
9 10 11 24
Whole numbers MAe-4NA
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BLM
15
Dot Patterns to 6
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
Unit
6 16
Whole numbers MAe-4NA
Teacher’s Note: Patterns can be made on paper plates or printed, laminated and made into sets of cards.
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BLM
16
Make a Dice
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Whole numbers MAe-4NA
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BLM
17
Number Fan: Numerals
2
1
3
7
6
4
5
0
9
10
8
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Unit
Unit
Unit
Unit
Unit
8 10 11 20 30
Whole numbers MAe-4NA
Teacher’s Note: This BLM can be photocopied onto card, laminated, cut out and made into a fan by joining with a binder ring split pin. Enlarge and make a fan for teacher modelling.
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BLM
20
In the Pond
4
six
3 2
three
1
two
one
five
6 four
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Unit
9
Whole numbers MAe-4NA
Teacher’s Note: This BLM can be printed and laminated to use for other number activities.
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BLM
21
Speckled Frogs
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Whole numbers MAe-4NA
15
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K.6
Kindergarten: Assessment Task Card Unit
6
DOT PATTERNS
Resources: NTO K.19 ‘How Many Dots?’, BLM 15 ‘Dot Patterns to 6’, NTO K.4 ‘Numbers’
1
Present NTO K.19 ‘How Many Dots?’ and check if the student can automatically recognise how many dots.
2
Give the student a set of cards made from BLM 15 ‘Dot Patterns to 6’. Present NTO K.4 ‘Numbers’ and randomly generate a number from 0 to 6. Have them read the number and find the matching number card.
3
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is more than the dot pattern displayed.
4
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is less than the dot pattern displayed.
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
K.6
Kindergarten: Assessment Task Card Unit
6
DOT PATTERNS TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Have the student practise reading dot patterns by playing board games, e.g. ‘Number Game Board’ in Nelson Maths Building Mental Strategies Big Book 1, pp. 12–13.
Q2
Have the student use NTO K.19 ‘How Many Dots?’ set to numbers from 0 to 6 and randomly generate either dot patterns or numerals for recognisation.
Q3
Give the student the set of cards made from BLM 15. Using NTO K.19 to generate a number between 0 and 6, have the student find a card with the same dot pattern. Then have them find the cards that show more and show less.
Q4
Select a card from BLM 15, and have the student guess the card by asking ‘Is it less?’ questions, e.g. ‘Is it less than 3?’
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution.
Nelson Maths Australian Curriculum NSW
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Teacher’s Resource
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Dot Plates
DATE:
**
Show 5 in different ways. Use a paper plate and some counters. Draw some of the ways you found.
5 Play a game. You will need: •• a dice •• a partner How to play: •• In turn, roll a dice. •• Each time you roll 5, cover one of the paper plates above with a piece of paper. •• The first player to cover all their plates wins.
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Unit
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Glub! Glub!
DATE:
**
Draw dots on each frog to match the number of bugs it will eat. One has been done for you.
**
On the lily pad, write the matching number word. One has been done for you.
five a line matching each frog to a lily pad **Draw and a bug. One has been done for you.
five Unit
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six
one
two
Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Hungry Frogs
DATE:
You will need: • a partner • one set of cards for each player made from BLM 15 ‘Dot Patterns to 6’ How to play: • Choose a frog. Turn over all your cards and place them in a pile. • Take a card from your pile. Your partner needs to do this, too. • The player who has more dots on their card can colour their first lily pad. • Keep turning over cards. The player with more dots each time colours a lily pad. • The first player to reach the fly wins.
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Unit
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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DATE:
Unit
6
STUDENT ASSESSMENT
**
Help Tommy Turtle get to the letter box. Colour in the stepping stones that show 5.
5
3
4
5
6 5
a friend for Tommy Turtle who has **Draw more dots than Tommy.
a friend for Tommy Turtle who has **Draw less dots than Tommy.
Draw a friend with the same number of dots as Tommy Turtle. Use a different pattern.
Unit
6
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Unit
12
2D Shapes
U
MEASUREMENT AND GEOMETRY Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
ML
circle, corners, edges, rectangle, square, triangle
LESSON PLAN
TUNING IN BLOCKS
You will need: pattern blocks, attribute blocks and other sets of blocks containing a variety of shapes
1
Provide students with different sets of blocks, e.g. pattern blocks, attribute blocks or any that have a variety of flat shapes. Have students make pictures using the different-shaped blocks. Give students the opportunity to see one another’s pictures. Have students put the shapes back into their containers. Observe which students have difficulty matching shapes to the holding space as this will help determine which students may need support.
WHOLE-CLASS INTRODUCTION SHAPES IN THE CLASSROOM You will need: NTO K.38 ‘What Shape Is This?’ Using NTO K.38 ‘What Shape Is This?’, select a shape, e.g. circle, and ask students to look around the room to see if they can find something that has the same shape in it. It is not necessary at this stage to name the shape as a circle; however, some students may know the name of the shape. If possible, let students bring to the front of the class the objects they find that contain a circle. Have them trace the circle shape with their finger to make it clear to the class where the circle is located. Continue until most objects containing circles have been identified. Repeat for other shapes, e.g. square, rectangle and any others that can be found in the classroom. Prior to the lesson, you may need to make sure that there are a range of objects in the classroom to match the different shapes explored.
INDEPENDENT TASKS Note: Choose from Tasks 1, 2 or 3. You will need: BLM 30 ‘I Can Find’, NTO K.39 ‘Match This Shape’, Student Book p. 26 ‘Shapes You Can See’
TASK 1:
SHAPES I CAN FIND
Give each student a copy of BLM 30 ‘I Can Find’ and explain that they need to find an object or objects in the classroom for each shape and draw it. So that each BLM can be made into a book, have students fold their page in half horizontally and then vertically.
TASK 2:
INTERACTIVE TASK
Using NTO K.39 ‘Match This Shape’, students work independently on computers to select the same shape from five alternatives.
TASK 3:
STUDENT BOOK p. 26 ‘Shapes You Can See’
TEACHING GROUP You will need: a set of cards made from BLM 31 ‘Shape Cards 1’ and BLM 32 ‘Shape Cards 2’ WHERE IS THE SHAPE? • For students who require support, show them a card with a rectangle made from BLM 31 ‘Shape Cards 1’. Have them trace the shape with their finger and imagine what the rectangle could be. Draw the suggestions students give. Students may need to go on a walk around the classroom while you hold up the shape card and then identify particular shapes in objects. Repeat with another shape, e.g. circle. Give students either a rectangle or a circle to trace onto a piece of paper or a small whiteboard, and have them draw an object in the classroom that contains that shape.
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FIND MY SHAPE • For students who require a challenge, expose them to a greater range of shapes, e.g. shapes included in BLM 32 ‘Shape Cards 2’. Have two sets of cards made from BLMs 31 and 32 ‘Shape Cards’. Place one set where they are visible to all. Invite a student to select a card from the second set (making sure the other students do not know the shape they selected). Have them describe their shape and invite other students to find it. Encourage students to describe their shape in terms of features, e.g. number of sides and corners.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their ‘I Can Find’ books they made using BLM 30 ‘I Can Find’ in Independent Tasks, Task 1. Ask, ‘What other objects contain the same shape?’ As students share their drawings, make a chart of what the students drew for each shape. • Have students share their completed Student Book p. 25 with a partner, and then select some students to come and explain how they were able to find the shapes. Ask, ‘How did you know that you were correct?’ • For students from the Teaching Groups, have them share their work and ask, ‘How were you able to find the objects with that shape? How did you know it was the same shape?’
LESSON PLAN
TUNING IN SHAPES IN OUR SCHOOL You will need: BLM 31 ‘Shape Cards 1’
2
Enlarge a number of BLM 31 ‘Shape Cards 1’ and make these into cards. Give each student a card and take students on a walk around the school to see if they can see their shape somewhere in the school environment. Take digital photos of students finding their shape in the school environment for display or to put into a class Maths Journal.
WHOLE-CLASS INTRODUCTION NAMING SHAPES You will need: NTO K.38 ‘What Shape Is This?’, cards made from BLM 31 ‘Shape Cards 1’ Present NTO K.38 ‘What Shape Is This?’ to students or alternatively use a card made from BLM 31 ‘Shape Cards 1’. Ask students to look carefully at the shape and provide words to describe it. Encourage students to look at number of edges and corners, colour and size. Ask, ‘Does anyone know the name of the shape?’ If necessary, tell students the name of the shape. Repeat for other shapes.
INDEPENDENT TASKS Note: Choose from Tasks 1, 2 or 3. You will need: BLM 31 ‘Shape Cards 1’, BLM 32 ‘Shape Cards 2’, scissors, glue, sheets of paper, coloured pencils, NTO K.40 ‘Shape Express’, Student Book p. 27 ‘Find the Shape’
TASK 1:
SHAPE PICTURES
For this task each student will select a card from BLM 31 ‘Shape Cards 1’ or for more able students a card from BLM 32 ‘Shape Cards 2’. To find out which students know the names of some shapes, ask them to name the shape they would like to use. Students then need to cut out the shape and paste it onto a sheet of paper. Using coloured pencils, students make the shape into a picture.
TASK 2:
INTERACTIVE TASK
Have students use NTO K.40 ‘Shape Express’ where they need to complete the train by finding the matching shape.
TASK 3:
STUDENT BOOK p. 27 ‘Find the Shape’
TEACHING GROUP You will need: BLM 31 ‘Shape Cards 1’, scissors, glue, sheets of paper, BLM 32 ‘Shape Cards 2’ RECTANGLES • For students who require support, work with them in a small group and have them cut out a rectangle from BLM 31 ‘Shape Cards 1’. Before they paste the rectangle onto a sheet of paper and use coloured pencils to make it into a picture, have them explore the features of the shape. They can do this by folding
Unit 12
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2D Shapes
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the rectangle to find that the four corners are the same and that the opposite sides are the same, but that there is a pair of long sides and a pair of short sides. As a group, brainstorm things that could be rectangular in shape, e.g. a book, a laptop, a tabletop, and have students complete their picture. LOTS OF SHAPES • For students who require a challenge, have them select a number of shapes from BLM 31 ‘Shape Cards 1’ or BLM 32 ‘Shape Cards 2’. Then they need to plan and draw a picture where these shapes might be found.
REFLECTION Select from the following to suit your class and their learning outcomes: • Select students to come to the front and name the shape and how they used it to make a picture in Independent Tasks, Task 1. Record what students say, e.g. ‘I used a square to make a picture of a house’, and make a display or a book of students’ work. • Get students to show where they put a rectangle in their picture ‘Rectangles’ in the Teaching Group. Ask them to explain how they knew the shape was a rectangle and not another shape. Ask students to identify and name the other shapes that they can see.
LESSON PLAN
TUNING IN I SPY SOMETHING IN THE CLASSROOM
3
Select an object in the classroom that has a particular shape, e.g. the door. Say, ‘I spy something in the classroom that is a big rectangle.’ Select students to go and point to an object that might be the object you are thinking about. Once a student points to the door, select another object in the shape of another shape, e.g. square, triangle or circle, and repeat the activity. This is a good time to identify students who cannot recognise shapes and need support in the Teaching Group.
WHOLE-CLASS INTRODUCTION MATCHING SHAPES You will need: a large hoop (or draw a circle on the floor with chalk that can be removed later), attribute blocks Tip the attribute blocks onto the floor so that all students can see them. Select a block, e.g. a rectangle, and have students describe the shape by describing its colour, number of sides, size and thickness. Place the block into a hoop on the floor and say, ‘I like rectangles. Can anyone find another block that is a rectangle?’ Select students to find other blocks with rectangles and get them to place them inside the hoop or circle. Continue until all of the rectangles have been placed into the hoop or circle. Ask students to name the shapes in the hoop or circle and tell them that the shapes outside the hoop or circle are not rectangles. Repeat for other shapes and attributes, making sure that students understand which shapes have a common attribute and which do not.
INDEPENDENT TASKS Note: Choose from Tasks 1, 2 or 3. You will need: BLM 33 ‘Shape Bingo’, attribute blocks, a bag, counters, NTO K.41 ‘Make a Picture’, Student Book p. 28 ‘Shape Caterpillars’
TASK 1:
SHAPE BINGO
Model the following tasks before students work in pairs or small groups. Provide students with one of the four bingo templates from BLM 33 ‘Shape Bingo’. (Note that the one in the top left-hand corner is the easiest and the one in the bottom right-hand corner is more difficult). Ask students to colour two of their shapes red, then another two blue and another two yellow. Tell students that they can colour the remaining shapes red, blue or yellow. Place the circles, squares, triangles and rectangles from the attribute blocks in a container or bag. Select a shape and hold up for students to see. Tell them to look at their bingo board, and if they have the same shape in the same colour, they can cover it with a counter. Continue selecting shapes from the container or bag until a student has covered either a row or all of the bingo board.
TASK 2:
INTERACTIVE TASK
Have some students use NTO K.41 ‘Make a Picture’ to recreate a picture by selecting the correct shapes.
TASK 3:
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STUDENT BOOK p. 28 ‘Shape Caterpillars’
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Teacher’s Resource
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TEACHING GROUP You will need: NTO K.39 ‘Match This Shape’, BLM 31 ‘Shape Cards 1’, BLM 32 ‘Shape Cards 2’, a bag, green, red, blue and yellow counters MATCH THE SHAPE • For students who require support, present NTO K.39 ‘Match This Shape’. When a shape appears on the screen, ask students to look carefully at the shape and ask questions about its features, e.g. ‘How many sides does this shape have? Are the sides the same length? How many corners does the shape have? What colour is the shape?’ Invite a student to come to the board and explain which shape they think has the same number of sides, corners and colour, and then get them to test their prediction by selecting the shape. Reset and repeat so that students continue to identify features of the shape to help find the match. BINGO CHALLENGE • For students who require a challenge, have them fold a piece of paper in half and half again and then turn the paper 90 degrees and fold in half and in half again so that their paper is a 4 x 4 grid. Give them BLMs 31 and 32 ‘Shape Cards’ to create their own bingo board. Have students colour their shapes red, blue, green or yellow. In a bag place a set of cards made from BLMs 31 and 32 ‘Shape Cards’ and a red, blue, green and yellow counter. Have one student select a card and counter from the bag, while the others look for the shape in that colour on their bingo board. If a student has that shape in that colour, they cover it with a counter. Continue until one student has ‘bingo’ by getting four counters in a row.
REFLECTION Select from the following to suit your class and their learning outcomes: • Put a selection of attribute blocks in front of students and then ask them to look at the shapes and see if they can find a given shape, e.g. a triangle. Ask, ‘How do you know that the shape is a triangle? How do you know that it is not a circle?’. Repeat. • Get students to show the caterpillars they designed in Independent Tasks, Task 3. Have students explain the shapes they chose and why.
Assessment • Have students complete Student Assessment p. 29. • Review with students Assessment Task Card K.12. During the three lessons: • Note on a class list which students in Lesson Plan 2, Independent Tasks, Task 1, were able to name the shape they wished to use. • Make a note of students completing the scaffolding tasks or more challenging activities in the Teaching Group. • Review Student Book pages and make notes on which students are experiencing difficulties and those able to complete the tasks. • Note students’ responses to Reflection questions.
Recommendations for Future Learning Specific to Student Assessment p. 29; if the student is experiencing difficulty: Q 1 Provide more experiences for the student to explore the features of shapes. Make sets of laminated shapes from BLM 31 ‘Shape Cards 1’. Have the student outline the shapes and then describe what they see. Make a set of cards from BLM 31 ‘Shape Cards 1’ and play flashcard games so the student can recognise and name the shapes. Give the student cards made from BLM 31 ‘Shape Cards 1’ and have them identify objects that contain Q 2 that shape in the classroom and school environment. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card K.12 for specific recommendations. 2. Have the student explore NTO K.39 ‘Match This Shape’ and NTO K.40 ‘Shape Express’. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 1 Unit xx, pp. xx–xx. 2. Extending the student in any of the listed activities or tasks by using more shapes, e.g. semi-circle, trapezium, hexagon, pentagon, rhombus and kite.
Unit 12
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2D Shapes
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Shapes You Can See
DATE:
at each shape. Draw something from your **Look classroom that has the same shape.
Find another shape in the classroom and draw it.
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Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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Find the Shape
DATE:
**
Look at the picture below. Colour all the rectangles blue.
**How many rectangles are in the picture? What other shapes can you see? **
Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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Shape Caterpillars
DATE:
**Finish the patterns on the caterpillars.
**Draw your own shapes on the caterpillar.
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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DATE:
Unit
12
STUDENT ASSESSMENT
**Look at all the shapes. Colour the triangles red.
**This is a rectangle.
Draw something from your classroom that has
a rectangle.
Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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Unit
8
Numbers Beyond 20
NUMBER AND ALGEBRA Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
ML
consecutive, eighty, fifty, forty, ninety, one hundred, ones, seventy, sixty, tens, thirty, twenty
LESSON PLAN
TUNING IN
HOW FAR CAN YOU COUNT? Have students sit or stand in a circle and designate someone to begin counting by ones from zero, with each student counting the next consecutive number. See how far students can go before making a mistake. Write down the last correct number. Have students try again to see if they can count further.
1
WHOLE-CLASS INTRODUCTION WRITING NUMBERS On the board, write the numerals from 1 to 10 and underneath from 11 to 20 and have students read them. Point to the 20 and say, ‘This is how we write 20. Can anyone write the other numbers in the 20s?’ Invite a student to write the numbers 21 to 29. Then ask, ‘What number comes after 29?’, and as students answer, write 30 on the board. Ask, ‘Do you notice anything about the numbers?’ Draw students’ attention to the repeating nature of the final digit pattern. Continue by asking a student to write the other numbers in the 30s. Then ask what comes next and write 40 on the board. Continue having students write the numbers up to 100. Point to different numbers and see if students can read them.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 6 ‘Blank Number Line’, scissors, Word, Student Book p. 38 ‘Number Bingo’
TASK 1: NUMBERS TO 100 Have students work in a group of three to make a number line to 100. Give each student a copy of BLM 6 ‘Blank Number Line’. Have them cut out the sections and work out which numbers individual students will write. Note: number lines go up to 120 – have students cut off the number line at 100. Remind students that the numbers are on the board for support. Have students make number lines to 100 beginning at zero.
TASK 2:
INTERACTIVE TASK
Using Word, students make a 10 x 10 table and have them fill in the numbers from 1 to 100 to make a 100 chart.
TASK 3:
STUDENT BOOK p. 38 ‘Number Bingo’
TEACHING GROUP You will need: NTO 1.1 ‘Number Cards’, number tiles made by cutting up BLM 14 ‘100 Chart’ MAKING A NUMBER LIST • For students who require support, begin revising numbers that students know and gradually introduce larger numbers. Set NTO 1.1 ‘Number Cards’ to show numerals to 20, and have students read numbers as they appear. Then increase the range of numbers to 30 for students to practise reading. Have a number race whereby students form a starting line and the first student to recognise the number takes one step forward. Ask students to write down the numbers to 30. Introduce the next ten numbers, writing them on the board and saying them and getting students to repeat. Randomly point to the numbers and have students say them. Have students add the next ten numbers to their list. Once students have written down the numbers to 50, call out random numbers and have students point to them. Keep the number lists to add to in later lessons.
Nelson Maths Australian Curriculum NSW
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PUT THEM IN ORDER • For students who require a challenge, give them a set of number tiles made from BLM 14 ‘100 Chart’ and have them put the numbers in order either in a 10 x 10 grid pattern or as a long line. Have students work with a partner.
REFLECTION Select from the following to suit your class and their learning outcomes: • Write numbers on the board, e.g. 68, 33, 92, and have students read the numbers. Ask, ‘How did you know what the numbers were? What helps you to read the numbers?’ • Ask, ‘When you write all the numbers to 100, how can you make sure that you have not missed any? What strategies do you use?’
LESSON PLAN
TUNING IN AROUND THE WORLD
2
You will need: a set of number cards from 1 to 100 made from an enlarged copy of BLM 14 ‘100 Chart’ Hold up number cards in random order and have students read them. Play ‘Around the World’ whereby students sit in a circle and two students sitting next to one another are selected to stand and see who can read the number the quickest. The student who reads the number the quickest remains standing and the next student in the circle competes. The game continues until every student has had a turn.
WHOLE-CLASS INTRODUCTION A CHART OF NUMBERS You will need: NTO 1.21 ‘Numbers to 100’ Present NTO 1.21 ‘Number to 100’ and point to the 1 and 100. Have students read the numbers. Tell students that you need their help to make a 100 chart. Ask, ‘What number comes after 1?’ When students have answered, click onto the first blank space to reveal the number. Continue asking for the next number and invite students to come and click on the space to reveal the next number until all the numbers on the chart are revealed.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 15 ‘Make Your Own 100 Chart’, number tiles made by cutting up BLM 14 ‘100 Chart’, NTO 1.21 ‘Numbers to 100’, counters, a dice, Student Book p. 39 ‘Lucky Slides’
TASK 1:
TIC TAC TOE
Give students a copy of BLM 15 ‘Make Your Own 100 Chart’ and have them fill in the numbers from 1 to 100. If students need support, display NTO ‘Numbers to 100’ with the numbers revealed. Once students have filled in the numbers, have them play ‘Tic Tac Toe’.
TASK 2:
INTERACTIVE TASK
Have students work in pairs. Give each pair a set of number tiles made from BLM 14 ‘100 Chart’. One student from each pair selects a number for the other student to locate on NTO 1.21 ‘Numbers to 100’. Continue until all of the numbers from 1 to 100 have been located.
TASK 3:
STUDENT BOOK p. 39 ‘Lucky Slides’
TEACHING GROUP You will need: BLM 15 ‘Make Your Own 100 Chart’, number tiles made from BLM 14 ‘100 Chart’ A FEW MORE NUMBERS • For students who require support, continue to revise numbers that they know. Have students read through the number list they made in ‘Making a Number List’ in Lesson Plan 1, Teaching Group. Have students stand in a circle and throw or roll a ball across the circle to each other and the student who catches the ball says the next consecutive number. Support students to count past 50 to 80. Have students add the numbers they have counted to their number list. BURIED TREASURE • For students who require a challenge, have them complete a 100 chart using BLM 15 ‘Make Your Own 100 Chart’. Next, have pairs of students use their 100 charts to play a strategy game. One student selects a number tile (these can be made from BLM 14 ‘100 Chart’). The number on the tile must be used as part of a row of three adjacent numbers on the student’s 100 chart, e.g. if number tile 25 is chosen, the row of three numbers – or ‘bars of buried treasure’ – could be 24, 25, 26 or 25, 15, 5 or 25, 36, 47. (Note: numbers
Unit 8
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Numbers Beyond 20
31
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may be diagonally adjacent on the 100 chart). The first student colours in their bars of treasure on the 100 chart, without showing their partner. The second student tries to ‘find’ the bars of buried treasure by guessing any number that forms part of the treasure. For example, students ask: ‘Is number 25 in your bar of buried treasure?’ Pairs swap roles when the bars of buried treasure have been guessed correctly.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share the 100 charts they completed in Independent Tasks, Task 1, and ask, ‘When you wrote the numbers, what were you thinking that helped you write the correct number?’ • Ask in relation to ‘Buried Treasure’ in the Teaching Group, ‘What strategies did you use to win?‘
LESSON PLAN
TUNING IN POINT TO THE NUMBER
3
You will need: NTO 1.21 ‘Numbers to 100’ Present NTO 1.21 ‘Numbers to 100’ with numbers showing and the pointer selected. Ask, ‘Can anyone point to the number that tells us how many students are in the class?’ Continue to ask students to point to numbers that are significant to them, e.g. their classroom number, the number in their address and so on.
WHOLE-CLASS INTRODUCTION HOW THE NUMBERS ARE ARRANGED You will need: NTO 1.21 ‘Numbers to 100’ Present NTO 1.21 ‘Numbers to 100’ with the numbers showing and ask, ‘Have you noticed anything about the way that the numbers on a 100 chart are arranged?’ Discuss that the numbers are in consecutive order, the final digit pattern is repeated in each row and that, as you move down a column, there is an increase of one in the ‘tens’ number. Hide the numbers on the NTO 1.21 ‘Numbers to 100’, click one number and have students read the number. Then point to the next space and ask, ‘What number will come next?’ Have students uncover the next space to check their answer. Point to the first number uncovered and ask, ‘What number will come before this number?’ Again have students check their answer by uncovering the space. Continue selecting numbers and asking students to name the numbers that comes after and before.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: Sets of number tiles made from BLM 14 ‘100 Chart’, NTO 1.21 ‘Numbers to 100’, Student Book p. 40 ‘What’s the Number?’
TASK 1:
CONSECUTIVE NUMBERS
Have students work in small groups. Give them a set of number tiles made from BLM 14 ‘100 Chart’ and have them spread the tiles out, face-down, on the floor or tabletop. Explain to students that they are going to try to get two number tiles that are consecutive numbers. So, they turn over one tile and then turn over another one. The second tile needs to be the number that comes before or after the number on the first tile for them to keep the tiles and have another turn. Otherwise they have to turn the tiles back over and it is the next person’s turn.
TASK 2:
INTERACTIVE TASK
Have students use NTO 1.21 ‘Numbers to 100’ to explore consecutive numbers. Randomly click on a number. Students write it down and then write down the number that comes after and the number that comes before, using the NTO to check their answers.
TASK 3:
STUDENT BOOK p. 40 ‘What’s the Number?’
TEACHING GROUP You will need: NTO 1.21 ‘Numbers to 100’, a set of number tiles made from BLM 14 ‘100 Chart’, a copy of BLM 14 ‘100 Chart’
MAKE IT TO 100 • For students who require support, have them continue to complete their number list from ‘A Few More Numbers’ in Lesson Plan 2, Teaching Group. Present NTO 1.21 ‘Numbers to 100’ with the numbers hidden. Begin clicking the numbers in order from 1 to 80, having the students recite the numbers as you do. Ask, ‘We know that the last number was 80, so what will the next number be?’ Check students’ prediction by revealing it on the NTO. Have students continue predicting the numbers to 89 and then ask them to write them on their number list. Tell students to look at the last column, have them read the Nelson Maths Australian Curriculum NSW
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numbers 10, 20, 30, 40 50, 60, 70, 80 and ask, ‘What do you think the next number will be? How do you write that?’ Have students add 90 to their list and then have them check on the NTO that they are correct. Have students write the remaining numbers to 100 and then check on the NTO. WHAT COMES NEXT? • For students who require a challenge, put them into small groups and give each group a set of number tiles made from an enlarged copy of BLM 14 ‘100 Chart’. Have them shuffle the tiles, and then each student takes five. The remaining number tiles are placed in a pile face-down. One tile from the pile is turned over and placed on a 100 chart (use another copy of BLM 14 ‘100 Chart’). The aim of the game is to be the first student to get rid of their number tiles, which they do by taking it in turns to place a tile on the 100 chart. They can only place a tile if it is the number that comes before or after or would appear above or below the number/s on the 100 chart. If students are unable to place a number tile, they must pick up another tile from the pile.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘When exploring a 100 chart, was it always easy to work out the numbers that come before and after another number? What strategies do you use to help you work it out?’ • Ask, ‘Are there some numbers that come after each other that are more difficult to remember than others? Why?’
Assessment • Have students complete Student Assessment p. 41. • Review with students Assessment Task Card 1.8. During the three lessons: • Collect created items, e.g. completed number lines and 100 charts, as work samples for student portfolios. • Observe students as they complete ‘Consecutive Numbers’ in Lesson Plan 3, Independent Tasks, Task 1, and mark on a class list students who are able to identify pairs of consecutive numbers. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 41; if the student is experiencing difficulty: Q 1 Provide more practice with oral counting. Look for opportunities within the school environment, e.g. classroom numbers, classroom charts that list numbers of books borrowed, for them to read numbers up to 100. Q 2 Have the student complete 100 charts and use as game boards and to play games, e.g. ‘Tic Tac Toe’, which will reinforce understanding of how the numbers are organised. Q 3 Have the student use NTO 1.21 ‘Numbers to 100’ whereby they can explore numbers that come before and after. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 1.8 for specific recommendations. 2. Review Nelson Maths: Australian Curriculum Year 1 Units 22 and 23. 3. Have the student complete Nelson Maths Building Mental Strategies Big Book 2, p. 6. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Completing Nelson Maths Building Mental Strategies Big Book 3, p. 3, to explore larger numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 2 Unit xx, pp. xx–xx. 3. Extending the student in any of the listed activities or tasks by using larger numbers.
Unit 8
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Numbers Beyond 20
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BLM
6
Blank Number Line
Paste here
Paste here
Paste here
Paste here
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution. Unit
8
Whole numbers MA1-4NA
Teacher’s Note: This BLM can be cut out and individual sections used or a number of sections pasted together.
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BLM
14
100 Chart
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution. Unit
1 8
Whole numbers MA1-4NA
Teacher’s Note: This BLM can be photocopied and laminated for re-use in the classroom. Make sets of number tiles from 1 to 100 by enlarging, copying each set on different-coloured paper and cutting into number tiles.
35
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Unit
15
Make Your Own 100 Chart
Fill in the numbers from 1 to 100.
1
10
14 43
27
35
59
62 86
78 100
Tic Tac Toe You will need: a partner, a completed 100 chart, a different-coloured pencil from your partner • Take it in turns to tell your partner which number to colour in for you. • If your partner has coloured three numbers in a row for you, then you score a point. © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution. Unit
1 8
Whole numbers MA1-4NA
36
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1.8 F.1
Year Foundation: 1: Assessment Assessment Task Card Task Card Unit
NUMBERS BEYOND 20
8 1
Resources: NTO 1.21 ‘Numbers to 100’, a set of number tiles made by cutting up a copy of BLM 14 ‘100 Chart’
1
Present NTO 1.21 ‘Numbers to 100’ set to show the numbers. Randomly point to different numbers and have the student read them.
2
Have the student write the following numbers as you say them:
89, 13, 48, 72, 31, 50
3
Give the student a copy of BLM 14 ‘100 Chart’ and a matching set of number tiles made from BLM 14 ‘100 Chart’. Have them randomly select number tiles and place them on the corresponding number on the 100 chart.
4
Have the student select number tiles and name the number that comes before and after the number they have selected.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
1.8 F.1
Year Foundation: 1: Assessment Assessment Task Card Task Card Unit
8 1
NUMBERS BEYOND 20
TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Continue to provide practice in reading numbers by playing races involving who can read the number first or playing ‘Around the World’ in Lesson Plan 2, Tuning In.
Q2
Look for opportunities for the student to read numbers in the school environment, e.g. team or sporting scores.
Q3
If the student takes a while to place number tiles on a 100 chart and appears to be going through numbers from 1 onwards to find a number, then they have not demonstrated an understanding of how the numbers are placed. Have them complete a blank 10 x 10 grid writing the numbers to 99 or 100. Ask them to point to a particular number and read all the numbers in that column and row, and discuss what is common to all the numbers in that column and row.
Q4
Initially, have the student point to numbers on NTO 1.21 ‘Numbers to 100’ and name the number that comes before and after. Then ask them to visualise a 100 chart and think about where a number would be and what numbers they would see either side of it. Play ‘Consecutive Numbers’ in Lesson Plan 3, Independent Tasks, Task 1, whereby the student places number tiles side by side to see if they look like consecutive numbers.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution.
Unit 8
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Decimals to 2 Decimal Places
37
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Number Bingo
DATE:
You will need: a partner, a copy of BLM 14 ‘100 Chart’, scissors, a paper bag 1
Choose numbers between 1 and 100.
Write each number in the grid below.
2
Cut up BLM 14 ‘100 Chart’ to make number tiles.
Place the number tiles in a paper bag.
3
With a partner, take it in turns to pull a number
tile from the paper bag. Read the number.
4
If you have that number in your grid, cross it off.
5
The first person to cross off all of their numbers wins.
6
Use the grid below to play again.
38
Unit
8
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Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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Lucky Slides
DATE:
You will need: a dice, small counters 1
Fill in the missing numbers to complete the game board.
0
1
2
10
13 21
22
30
4
5
14
15
52
71
90
64
46
66
91
85
39
47 57
58
67
68
76
72 84
19
38
55
80
9
27
45
63
17
35
40
60
16
24 33
51
8
78
79
98
99
86 97
2 To play a game with a partner, put your counters on 0. 3 In turn, roll the dice and move that many spaces.
4 Look carefully so you follow the numbers in the correct order.
If you do not follow the correct order, you have to go back to 0.
5 If you land on a number at the top of the slide, ‘slide’ down
to the number at the bottom.
6 The first to 99 wins!
Unit
8
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Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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What’s the Number?
DATE:
You will need: a set of number tiles made BLM 14 ‘100 Chart’
for each table, glue
1
Select a number card. Paste it in the space below. Think about
a 100 chart. Now write the number that comes before and
after. Do this 3 more times.
2
Three groups of children played a game.
Work out who came 1st , 2nd and 3rd for each group.
Their scores were: a Abdul: 78
Jake: 79 2nd
1st b Lucy: 84
Iman: 86 2nd
1st
c Carlos: 39 Nat: 41 2nd
1st
Lee: 76 3rd Maria: 85 3rd Tom: 40 3rd
one more than Jack, Jo scored
3
Jack scored 79. Jan scored
one less than Jack and Jed scored one more than Jan.
What were their scores? Write them in order.
40
Unit
8
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Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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DATE:
Unit
8
STUDENT ASSESSMENT
You will need: a set of number tiles made from BLM 14 ‘100 Chart’
1
Have your teacher or a partner select 8 number tiles.
As they read them to you, write down each number.
2
Fill in the missing numbers in the 100 chart.
1 19 24
50 53
75
100 3
Unit
8
Marketing Sampler.indb 41
Write the number that comes after each number. 71
17
39
63
Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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Unit
10
Length and Area
Measurement and Geometry Length: MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres Area: MA1-10MG measures, records, compares and estimates areas using uniform informal units
ML
estimating, long, longer, longest, measuring, tall, taller, tallest, area, surface, cover
LESSON PLAN
TUNING IN
HOW CAN YOU MEASURE? Present a problem to students about wanting to find out which is the longer of two things that cannot be moved. Select something within the classroom or school environment, e.g. your desk and an upright cupboard, and ask, ‘How can we work out which is longer – my desk or the cupboard – when we cannot place them side by side?’ Discuss with students their ideas, including the idea of using some sort of units that are the same size to measure the objects.
1
WHOLE-CLASS INTRODUCTION MAKING A GOOD ESTIMATE You will need: footprints cut out from BLM 18 ‘Dinosaur Footprints’ Show students the dinosaur footprints cut out from BLM 18 ‘Dinosaur Footprints’ and tell them that these will be used to measure the desk and the cupboard. Tell students you would like them to think about how many footprints long the desk and cupboard might be and write students’ estimates on a class list. Invite two students to measure the desk and two students to measure the cupboard. Ask, ‘Which is longer? How do we know?’ Look at the class list and find the students whose estimates were closest and ask, ‘How did you make your estimation?’ Discuss the idea of estimating by thinking about how many of the footprints would fit along the desk or cupboard.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 18 ‘Dinosaur Footprints’, scissors, chalk, Student Book p. 40 ‘Two Footprints Long’
TASK 1:
ESTIMATE AND MEASURE
Have students work with a partner or small group. Give each pair or small group a copy of BLM 18 ‘Dinosaur Footprints’ and have them cut out the footprints. Students then choose two objects in the classroom to measure. Before they measure, they need to record an estimate of how many footprints long they think each object will be and then work together to measure. When students have finished measuring, they need to write about what they did and a statement about which object was the longest and how they know.
TASK 2:
DRAW A DINOSAUR
Have students work with a partner or small group to draw a dinosaur that is five or 10 footprints long or tall using chalk outside the classroom on a concrete or asphalted area.
TASK 3:
STUDENT BOOK p. 40 ‘Two Footprints Long’
TEACHING GROUP
You will need: BLM 18 ‘Dinosaur Footprints’, scissors MORE OR LESS THAN A FOOTPRINT • For students who require support, continue to have them compare individual classroom objects to decide if they are more or less than a dinosaur’s footprint. Have students cut out a footprint from BLM 19 ‘Dinosaur Footprints’, and then holding the footprint in their hand, have them look around the classroom to find something they think will be more than the footprint. Have students collect the object and make a direct comparison. Then ask students to find something in the classroom they think will be less than the footprint and directly compare the object. Have students write about their findings. Nelson Maths Australian Curriculum NSW
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FIVE THINGS • For students who require a challenge, have them work with a partner or small group to cut out a footprint from BLM 18 and look for things in the classroom that might be at least as long as three footprints. Have students select up to five objects and measure them with the footprints and then order the five objects from longest to shortest. Have students record their findings.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from Independent Tasks, Tasks 1 and 2, or from the Teaching Groups, and ask, ‘Was it easier to measure some things than others? Why?’ • Ask, ‘What did you do when you were measuring and the footprint went past the end of the object? How did you count that?’
LESSON PLAN
TUNING IN
2
MEASURING DINOSAUR FOOTPRINTS You will need: three pieces of string 5 cm, 27 cm and 75 cm long or drawings of dinosaur footprints (of these lengths) on paper or on the floor using chalk Prior to the lesson, make sure that all rulers are out of sight. Hold up the pieces of string or point to the footprints, explaining to students that dinosaur footprints were discovered at Lake Quarry in Winton, Queensland, that the footprints belonged to three different types of dinosaurs and that the string (or the drawings) show the average size of the footprints. Ask, ‘What do we have in the classroom that we can use to measure the footprints?’ During discussions of possible objects, stress that whatever is to be used to measure needs to be of uniform size.
WHOLE-CLASS INTRODUCTION MEASURE IT You will need: NTO 1.24 ‘Measure It’ Present NTO 1.24 ‘Measure It’ and select an object, e.g. a shoe, to measure. Choose between the paperclip, craft stick or square counter. Have students estimate how many of each item will be needed to measure the shoe, and then invite a student to measure using the unit of choice and students counting the units. Counting the units presents a good chance to discuss what to do if the units are more than the object.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3 You will need: three pieces of string 5 cm, 27 cm and 75 cm long, paperclips, craft sticks, counters, playing cards, NTO 1.24 ‘Measure It’, Student Book p. 41 ‘Paperclips or Counters?’
TASK 1:
MEASURING WITH THINGS
Have students work with a partner and choose two of the dinosaur footprints (or pieces of string) to measure. Have them record an estimate first and then measure, choosing from a range of informal uniform units, e.g. paperclips, counters, craft sticks, playing cards. Have students record their results.
TASK 2:
INTERACTIVE TASK
Have students explore NTO 1.24 ‘Measure It’ choosing different informal units to measure objects.
TASK 3: STUDENT BOOK p. 41 ‘Paperclips or Counters?’
TEACHING GROUP
You will need: paperclips, craft sticks, playing cards HOW LONG IS A TABLE? • For students who require support, have them focus on one object and the skills involved in using uniform units to measure its length. As a group, decide on an object in the classroom to measure, e.g. a tabletop. Explain to students that they are to measure the length of the tabletop using paperclips. Give each student a paperclip and ask, ‘How many paperclips do you think will fit end to end from one edge of the tabletop to the other?’ Have students write down their estimates. Then have them work in pairs or small groups to measure the tabletop. Have students compare results and discuss reasons for any discrepancies.
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MEASURING WITH DIFFERENT UNITS • For students who require a challenge, have them explore using different uniform units. As a group, decide on a number of things in the classroom that can be measured, e.g. the width of the doorway, the shortest side of your desk, the width of a computer keyboard. Have each pair of students use something different to measure with, e.g. paperclips, craft sticks or playing cards. Have students record estimates before they measure. When students have finished measuring, have them share results. Record the different results and ask, ‘Were the results the same? Why not?’
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their results from Independent Tasks, Tasks 1 and 2, or from the Teaching Groups, and ask, ‘Did everyone get the same results? Why not?’ • Have the students who estimated well explain what strategies they used. • Have students explain how they measured and record a list of the key things they need to remember on the board or poster paper.
LESSON PLAN
TUNING IN
3
WHAT DO WE MEAN BY AREA? You will need: a normal classroom table In order to ensure that students understand the difference between length and area, have students trace along the edge of a classroom table with their index fingers and identify this as the ‘length’ of the table top. Next, ask them to start at one corner of the table top and to pretend that they are cleaning the whole surface of it with the palms of their hands. Identify this as the surface of the table top and that they have rubbed their hands over the whole of the area of the table top.
WHOLE-CLASS INTRODUCTION THE AREA OF A TABLE TOP You will need: Several books of the same type/size or sheets of A4 paper.’ Remind students of the Tuning In activity in order to ensure that they understand what is meant by the area of something. Say something like, ‘We are going to put the books (sheets of paper) side-by-side on the table top so that they cover the whole area. How many do you think we will need?’ Carry out the activity and identify the area as ** books/sheets of paper.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: counters/blocks, the cover of a book, NTO 1.53 ‘Larger or smaller area?’ 10 cm x 10 cm squares of coloured paper, a piece of card 30 cm x 20 cm divided into 10 cm x 10 cm squares, Student Book p. 42 ‘Area’
TASK 1:
WHAT’S THE AREA?
Working with a partner, students estimate the number of counters that will be needed to cover the front of a book. They could record their guesses and then carry out the activity. Afterwards they record the actvitiy by writing something like, ‘It took 20 counters to cover my book. The area of my book is 20 counters.’
TASK 2:
INTERACTIVE TASK
Have students explore the comparison of two areas area using NTO 1.53 ‘Larger or smaller area?’
TASK 3: STUDENT BOOK p. 42 ‘Area’
TEACHING GROUP
You will need: 10 cm x 10 cm squares of coloured paper, a piece of card 30 cm x 20 cm divided into 10 cm x 10 cm squares, BLM 52 ‘Two-centimetre Grids’ LET’S COVER IT • For students who require support, work with a small number of uniform, informal units (10 cm x 10 cm squares) and a piece of card 30 cm x 20 cm divided into 10 cm x 10 cm squares. Identify what is meant by the area of the card by rubbing a hand over the whole surface (see Tuning In). Ask the students how many of the coloured squares they think will be needed to cover the card. Carry out the activity by placing
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the squares on the card side-by-side, one at a time. Identfy the area of the card as 6 squares. Also use BLM 52 ‘Two-centimetre Grids’. Students estimate how many (2 cm) counters will be needed to cover the rectangles and then carry out the activity and complete Student Book, page 42, ‘Area’. USING DIFFERENT UNIFORM, INFORMAL UNITS • For students who require a challenge, have them explore using various uniform, informal units to find the area of a 10 cm x 10 cm sheet of paper. Ask, ‘Is the total number of counters the same as the total number of blocks, for example? Why or why not?’ Subsequent discussion could lead to the understanding why the use of a formal unit for finding area would be advantageous.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their results from Lesson Plans 1 and 2 Independent Tasks, Task 1, or from the Teaching Groups, and ask, ‘Did everyone get the same results? Why not?’ • Have students who estimated well explain what strategies they used. • Have students explain the difference bewteen what we mean by the length of something and the area of something.
Assessment • Have students complete Student Assessment p. 43. • Review with students Assessment Task Card 1.10. During the three lessons: • Collect created items from Lesson Plan 1, Independent Tasks, Task 1, and Lesson Plan 2, Independent Tasks, Task 1, as work samples for student portfolios. • Observe students as they complete Lesson Plan 1, Independent Tasks, Task 1, and Lesson Plan 2, Independent Tasks, Task 1, and mark off on a class list students who are able to make reasonable estimates and measure the length of objects reasonably accurately. • Make note of the way that students estimate area in Lesson Plan 3. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future learning Specific to Student Assessment p. 43; if the student is experiencing difficulty: Q 1–2 Provide more experiences in the classroom for the student to measure and compare two objects according to length, e.g. finding who has the longest shoe. Q 3 Have the students use a variety of informal units to find the area of the same object. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 1.10 for specific recommendations. 2. Have the student directly compare objects and determine the longest prior to using uniform informal units. 3. Review Nelson Maths: Australian Curriculum Kindergarten Unit 7. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 2 Unit 3. 2. Extending the student in any of the listed activities or tasks by using more than two objects to measure the length and compare using uniform informal units. Discuss the advantage of using uniform, formal units for measurement.
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Two Footprints Long
DATE:
You will need: a copy of BLM 18 ‘Dinosaur Footprints’, scissors 1
Cut out your dinosaur footprints.
2
Look around your classroom. Draw 3 objects that might be
2 footprints long.
3
Now measure the objects and record what you found out.
Objects (Draw here)
4
46
How many footprints long?
Write what you found out when you measured
How did you decide which objects might be
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long?
Length and Area (TRB pp. 58–61) Length MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres
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Paperclips or Counters?
DATE:
You will need: paperclips, counters 1
Choose what you are going to use to measure the length
of each object. Write it here:
2
First estimate how long you think each object will be.
3
Now measure each object.
Object
Estimate
How many?
Book
Strap on school bag
4
Which object is longer?
How do you know?
5
Check with a partner. Did they get the same results as you?
How do you think that happened?
Unit
Length and Area (TRB pp. 58–61) Length MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres
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Area
DATE:
1
Use counters to find the area of each shape.
How many counters for each shape?
Colour the shape with the largest area red.
Colour the shape with the smallest area blue.
2
Count the squares to find the area of each letter.
Which has the largest area?
Which has an area that is 1 square bigger than “T”?
Which have the same area?
Draw a letter “L” that has an area of 7 squares.
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Length and Area (TRB pp. 58–61) Area MA1-10MG measures, records, compares and estimates areas using uniform informal units
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DATE:
Unit
10
STUDENT ASSESSMENT
You will need: counters • Look at the snakes. Estimate how long you think each snake might be if you measured it with counters. • Now measure the snakes with counters.
Estimate
Number of counters long
Sammy
Sid
• W hich two letters have the same area? Use counters to find out.
Unit
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The letters with the same area are
and
Length and Area (TRB pp. 58–61) Length MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres Area MA1-10MG measures, records, compares and estimates areas using uniform informal units
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Unit
4
Numbers Up to 1 000
NUMBER AND ALGEBRA Whole numbers: MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
ML
digit, hundreds, ones, number cards, MAB blocks, spike abacus, tens
LESSON PLAN
TUNING IN
1
READING NUMBERS You will need: NTO 2.1 ‘Numbers’ Present NTO 2.1 ‘Numbers’ set to show three cards with numbers from 0 to 9. Place the cards close together and have students read the 3-digit number. Rearrange the cards and have students read the new number formed. Continue having students practise reading 3-digit numbers by using the NTO to generate cards that can be arranged to form the numbers.
WHOLE-CLASS INTRODUCTION USING NUMBER CARDS You will need: NTO 2.xx ‘Number Cards’ Present NTO 2.xx ‘Number Cards’. Select a random number and have students read the number. Then ask them to say the number aloud and ask, ‘How many hundreds did you say?’ Invite a student to select the number card for that many hundreds. Have students say the number again. Invite a student to select the tens card and have them say the number again. Finally, have a student select the ones card and have the class say the number again. Generate more numbers, inviting students to say the number and then show it using the number cards.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of arrow cards made from BLM 2 ‘Arrow Cards 1’, BLM 3 ‘Arrow Cards 2’, a set of cards made from BLM 1 ‘Number Cards’, NTO 2.xx ‘Number Cards’, Student Book p. 60 ‘Arrow Cards’
TASK 1:
MATCH THE NUMBER
Have students work in pairs. Give each pair a set of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’ and a set of number cards made from BLM 1 ‘Number Cards’. One student selects a number card (their partner is not allowed to see it) and reads the number aloud while their partner forms that number using arrow cards. This student can then check their arrow card by looking at the number card, and if they are correct, they keep the number card. Students then reverse roles. The student with the most number cards wins.
TASK 2:
INTERACTIVE TASK
Have students explore NTO 2.xx ‘Number Cards’ by randomly generating a number and using the number cards to show the number.
TASK 3: STUDENT BOOK p. 60 ‘Arrow Cards’
TEACHING GROUP
You will need: sets of arrow cards made from BLM 2 ‘Arrow Cards 1’, BLM 3 ‘Arrow Cards 2’ (100 card only), NTO 2.xx ‘Number Cards’ 100 MORE • For students who require support, begin by having them make 2-digit numbers using a set of arrow cards made from BLM 2 ‘Arrow Cards 1’. Working with a partner, have them sort their cards into columns of ones and tens. Have students show 2-digit numbers. Say the number and have students repeat the number and find the two cards to show the number. Continue having students make 2-digit numbers, and when they are ready, have them show 28 and then ask then to place the 100 card (from BLM 3 ‘Arrow
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Cards 2’) underneath and read the number. Continue having students make 2-digit numbers and then placing the 100 card underneath and reading the number. USING THE 1 000S CARDS • For students who require a challenge, have them work with higher numbers. Present NTO 2.xx ‘Number Cards’ and select the 1 000s cards. Point to different cards and have students read them out. Select a 1 000s card, hundreds card, tens cards and a ones card and have students read the number. Double click on the hundreds card to remove it and have students read the number. Double click on the tens card and have students read the number. Repeat a few more times, showing a number and having students read the number aloud. Have students randomly generate a number and then make the number.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask students ‘When you make a number with arrow cards or on the computer, what are you thinking? • Tell students that you want them to show the number 942 (either using arrow cards or NTO 2.1 ‘Numbers’) and have them explain how they would do it. Ask, ‘How do you know you are correct?’ • Present NTO 2.xx ‘Number Cards’ and randomly generate a number, but ask students to show a number that is 100 more or less.
LESSON PLAN
TUNING IN
2
DOES ANYONE HAVE? You will need: a set of number cards made from an enlarged copy of BLM 1 ‘Number Cards’ Give a number card to each student and ask, ‘Does anyone have a number with six tens?’ Have those students stand up and show their cards. Ask, ‘Does anyone have a card with more than five hundreds?’ Continue asking questions about place-value components and note any students who are having difficulty and may need support in the Teaching Groups.
WHOLE-CLASS INTRODUCTION SPIKE ABACUS You will need: NTO 2.xx ‘Spike Abacus’, a set of number cards made from an enlarged copy of BLM xx ‘Number Cards’, small whiteboards Present NTO 2.xx ‘Spike Abacus’ and explain to students that they can use a spike abacus to model numbers. Place one bead on the hundreds spike, two beads on the tens spike and three beads on the ones spike. Ask, ‘What number has one hundred, two tens and three ones?’ Invite a student to write the number on the board. Make another three-digit number with seven beads on the hundreds spike, four beads on the tens spike and six beads on the ones spike, and ask, ‘What number has seven hundreds, four tens and six ones?’ Continue making numbers and asking students to write down the number on small whiteboards. Next, select a number card made from BLM xx ‘Number Cards’ and ask, ‘Can anyone show this number on the spike abacus?’ Invite a student to show the number and then check the number of beads for each place-value component and check against the number card. Continue inviting students to select a number card and show the number on the spike abacus.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’, a spike abacus and beads, BLM 1 ‘Number Cards’, NTO 2.xx ‘Spike Abacus’, Student Book p. 61 ‘Numbers on a Spike Abacus’
TASK 1:
SPIKE ABACUS AND ARROW CARDS
Have students work with a partner whereby one student shows a number on the spike abacus and their partner must show that number using arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’. Then have the student with the arrow cards show a number and their partner must show that number on the spike abacus. Have students alternate roles using the modelling equipment.
TASK 2: INTERACTIVE TASK Give students a set of number cards made from BLM 1 ‘Number Cards’, and have them use NTO 2.xx ‘Spike Abacus’ to model a selected number. They can check they are correct by selecting the ‘show number’ button.
TASK 3:
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STUDENT BOOK p. 61 ‘Numbers on a Spike Abacus’
Numbers Up to 1 000
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TEACHING GROUP
• You will need: small whiteboards, Blu Tack or playdough, wooden skewers (with sharp ends cut off), beads (can be made from playdough), NTO 2.xx ‘Spike Abacus’ MAKING A SPIKE ABACUS • Give each student a small whiteboard and enough Blu Tack so that two skewers can stand upright on the board. Have students label the skewer on the right ‘Ones’ and the skewer on the left ‘Tens’. Say a 2-digit number, e.g. 32, and ask, ‘How many tens?’ Have students place that many beads on the tens skewer and ask, ‘How many ones?’ Have students place that many beads on the ones skewer. Continue. FOUR SPIKES • For students who require a challenge, have them use a spike abacus to make 4-digit numbers. Present NTO 2.xx ‘Spike Abacus’ and select the ‘show thousands’ button to reveal the fourth spike. Place some beads on the spikes, and have students write the number shown on small whiteboards. Invite a student to read their number and ask, ‘How did you work that out?’ Repeat a few more times, displaying numbers and having students write down what number is shown. Next, invite a student to write a 4-digit number on their whiteboard and show that number on the NTO. Have the student reveal the number on the whiteboard and the group determine if it matches the number shown on the spike abacus.
REFLECTION Select from the following to suit your class and their learning outcomes: • Present NTO 2.xx ‘Spike Abacus’ showing 438. Ask, ‘What number is shown? How do you know?’ • Ask, ‘I placed five beads on a three-spike abacus. What number could I have shown?’ Using a spike abacus, discuss possible answers and have students explain how they worked out the problem.
LESSON PLAN
TUNING IN
3
WHAT NUMBERS CAN YOU MAKE? You will need: NTO 2.1 ‘Numbers’ Present NTO 2.1 ‘Numbers’ set to show three number cards between 0 and 9. Have students look at the numbers, and move three of the numbers close to one another and say the 3-digit number. Ask, ‘What other numbers can we make using the three numbers displayed?’ Have students come to the board and rearrange the cards to make other 3-digit numbers. Ask, ‘What is the largest number you can make? What is the smallest number you can make?’
WHOLE-CLASS INTRODUCTION WHAT’S MY NUMBER? You will need: NTO 2.xx ‘Number Cards’ Write a 3-digit number on a piece of paper and keep it hidden. Present NTO 2.xx ‘Number Cards’ and ask, ‘What do you think my number is?’ Instead of saying the number, invite a student to show what they think the number could be. If any of the components are correct, leave the card displayed, but if they are not part of the number, double click to remove the incorrect cards. Continue to invite students to show their guesses, leaving the correct components and removing the incorrect components until the mystery number is worked out.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of 3 dice, BLM 4 ‘Number Stairs’, NTO 2.xx ‘Playing Cards’, Student Book p. 62 ‘Climbing Up the Ladder’
TASK 1:
NUMBER STAIRS
Have students play with a partner whereby they take it in turns to roll the three dice to form a 3-digit number. Students place the number in any space on BLM 4 ‘Number Stairs’, provided the numbers decrease as they go down the stairs. If students cannot make a number that will fit, they forfeit their turn. The first student to complete their stairs with the numbers in order from highest to lowest wins.
TASK 2: INTERACTIVE TASK Have students work with a partner to use NTO 2.xx ‘Playing Cards’ to deal three cards and rearrange the digits to make the largest number they can. Their partner draws three cards to see if they can make a larger number.
TASK 3:
STUDENT BOOK p. 62 ‘Climbing Up the Ladder’
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TEACHING GROUP
You will need: a deck of playing cards with the tens and picture cards removed, a dice BEAT IT • For students who require support, work with 2-digit numbers until they are able to extend their place- value understanding to hundreds. Have students play with a partner whereby the first player draws two playing cards from the deck and forms the largest number they can. Their partner then draws two cards to make a number that will ‘beat it’. The student who has formed the highest number keeps all four cards. The student with the most cards wins. CLOSEST TO 999 • For students who require a challenge, have them draw up a table or grid with three columns in which they write the headings ‘Hundreds’, ‘Tens’ and ‘Ones’. The object of the game is to get a score as close to 999 without going past it. The dice is rolled six times, and for each roll, students will decide if it is to be a hundred, ten or one. After six rolls of the dice, students add up their score and the score that is closest to 999 wins, but if the total is more than 999 they have lost.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask in relation to Independent Tasks, Tasks 1 and 2, ‘When you rolled the dice or drew the cards, how did you decide what was the best number to make?’ • Ask in relation to the Independent Tasks and the Teaching Groups, ‘What strategies did you use to win the game?’
Assessment • Have students complete Student Assessment p. 63. • Review with students Assessment Task Card 2.4. During the three lessons: • Observe students in Lesson Plan 2, Independent Tasks, Task 1, and mark on a class list students who are able to represent 3-digit numbers with arrow cards and on a spike abacus. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 63; if the student is experiencing difficulty: Q 1 Have the student work with a range of materials to model 2-digit and then 3-digit numbers, e.g. craft sticks, Unifix blocks, MAB blocks, and use arrow cards to label models. Q 2–3 Have the student model 2-digit numbers on a spike abacus before moving to 3-digit numbers. Q 4 Provide opportunities for the student to explore making 2-digit numbers by drawing playing cards or rolling dice. Q 5 Look for opportunities in the classroom where the student needs to order numbers, e.g. scores in games, team points and so on. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 2.4 for specific recommendations. 2. Have the student work with 2-digit numbers in any of the listed activities or tasks prior to moving to 3-digit numbers. 3. Review Nelson Maths: Australian Curriculum Year 1 Unit 15. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Completing Nelson Maths Building Mental Strategies Big Book 3, pp. 14–15, to reinforce mental strategies involved in ordering numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 3 Unit xx, pp. xx–xx. 3. Extending the student in any of the listed activities or tasks by using 4-digit numbers.
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Numbers Up to 1 000
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BLM
1
Number Cards
237
73
615
516
948
840
909
217
643
821
395
781
702
372
515
416
489
94
150
634
803
362
123
468
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
Teacher’s Note: This BLM can be photocopied, laminated and cut up to make cards to use for modelling and sorting activities.
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BLM
2
Arrow Cards 1
1 2
7
5
3
6
4
8 0 6
9
8 0
4 0
7 0
3 0
6 0
2 0
5 0
1 0
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
Teacher’s Note: To make the cards, cut around the outside borders and along the dotted diagonal lines. Place cards one on top of the other, aligning the arrows, to build combinations of numbers with hundreds, tens and ones.
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BLM
4 0 0
7 0 0
8 0 0
2 0 0
3 0 0
1 0 0
6 0 0
Arrow Cards 2
5 0 0
3
9 0 0 © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
Teacher’s Note: To make the cards, cut around the outside borders and along the dotted diagonal lines. Place cards one on top of the other, aligning the arrows, to build combinations of numbers with hundreds, tens and ones.
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BLM
4
Number Stairs
1 000
1 000
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
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2.4
Year 2: Assessment Task Card Unit
4
NUMBERS UP TO 1 000
Resources: BLM 2 ‘Arrow Cards 1’, BLM 3 ‘Arrow Cards 2’, a spike abacus, NTO 2.xx ‘Dice’
1
Say the following numbers and have the student show using arrow cards:
472, 967, 214, 504, 370
2
Show the following numbers on a spike abacus and ask the student what number is shown:
274, 856, 247, 201, 960
3
Have the student show the following numbers on a spike abacus:
324, 178, 670, 302
4
Using NTO 2.xx ‘Dice’, show three dice. Ask the student what is the smallest 3-digit number they can make from those numbers. Ask the student what is the largest 3-digit number they can make from those numbers.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
2.4
Year 2: Assessment Task Card Unit
1
NUMBERS UP TO 1 000 TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Provide opportunities for the student to show 2-digit numbers using arrow cards or NTO 2.xx ‘Number Cards’ before moving to 3-digit numbers.
Q2–3 Have the student model numbers using MAB blocks, and then have them show the same numbers modelled with arrow cards. Have the student show the same numbers on a spike abacus. Q3–4 Provide opportunities for the student to play games, e.g. BLM 4 ‘Number Stairs’ or ‘Ladder Games’, similar to ‘Climbing Up the Ladder’ (Student Book p. 62), whereby the student uses their place-value understandings, and the number of cards or dice used can also match the student’s level of place-value understanding.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution.
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Arrow Cards
DATE:
You will need: a set of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’ 1 Using your arrow cards, make numbers to match the MAB models. Write your numbers beside each model. a
b
c
d
2 Use your arrow cards to make the numbers below. Write your number in the box. a A number that is more than 700 but has no tens b A number that is less than 700 but has no ones c A number that is between 700 and 900
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Numbers on a Spike Abacus
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1 Write the numbers that are shown on the abacus.
H
T
O
H
H
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T
O
O
H
H
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H
H
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2 Show the following numbers on the abacus.
905 227 69
562
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H
380
H
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H
631
H
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H
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454
713
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3 Show the following numbers on the abacus. Write the number beside the abacus. a 10 less than 256
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b 100 less than 789
H
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Climbing Up the Ladder You will need:
DATE:
a partner, 3 dice
1 In turn, roll the dice and make a 3-digit number. Write your
number on a rung of the first ladder. The numbers need to get
bigger as you go up the ladder.
2 Once you have written a number, it must stay on that rung. 3 Keep rolling the dice and placing your numbers until each player has filled their ladder.
4 You score 1 point if the numbers are in order from smallest
to largest.
5 The person with the most points after 8 rounds wins.
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DATE:
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STUDENT ASSESSMENT
You will need: a set of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’, a dice 1 Use the arrow cards to make the numbers. Write them.
H
T
O
H
T
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2 Write the numbers that are shown on the abacus.
H
T
O
H
T
O
H
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H
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3 Show the following numbers on the abacus. 147 302 415
562
H
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H
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H
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4 Roll a dice 3 times. Write each number in a box.
Use the numbers to write as many 3-digit numbers as you can. 5 Order your numbers from smallest to largest.
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Unit
10
Position
MEASUREMENT AND GEOMETRY Position: IMA1-16MG represents and describes the positions of objects in everyday situations and on maps
ML
above, back to back, backwards, behind, below, between, centre, forwards, half turn, in front of, left, middle, near, next to, right, quarter turn, side by side, top, towards, under, underneath, upside-down
1
LESSON PLAN
TUNING IN
MIME IT Have students work with a partner or in small groups. Explain to students that they are going to mime – actions without speaking – words that are used to give directions. Ask students, ‘What words might you use if you were going to explain to someone how to get from one place to another?’ Record their suggestions. Whisper a word to each group so that no one else can hear and have students mime the word for the class to guess.
WHOLE-CLASS INTRODUCTION ROBOTS Tell students someone is going to be a ‘robot’ and they will move around the room. Explain that the robot cannot think for itself and needs to be programmed so that it can move around the room. Inform students that you are the robot and that they will need to tell you how to move from one place to another in the classroom. Pick two classroom objects to move between that will require at least one turn. Invite different students to give instructions and follow them. If you are instructed to turn, complete a 360 turn unless the students tell you otherwise. At that point, discuss with students the need for more specific language, e.g. quarter turn or half turn. Continue until you have reached your destination. Next, invite a student to be the ‘robot’ and another student to give the instructions to move from place to place, e.g. from the door to your desk, from the board to the bookshelf, from the sink to the computers, and so on.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: disposable or plastic plates of varying sizes, cups, bowls, cutlery, toy food items, LO 1074 ‘Direct a Robot: Which Way?’, Student Book p. 68 ‘Pattern Block Pictures’
TASK 1:
DINNER TIME
Have students work in pairs, each with a variety of the materials above. Have a student make an arrangement using plates or bowls, cups and cutlery, and placing different food on the plates. This arrangement can be covered with a cloth or a barrier placed between so that it is hidden from their partner. The student then explains what they have done and the position of items in relation to one another so that their partner can draw the arrangement as they have laid it out. When they have finished, they check to see which things are in the correct position and which are not, and discuss why this might have happened. Students then change roles.
TASK 2:
INTERACTIVE TASK
Have students explore LO 1074 ‘Direct a Robot: Which Way?’ whereby they need to select the direction the robot turns in order to take the shortest route to collect samples before returning to their spaceship.
TASK 3:
STUDENT BOOK p. 68 ‘Pattern Block Pictures’
TEACHING GROUP
You will need: NTO 2.xx ‘Pattern Blocks’, a set of pattern blocks, a digital camera ARRANGING BLOCKS • For students who require support, have them follow step by step as an arrangement is made on NTO 2.xx ‘Pattern Blocks’ and discuss positional language. Present NTO 2.xx ‘Pattern Blocks’, and explain that as
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an arrangement of shapes is made on the NTO, students will make the same arrangement with pattern blocks. Select a shape, e.g. a square, place it in the centre of the board and ask, ‘How can we describe where we put the square?’ Have students find a square and place it in the centre of the space in front of them. Then select another shape, e.g. a hexagon, place it under and touching the square and ask, ‘How can we describe where we put the hexagon?’ Have students place the hexagon in their own arrangement. Select another shape, e.g. a trapezium, place it above and touching the square and ask, ‘How can we describe where we put the trapezium?’ Have students place the trapezium. Continue placing shapes and have students use directional language to describe the position of each shape as they place in their own arrangement. CAN YOU MAKE A MATCH? • For students who require a challenge, have them create an arrangement of shapes and write a description for a partner to follow to create the same arrangement. Take digital photos of original arrangements, and after instructions have been followed by a partner, pairs can check the photo to see if they are correct. If a matching arrangement has not been made, have students determine why and modify their instructions.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students show their work from Independent Tasks, Tasks 1 and 3, and ask, ‘Why do you think that the pictures were not identical?’ Discuss why some things may have been different sizes and maybe things may not have been placed in the correct place. • Ask in relation to ‘Can You Make a Match?’ in the Teaching Group, ‘What was the first instruction you gave? Why did you choose that?’
LESSON PLAN
TUNING IN
2
BIRD’S-EYE VIEW You will need: a box, a large can, a large ball, NTO 2.xx ‘Bird’s-Eye View’ Pass a box to students and ask them to look down on the box and think about the shape that they can see. Ask, ‘If you could fly and look down on this, what shape do you think you would see?’ Continue to pass the other objects (can and ball) to students. Have them look down on these objects and ask them what shape they think they might see if they were a bird flying over it. Present NTO 2.xx ‘Bird’s-Eye View’ and explain to students that the shape that they see on screen is what a bird would see if it was flying high above an object. Ask, ‘What do you think it could be? What makes you think that?’ Invite a student to check by selecting an object. Continue presenting other bird’s-eye views and asking students what object they think it might be and why.
WHOLE-CLASS INTRODUCTION AS THE CROW FLIES You will need: As the Crow Flies: The First Book of Maps by Gail Hartman (Bradbury Press, 1991) Hold up the cover of As the Crow Flies: The First Book of Maps and ask, ‘What can you see?’ Have students describe all the different things they can see and ask, ‘Why do you think the crow can see so much?’ Discuss with students the idea that the crow is so high in the sky that it can see further than if it was on the ground as there is nothing blocking its view. Read the book and discuss the difference between the picture and the map for each animal.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: a digital camera, NTO 2.xx ‘Bird’s-eye View’, Student Book p. 69 ‘Ebony’s Run’
TASK 1: AS THE CHILD SEES Have students look out of the window and name at least three things that they can see. Explain that you want them to draw their map just as there was a map for the eagle, rabbit, crow, horse and gull showing what they saw. Ask, ‘What shape do you think our classroom would be if we were looking down on it from above?’ Have them begin their map by drawing the shape that represents the classroom and then have them draw the other things they identified when looking out of the window.
TASK 2:
INTERACTIVE TASK
Students could use a digital camera to take ‘bird’s-eye view’ pictures of classroom objects. Ask them to share these with other students and to see if the other students can identify the objects. Alternatively students could further explore NTO 2.xx ‘Bird’s-Eye View’.
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TASK 3: STUDENT BOOK p. 69 ‘Ebony’s Run’
TEACHING GROUP
You will need: a fairytale picture book, glue, BLM xx ‘Funtime Park’ FAIRYTALE MAP • For students who require support, read or tell the story of a fairytale, e.g. Goldilocks and the Three Bears, Little Red Riding Hood, Cinderella or The Three Little Pigs. Ask, ‘What are the different places in the story?’ Make a list of the places and have individual students draw a picture of one of the places on a small piece of paper. Then, on a large sheet of paper, have the students place their pictures where they think each place should go. Reread or retell the story and make sure that the drawings have been placed in the correct position. Have students paste the pictures in place. MAP OF A THEME PARK • For students who require a challenge, give them a copy of BLM xx ‘Funtime Park’ whereby they need to read the directions and make a map of the park.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from ‘Fairytale Map’ in the Teaching Group, and ask, ‘How did you know where to draw things on your map? How do you know that you have put them in the correct place?’ • Ask in relation to ‘Map of a Theme Park’ in the Teaching Group, ‘What do you think was the most difficult thing about drawing a map?’ • Discuss with students the things they need to remember when drawing maps and make a poster of their suggestions to display in the classroom for reference during other mapping activities.
LESSON PLAN
TUNING IN
WHERE DO I LIVE? You will need: Where Do I Live? by Neil Chesanow (Barron’s Educational Series) Explain that you are going to read a book about a student who lives in the United States of America and she explains where she lives. Read the story to students, then ask, ‘Where do you live?’ and invite students to explain where they live.
3
WHOLE-CLASS INTRODUCTION OUR SCHOOL You will need: access to SpatialGenie at www.spatialgenie.edu.au (you will need to register for a free login prior to the lesson) Present SpatialGenie to students showing a map of the world. Under ‘My Map’ select the satellite view. Explain to students that this view is just like being in a rocket and coming back to Earth. Double click onto Australia for a closer view. Double click onto your state. Then keep double clicking until you have zoomed in to your school. Point to different buildings of the school and ask students what they think each is. Have students identify places they may know that are close to the school, e.g. shops or parks. You can scroll across from ‘My Map’ to ‘Street View’, and using the icon of an orange figure on the toolbar at the top of the map, you can get a street view of the school building. Once you have explored the school from different angles, scroll back to ‘My Map’ and click on the normal view to see it represented as a map. Have students look at the map and ask, ‘What do you recognise on the map?’ Discuss any specially marked features, e.g. parks, shops and the names of streets.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: SpatialGenie, Student Book p. 70 ‘Our School’
TASK 1:
OUR NEIGHBOURHOOD
Explain to students that you want them to make a map of the neighbourhood where their school is. Ask, ‘What do we have in our neighbourhood that we would record on a map?’ Make a list of students’ responses so they can include them on their own map. Have students draw a map and include their home if they can.
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TASK 2:
INTERACTIVE TASK
Have students explore SpatialGenie to see if they can find their house, and have them look at it as a satellite view and as a map. Have them also use the street view to find their house.
TASK 3: STUDENT BOOK p. 70 ‘Our School’
TEACHING GROUP CLASSROOM MAP • For students who require support, guide them through the process of drawing a map. Begin by asking what is the shape of the classroom if students were looking down on it, and have them draw that. Next, determine the key feature, e.g. tables, and have students count how many and look at the arrangement. Then have students draw the tables on their maps. Continue identifying objects in the classroom and determining which shapes will give a bird’s-eye view of the object and add those to the map. WHICH ROOM? • For students who require a challenge, have them work with a partner whereby one student instructs the other student what to draw for a map of a room of their choice. They can choose a room in the school and their partner should be able to guess which room it is when the map is complete.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their maps from Independent Tasks, Task 1, and have them explain what they drew first and then how they proceeded. Ask, ‘The maps look a bit different. Why?’ • Have students show their maps from ‘Classroom Map’ in the Teaching Group to a partner, and ask, ‘What do you think was good in your partner’s map? What do you think they could improve next time?’
Assessment • Have students complete Student Assessment p. 71. • Review with students Assessment Task Card 2.10. During the three lessons: • Collect created items, e.g. drawings and maps, as work samples for student portfolios. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 71; if the student is experiencing difficulty: Look for opportunities in the school environment for the student to describe how to get from one place Q 1 to the next, e.g. when sending students on messages, ask them to describe the route they would take. Have the student draw classroom objects from different points of view and have others try to determine Q 2 which view the drawing was done from. Increase the difficulty by placing more than one object. Provide street directories, atlases and other simple maps for the student to explore. Q 3 If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 2.10 for specific recommendations. 2. Provide experiences with simple maps of familiar areas, e.g. local parks and shopping centres. 3. Review Nelson Maths: Australian Curriculum Year 1 Unit 7. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 3 Unit xx, pp. xx–xx. 2. Extending the student in any of the listed activities or tasks by including the use of scale.
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Pattern Block Pictures
DATE:
You will need: BLM xx ‘Pattern Blocks’, glue, scissors, sheets of paper 1 Cut out the pattern blocks from BLM xx ‘Pattern Blocks’. Make a picture with the blocks and paste your picture below. Make sure your partner cannot see your picture.
2 Have your partner get another sheet of paper. Tell them where to draw the shapes so that they make a picture that is exactly the same as yours. 3 Now listen to your partner and draw what they tell you on another sheet of paper. 4 Is your partner’s picture the same as yours? How is it different?
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Position (TRB pp. 58–61) Position MA1-16MG represents and describes the positions of objects in everyday situations and on maps
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Ebony’s Run
DATE:
One day, Ebony got up early to go for a run. She walked out of her big house and ran down to the end of her street where there was a big forest. There were two paths into the forest, and she took the path on the right. She ran until she was in the middle of the forest, where she found a small cave. She heard a growl coming from the cave and quickly ran past the cave and further into the forest. Ebony thought she was lost until she came to a road. She turned left into the road and followed it all the way to her street. She ran along her street until she got home. Draw a map of where Ebony ran. Remember to include all of the places mentioned in the story.
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Position (TRB pp. 58–61) Position MA1-16MG represents and describes the positions of objects in everyday situations and on maps
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Our School
DATE:
1 List the things that are part of your school buildings. 2 List the things that are outside the buildings but part of the school. 3 Draw a map of your school. Make sure you include all the things on your lists. Remember that a map is a bird’s-eye view.
4 Is there anything else you can add to the map of the school?
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DATE:
Unit
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STUDENT ASSESSMENT
1 Write how you would get from your classroom to the office.
2 What could these be? You are looking at them from a bird’s-eye view.
3 Draw a map of your classroom.
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Unit
1
Numbers, Numbers, Numbers
NUMBER AND ALGEBRA Whole Numbers: MA2-4NA applies place value to order, read and represent numbers of up to five digits
ML
even, hundreds, larger, place value, odd, order, smaller, tens, thousands, units
1
LESSON PLAN
TUNING IN WHAT’S IN THE JAR?
You will need: beans, four jars or transparent containers Present students with four jars of beans, with one jar containing 9 beans, the next jar containing 31 beans, the next 53 beans and the final jar 147 beans. Ask, ‘Which jar has about 50 beans?’ Have students discuss their guess and the reasons for their guess. Invite four students to count out the beans in each jar. Record the numbers and tell students that these numbers have something in common that you will ask them about at the end of the lesson.
WHOLE-CLASS INTRODUCTION EXPLORING ODD AND EVEN NUMBERS You will need: sets of number cards made from BLM 1 ‘Number Cards 1’, counters Have students work with a partner. Give each pair some of the number cards made from BLM 1 ‘Number Cards 1’. Have students count out counters according to their number cards. Explain to students that they are going to determine if they have an odd or even number of counters and that this can be done by grouping counters in twos. If all the counters can be made into groups of two, the number is even. If there is a counter that cannot be grouped with another, the number is odd. Have students determine if their number is odd or even and make a list of the even numbers and the odd numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: NTO 3.1 ‘Ten Frames’, BLM 1 ‘Number Cards 1’, Student Book p. 82 ‘Odd or Even?’
TASK 1:
DOT PAIRS
Have students write some 1- and 2-digit numbers, e.g. how old they will be next birthday, the last two digits in their phone numer, their street number, the number of students in their class, etc. Students can then make models of the numbers by sticking dots (or drawing dots) in pairs onto a sheet of paper and writing the number beside their model. Have students share and discuss their numbers with a partner and then label their models either odd or even.
TASK 2:
INTERACTIVE TASK
Provide students with the numbers cards from BLM 1 ‘Number Cards 1’ that were not used in the ‘Exploring Odd and Even Numbers’ activity in the Whole-Class Introduction. Have them use NTO 3.1 ‘Ten Frames’ to determine if the numbers are odd or even.
TASK 3: STUDENT BOOK p. 82 ‘Odd or Even?’
TEACHING GROUP You will need: Unifix blocks, BLM 3 ‘Blank Chart’ FINGERS ON SHOW • For students who require support, give them some Unifix blocks and have them make the numbers to 10 by making them with two groups of blocks joined, e.g. 4 would have two groups of two blocks. Have students write a list of even numbers and odd numbers. Then have students play a game with a partner whereby they put one hand behind their back and decide how many fingers to hold up. On the count of Nelson Maths Australian Curriculum NSW
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three, both students show their hands. One student will score a point if the total number of fingers shown is even and the other will score a point if it is odd. HOW DO YOU KNOW IT IS AN EVEN NUMBER? • For students who require a challenge, give them a copy of BLM 3 ‘Blank Chart’ and have them choose any starting number and fill in the numbers on the chart. Discuss with students the conditions for a number to be even and have them colour all of the even numbers. Have students look at the even numbers and write a rule for how to identify an even number.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from the Whole-Class Introduction or from the Teaching Groups, and ask, ‘How do you know if a number is an even number?’ Then invite students to name even numbers that are more than 20, 50, 100, 200, 500 and 1 000. Ask, ‘Can you think of a rule for deciding if a number is odd or even?’ • Draw students’ attention to the four numbers that you recorded during ‘What’s in the Jar?’ in Tuning In, and ask them what the numbers have in common. Ask, ‘How do you know that they are all odd numbers?’
LESSON PLAN
TUNING IN
TELL ME ABOUT THE NUMBER Write a number on the board, e.g. 46, and ask students to think of as many things as they can about the number, e.g. it is an even number, it is made up of four tens and six ones, it is four less than 50, it is ten more than 36 and so on. Repeat for other numbers.
2
WHOLE-CLASS INTRODUCTION WORDS AND NUMERALS You will need: NTO 3.2 ‘Number Cards’, small whiteboards Present NTO 3.2 ‘Number Cards’, selecting the random number to be shown. Have students read the number and invite a student to show the number with the number cards. Explain that we can see the number written as a numeral, shown with number cards and ask, ‘How can you write the number in words?’ Have students say the number and then ask them to write the number in words on their whiteboards. To support students, write the words ‘thousand’, ‘hundred’, ‘ninety’, ‘eighty’, ‘seventy’, ‘sixty’, ‘fifty’, ‘forty’, ‘thirty’ and ‘twenty’ on the board or on cards. Repeat for other numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 4 ‘Blank Cards’, NTO 3.3 ‘Dice’, Student Book p. 83 ‘Number Sort’
TASK 1:
CARD GAME
Give each student two copies of BLM 4 ‘Blank Cards’. Have them make pairs of cards with numerals on half of the cards and the matching numerals in words on the other half. Students combine with a partner to play ‘Memory’, whereby all of the cards are placed face-down and students take it in turns to turn over two cards to find a pair. Alternatively, students could play ‘Go Fish’ or ‘Snap’.
TASK 2:
INTERACTIVE TASK
Have students work with a partner using NTO 3.3 ‘Dice’. Before rolling the dice, students decide if they will form an odd or even number. They roll four dice and rearrange to form a 4-digit odd or even number, which they record using words. Each time they meet the requirement, they score a point.
TASK 3:
STUDENT BOOK p. 83 ‘Number Sort’
TEACHING GROUP You will need: NTO 3.3 ‘Dice’, five dice for each student in the group STEP BY STEP • For students who require support, begin with 2-digit numbers and build up to 4-digit numbers. Present NTO 3.3 ‘Dice’ and select two dice to randomly generate two digits. Have students write the two possible 2-digit numbers and determine if the numbers are odd or even. Have students write the numbers in words. Have students add 100 to the numeric form of their numbers and ask them to read the numbers and write them in words. Then have students add 1 000 to the numeric form of their numbers and have them read the numbers and write them in words. Repeat the process by rolling the two dice again.
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FOUR CATEGORIES • For students who require a challenge, have them work with higher numbers. Give each student five dice that they use to form four 5-digit numbers: the highest odd number, the highest even number, the lowest odd number and the lowest even number. Have students write their numbers in words and compare with the group. A point is given to the student who is able to form the highest or lowest in each category, and a point deducted if they are unable to form a number for any of the categories. Have students continue to roll the dice and form more numbers.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students discuss any difficulties they encountered when writing numbers in words and ask, ‘How did you know that you had written the number correctly?’ • Create a chart of students’ strategies for writing numbers in words. Display the chart in the classroom.
LESSON PLAN
TUNING IN
3
POPCORN! Explain to students that they are going to play a game in which you will call out numbers, and if the number is odd they crouch down, but if the number is even, they jump up and say: ‘Popcorn’. Have students stand, and begin by calling out 1- and 2-digit numbers. As the game progresses, increase the numbers to 3- or 4-digit numbers.
WHOLE-CLASS INTRODUCTION MOVING NUMBERS You will need: number cards made from BLM 2 ‘Number Cards 2’ Have students sit on chairs in a circle and give each student a number card made from BLM 2 ‘Number Cards 2’. Explain to students that, if their number meets the criteria mentioned, they need to stand up and swap chairs with someone else. Begin by giving criteria like ‘more than 500’, ‘odd number’, ‘7 in the tens place’, ‘4 units’ or ‘4-digit number’. When students have had practice, say ‘even number’ and take away a chair as students are moving around so that one student is left in the centre of the circle. That student must give some criteria and try to find an empty chair to sit on while the others are moving.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: NTO 3.4 ‘Playing Cards’, Student Book p. 84 ‘Correct Statement’
TASK 1:
BEAT THE TEACHER
Model the following game, then have groups of three students play the game using NTO 3.4 ‘Playing Cards’ on individual computers. One student must act as the teacher, while the other two students make the 4-digit number. In pairs, have students draw four boxes joined together and in a horizontal line. Explain to students that the following activity involves them making the largest 4-digit number they can and both students need to agree where to place the numbers. Using NTO 3.4 ‘Playing Cards’, generate a card and students decide in which box to place the number. (You must also choose a 4-digit number, but do not reveal it to the class.) The game continues until four cards have been generated and students have placed the numbers into boxes. Say your 4-digit number to the class. If a pair’s number is lower than your number, they score 1 point, and if it is equal to your number, they score 3 points, but if it is higher than your number, they score 5 points. You score 10 points if you beat all the students. Note: when students are familiar with the game, make it more challenging by deciding that the number must be odd or even.
TASK 2:
INTERACTIVE TASK
Have students work with a partner. Using NTO 3.4 ‘Playing Cards’, the first student draws four cards that they rearrange to make the largest odd or even number they can. Their partner then draws four cards and tries to make a larger odd or even number.
TASK 1: STUDENT BOOK p. 84 ‘Correct Statement’
TEACHING GROUP You will need: dice BONGEL • For students who require support, have them work with smaller numbers. Have students work with two Nelson Maths Australian Curriculum NSW
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or three dice, playing with a partner or in a small group. Each student rolls the dice to form the largest number they can. The student with the largest number in this round writes the letter ‘B’. Students roll the dice again to form the largest number they can, and each time a student wins a round, they write a letter. The first student to form the word ‘BONGEL’ wins. HOW MANY NUMBERS? • For students who require a challenge, have them work with larger numbers. Give students five dice to roll and have them form and record the smallest number they can. Students roll the dice again to form a 5-digit number that is more than the previous number. Students continue to roll the dice, and each time they must form and record a number that is larger than the one before, and if they cannot, they must stop. Have students compare how many numbers they formed.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share the strategies they used to help them win the games they played. • Draw four boxes on the board and tell students that you want them to form the largest number they can. Roll a 10-sided dice, and ask, ‘Which box would you put the number in? Why do you think that is a good choice?’
Home Tasks Select from the possible Home Tasks: • Have students look at the newspaper (hard copy or online) for examples of numbers used in the media. Have them find examples of 4-digit numbers and what they are used for in daily life.
Assessment • Have students complete Student Assessment p. 85. • Review with students Assessment Task Card 3.1. During the three lessons: • Observe which students are able to read and write numbers in word and numeric form during ‘Card Game’ in Lesson Plan 2, Independent Tasks, Task 1 and mark on a class list. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 85; if the student is experiencing difficulty: Have the student use counters to explore which numbers can make groups of two without any left-over Q 1 counters. Have the student mark these even numbers on a 100 chart and identify patterns associated with even numbers. Q 2–3 Include numbers in word form in weekly spelling lists. Q 4 Have the student revisit what makes a number even or odd number and have them model 2-, 3- and 4-digit numbers using MAB blocks. Have them order numbers by comparing models. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 3.1 for specific recommendations. 2. Have the student work with 2- and 3-digit numbers in any of the listed activities or tasks prior to moving to 4-digit numbers. 3. Review Nelson Maths: Australian Curriculum Year 2 Unit xx, pp. xx–xx. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. The student completing Nelson Maths Building Mental Strategies Skills Book Year 4, pp. 10–11, to reinforce mental strategies with 4- and 5-digit numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 4 Unit xx, pp. xx–xx. 3. Extending the student in any of the listed activities or tasks by using larger numbers.
Unit 1
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Numbers, Numbers, Numbers
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BLM
1
Number Cards 1
24
48
27
34
43
36
38
42
19
25
23
20
30
33
31
45
14
37
26
29
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
Teacher’s Note: This BLM can be photocopied, laminated and cut up to make cards for number activities.
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BLM
2
Number Cards 2
348
2 604
215
111
239
1 380
564
92
1 487
935
74
2 460
803
158
1 643
857
2 596
971
726
29
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
Teacher’s Note: This BLM can be photocopied, laminated and cut up to make cards for number activities.
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BLM
3
Blank Chart
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
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BLM
4
Blank Cards
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
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3.1 F.1
Year 3: Assessment Task Card Unit
Numbers, Numbers, Numbers
1
Resources: NTO 3.3 ‘Dice’, blank ten frames, counters, a number line
1
Present NTO 3.3 ‘Dice’ with four digits generated on four dice. Have the student arrange the digits to form an even number. Have the student record the number and read it aloud.
2
Have the student use the four digits to form an odd number, record the number and read it aloud.
3
Have the student form two other numbers using the four digits and record with the two previous numbers.
4
Have the student write all of the numbers in order of smallest to largest.
5
Have the student write the numbers in word form.
Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
3.1 F.1
Year 3: Assessment Task Card Unit
1
Numbers, Numbers, Numbers TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1–2
Have the student use ten frames and counters to explore odd and even numbers to 10. Each time they determine that a number is odd or even, have them add a ten frame, then another. Discuss with the student that, it does not matter how many tens or hundreds are added to the number, it will remain an odd or even number depending on what is in the ones place.
Q3–4
Begin by having the student locate 2-digit numbers on a number line and use it to compare to other numbers. When the student is able to identify larger or smaller 2-digit numbers by their position on a number line, extend to 3-digit numbers.
Q5
Have the student write the words for the numbers 1 to 9 and then the numbers 20, 30 up to 90. Have them practise writing in words the numbers 20 to 99. Next have the student practise the numbers 11 to 19. When the student is proficient, have them learn the words for 100 and 1 000 and write the words for 3- and 4-digit numbers.
Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution.
Nelson Maths Australian Curriculum NSW
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Odd or Even?
DATE:
You will need: counters
1 Use counters to work out if the following numbers are odd or even. 1 2 3 4 5 6 7 8 9 10
2 Colour the odd numbers green and the even numbers yellow
in the chart below.
3 Use counters to work out if the following numbers are odd or even. 11 12 13 14 15 16 17 18 19 20
4 Colour the odd numbers green and the even numbers yellow
in the chart below.
5 Is there a pattern?
What is the pattern?
6 Use the pattern to colour all of the odd numbers green and all of the even numbers yellow.
1 11 21 31 41 51 61 71 81 91
2 12 22 32 42 52 62 72 82 92
3 13 23 33 43 53 63 73 83 93
4 14 24 34 44 54 64 74 84 94
5 15 25 35 45 55 65 75 85 95
6 16 26 36 46 56 66 76 86 96
7 17 27 37 47 57 67 77 87 97
8 18 28 38 48 58 68 78 88 98
9 19 29 39 49 59 69 79 89 99
10 20 30 40 50 60 70 80 90 100
7 What do you notice about all of the odd numbers? 8 What do you notice about all of the even numbers?
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Numbers, Numbers, Numbers (TRB pp. 22–25) Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
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Number Sort
DATE:
1 Write the following numbers in word form in the table below.
Make sure you put them in the correct box! 372
621
509
196
765
Even
1 2
54
440
3 007
Odd
Numbers more than 500
Numbers less than 500
2 Write your own 3-digit number here.
Write it in words in the table above.
Unit
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Numbers, Numbers, Numbers (TRB pp. 22–25) Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
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True Statement You will need:
DATE:
a partner, a 10-sided dice
1 Take turns to roll the dice. • E ach time you roll the dice, write the number in an empty box. • R epeat these steps until you have a number in every box. Score 1 point if you make each statement true. is an even number less than 550. is greater than 7 500. is a number less than 2 500 but greater than 2 000. is an odd number less than 5 500. is a number between 6 000 and 7 000. is a number more than 8 000. Total score:
2 Play the game again. See if you can get a better score. is an even number less than 550. is greater than 7 500. is a number less than 2 500 but greater than 2 000. is an odd number less than 5 500. is a number between 6 000 and 7 000. is a number more than 8 000. Total score:
3 Which numbers were the hardest to score a point on? Why?
Which numbers did you try to fill in first? Why?
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Numbers, Numbers, Numbers (TRB pp. 22–25) Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
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Unit
DATE:
1
STUDENT ASSESSMENT
1 Look at the numbers. Draw a circle around the odd numbers. 16 57 99 123 312 450 671 3 025
7 138 9 734
How do you know the numbers you circled are odd?
2 Write the following numbers in words. a 2 763 b 919 c 5 044 d 3 900 3 Write the following numbers as numerals. a Three thousand, four hundred and fifty-two b Eight thousand and forty-seven c Two hundred and ninety-six d Seven thousand and thirteen 4 Use the four digits below to make the following numbers.
1
8
7
6
a an even number more than 8 500 b an odd number less than 3 500 c a number between 5 000 and 8 000
Unit
1
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Unit
20
Chance
STATISTICS AND PROBABILITY Chance: MA2-19SP describes and compares chance events in social and experimental contexts
ML
certain, even chance, event, fair, impossible, likely, no chance, possible, outcome, unlikely
LESSON PLAN
TUNING IN
1
WHAT DOES IT MEAN? You will need: book titles or newspaper headlines including the word ‘chance’ Present book titles, e.g. Cloudy with a Chance of Meatballs (J Barrett, 1978) and Mostly Sunny with a Chance of Storms (M Roberts, 2010). Ask, ‘What does the word “chance” mean?’ Discuss to find out what students know about chance and its reference to the weather. Ask, ‘What is the chance that it will be cloudy and rain meatballs?’ Discuss the idea that some things have no chance of happening and can be described as impossible. Explain to students that particular terms are used to describe the chance of something happening, and write on the board the words impossible, certain, likely and unlikely. Have students brainstorm events that they think are impossible, certain, likely and unlikely, and record these.
WHOLE-CLASS INTRODUCTION HEADS OR TAILS? You will need: NTO 3.x ‘Coin Toss’ Present NTO 3.x ‘Coin Toss’ to students and ask, ’What can you see? What is on the other side of the coin?’ Explain to students that they are going to play a game whereby they need to predict if the coin toss will result in heads or tails. Have students stand and make their prediction by either placing their hands on their head if they think it will be a head and hands on their backside if they think it will be a tail. Flip the coin and those students who predicted correctly make another prediction and the others sit down. Continue until one student remains. Ask, ‘When a coin is tossed, how many possible outcomes are there? Is one outcome more likely than the other?’ Discuss with students that, when a single coin is tossed, there are two possible outcomes and that the outcome of a head or a tail is 1 out of 2, so both outcomes are equally likely and have an ‘even chance’ of happening.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: LO 115 ‘Slushy Sludger: Questions’, Student Book p. 90 ‘What’s the Chance?’
TASK 1:
WHAT WILL HAPPEN TODAY?
Working in pairs, students write or draw two things that have an ‘impossible’ chance of happening, two things that are ‘certain’ to happen, two things that are ‘likely’ to happen, two things that are ‘unlikely’ to happen and two things that have an ‘even chance’ of happening during a normal school day.
TASK 2:
INTERACTIVE TASK
Have students explore LO 115 ‘Slushy Sludger: Questions’ whereby a vending machine squirts coloured ‘slushies’ into ice-cream cones. Students work out which ‘sludge events’ are possible and then choose a matching probability word.
TASK 3: STUDENT BOOK p. 90 ‘What’s the Chance?’
TEACHING GROUP COULD HAPPEN 1 • For students who require support, ask them to think about things that could happen to them today. As a group, make a list, e.g. read a book, draw a picture, eat lunch, play with their friends, walk home. Encourage students to think of things that are personally relevant to them. Read through the list and ask, ‘Do you think some things are more likely to happen during a day at school than others?’ Discuss and have students draw a picture of something they think is likely to happen and something that is possible but unlikely to happen. Nelson Maths Australian Curriculum NSW
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COULD HAPPEN 2 • For students who require a challenge, have them work in pairs to write ten things that could happen in the classroom today. Discuss with students how some things are more likely to happen than others. Have students order their list from the least likely to the most likely. Have them share their list and reasoning with the group.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from the Independent Tasks and ask, ‘How did you decide which things were more likely to happen?’ • Ask, ‘If I told you it was likely/unlikely that we would do something tomorrow at school, what do you think it could be?’ Have students give their suggestions and discuss their reasoning.
LESSON PLAN
TUNING IN
2
WHEN PIGS HAVE WINGS Explain that there are many sayings that have something to do with chance. Write ‘It will happen when pigs have wings’ on the board, and ask students if they know what it means. Discuss with students that it means there is no chance or it is impossible. Ask, ‘If I roll a dice with the numbers 1 to 6, what is my chance of rolling a 7?’ Discuss possible outcomes and how there is no chance at all of rolling 7. Have students think of other things that there is no chance of happening. Record their ideas.
WHOLE-CLASS INTRODUCTION LUCKY THREE You will need: NTO 3.3 ‘Dice’ Present NTO 3.3 ‘Dice’ and ask, ‘If I roll the dice, what number could I get?’ Have students name the numbers that could be rolled. Tell students that you would like to roll a 3 because that is your favourite number. Ask, ‘Could I roll 3 next? Do you think it is likely that I will roll 3?’ Discuss with students that, while it is possible to roll 3 as it is one of the numbers on the dice, the chance of rolling 3 is 1 out of 6. Have students predict how many times they think the dice will need to be rolled before 3 comes up. Use the NTO and roll until 3 comes up. Ask, ‘If I want to roll 3 again, do you think it will take the same number of rolls? Why?’
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM x ‘Car Race’, card, scissors, yellow and red pencils, glue, BLM x ‘Spinner’, paperclips, sharp pencils, LO 2378 ‘Spinners: Predict and Test’, Student Book p. 91 ‘Spinners’
TASK 1:
RACING CARS
Using BLM x ‘Car Race’, students work in pairs to cut out and paste the race track on to card. They then cut out and colour the two cars, one yellow and one red. Using the first spinner on BLM x ‘Spinner’, students colour one section red and two sections yellow. Explain that they are to use the results of the spinner to move the cars along the track. Have students predict which car they think will win the race. Then conduct the race. When all races are complete, have students share their results. Have students look at the final positions of each car and discuss variations in results. Have students design and colour a spinner so that both cars have an even chance of winning. Students can conduct a race to test their spinner.
TASK 2:
INTERACTIVE TASK
Using LO 2378 ‘Spinners: Predict and Test’, students race two cars along a track determined by the results of a spinner. Students compare actual results with predicted results.
TASK 3: STUDENT BOOK p. 91 ‘Spinners’
TEACHING GROUP
You will need: NTO 3.x ‘Spinner’, BLM x ‘Spinner’, paperclips, sharp pencils, small whiteboards or paper, a dice SPIN THE SPINNER • For students who require support, have them explore spinners so that they can make the connection between the area on the spinner and the likelihood of occurrence. Present students with NTO 3.x ‘Spinner’ and have all segments the same colour. Ask, ‘When I spin the spinner, what colour do you think it will land on? Why?’ Discuss how, as the whole area of the spinner is one colour, it can only land on that colour. Invite all students to spin the spinner. Next click on one segment and ask, ‘When I spin the spinner, what colour could it land on? Which colour do you think it will land on? Why?’ Invite students to spin the spinner. Continue to click on segments, discuss possible outcomes and determine most likely outcomes and test.
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Chance
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SPINNING CHANCE • For students who require a challenge, give pairs of students a copy of BLM x ‘Spinner’ and have them make the fourth spinner. Using a dice, students roll the dice and record the number on the segments of the spinner. Have students write a statement about the likelihood of each number occurring on their spinner. Pairs of students then swap statements with another pair and use the information to make an identical spinner. Have students compare spinners. Have students compare both spinners they have drawn and ask, ‘Are they the same? Why?’
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from the Independent Tasks and the Teaching Groups, and discuss the findings from their chance experiments in Independent Tasks. Ask, ‘Did all outcomes have the same chance of happening? Why?’ • Present NTO 3.x ‘Spinner’ and click on five segments to change the colour. Ask, ‘Which colour is the more likely to occur? How do you know?’ Discuss with students how they can calculate the chance by counting the segments of same colour and comparing to the total number of segments in the circle. Change the colours on the spinner and ask, ‘What are the chances of each of the colours occurring now?’
LESSON PLAN
TUNING IN
3
WHICH LETTER? You will need: a 10-sided dice Take students to an area where they can line up side by side. Give each student a letter of the alphabet. Tell them that you are going to roll a 10-sided dice, and if the number rolled has their letter in it, then they can take a step forward. The first student to take five steps is the winner. After a student has won the game, ask, ‘Did everyone have the same chance of winning? Why?’ Discuss with students that some students with the letters a, b, c, d, j, k, l, m, p, q, y and z have no chance of moving forward as no number uses those letters, and that as the letter e is used in seven numbers, the student with the letter ‘e’ would be the most likely to win. Ask, ‘If we played the game again, do you think we would get the same result? Why?’
WHOLE-CLASS INTRODUCTION IN THE BAG You will need: a paper bag, counters Place a red, blue, green and yellow counter into the paper bag and ask, ‘If I take a counter from the bag, what colour might it be?’ Tell students that your favourite colour is red and ask, ‘What is my chance of taking a red counter from the bag?’ Discuss that red is one of four counters in the bag, so the chance is one in four. Shake the bag, select a counter from the bag and place it back in the bag until a red counter has been collected. Repeat. Ask, ‘How can I increase my chance of selecting a red counter from the bag?’ As students make suggestions (e.g. add more red counters, place only two counters in), have them work out the chance and trial. Continue trialling students’ suggestions.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 4 ‘Blank Cards’ with either a W, I or N written on the cards, paper bags, LO 116 ‘The Slushy Sludger: Best Guess’, Student Book p. 92 ‘Chance Machine’
TASK 1:
WIN
Students can play with a partner or in a small group. Each group needs a paper bag and three cards with the letters W, I and N, which are placed in the bag. Each student takes it in turns to shake the bag and select a card. They record the letter and place the card back in the bag. When a student has recorded at least one of each letter, they tally how many times they had to draw a card from the bag to make the word ‘WIN’. Have students share how many times it took. Ask, ‘What was the least and the most number of draws?’ Discuss the variation in results.
TASK 2:
INTERACTIVE TASK
Students can explore LO 116 ‘The Slushy Sludger: Best Guess’ whereby a vending machine squirts ‘slushies’ into ice-cream cones. The machine serves coloured slush randomly from four slots, and students work out which colour is the most common (most likely to be served). However, least common colours are sometimes served. After several guesses, students can check their results from the random sample.
TASK 3: STUDENT BOOK p. 92 ‘Chance Machines’
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TEACHING GROUP
You will need: paper bags, coloured counters, paper bags containing a different combination of eight counters HALF AND HALF • For students who require support, have them work with a partner to put an equal number of two differentcoloured counters into a paper bag. Ask, ‘If you were to draw a counter 20 times from the bag, how many of each colour do you think you would draw?’ Discuss students’ reasoning for their predictions. Have them shake the bag, draw a counter, record its colour and place it back into the bag. Repeat the process 20 times. Have students share their results and discuss in relation to their predictions. WHAT’S IN THE BAG? • For students who require a challenge, have students work with a partner whereby they draw a counter from a paper bag containing a different combination of eight counters. They then place the counter back into the bag and repeat this process 20 times. Have students record their results, and then based on their results, make a prediction about what they think is in the bag. Have students share predictions and discuss their reasoning.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share and disuss the results of their chance activities. Ask, ‘Were your results always the same?’ Why or why not? • In front of students, place a blue, green and yellow counter and four red counters into a paper bag. Ask, ‘What colour counter am I most likely to draw out of the bag? Does that mean I will draw out a red counter?’ Have students explain their reasoning.
Home Tasks Select from the possible Home Tasks: • Have students think about events that could happen at home in the next week. Have them think of an event that is certain to happen, one that is unlikely to happen, one that has an even chance of happening and one that is unlikely to happen. • Have students teach someone at home how to play WIN, a game played in Lesson Plan 3.
Assessment • Have students complete Student Assessment p. 93. • Review with students Assessment Task Card 3.20. During the three lessons: • Collect created items from Lesson Plan 1, Independent Tasks, Task 1, as work samples for student portfolios. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 93; if the student is experiencing difficulty: Q 1 Encourage the student to use the language of chance by having them predict the likelihood of a particular event happening each day, e.g. the principal coming into the room, the school being flooded, a student from another class entering the classroom. Check the student’s predictions before they leave at the end of the day. Q 2 Have the student use spinners to play games and utilise NTO 3.x ‘Spinner’ to explore the results of shading the spinner in different ways. Q 3 Look for opportunities to conduct chance experiments, e.g. drawing counters from a bag to group students randomly or holding reward raffles where students can earn tickets. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 3.20 for specific recommendations. 2. Review Nelson Maths: Australian Curriculum Year 2 Unit 13. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student make their own chance boardgame using a coloured spinner to move players around the board. Have them explore the concept of fairness in relation to how the game has been designed. 2. Moving forward to Nelson Maths: Australian Curriculum Year 4 Unit xx, pp. xx–xx.
Unit 20
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What’s the Chance?
DATE:
1 Read the statements below. Write a word from the box beside each statement to describe the chance of it happening.
likely
unlikely
even chance
impossible
certain
a You will roll an even number on a dice. b You will have fire drill practice today. c You will walk home from school today. d You will eat an ice-cream at lunchtime. e You will toss heads on a coin. f Tomorrow will be Friday. g Your teacher will turn into a fish. h The next lesson will be music. 2 Write down the statement you think is the most likely to happen.
Why do you think this?
3 Write down the statement you think is the least likely to happen.
Why do you think this?
4 Write down two other things that you think are unlikely to happen today. 5 Your teacher said that after lunch on Wednesday your class would be likely to do something. What might it be?
Why do you think that?
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Chance (TRB pp. 86–87) Chance MA2-19SP describes and compares chance events in social and experimental contexts
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Spinners
DATE:
You will need: a partner, a paperclip, a sharp pencil
1 Colour half of the circle green
and the other half yellow.
2 If you were to spin a paperclip 20 times, how many times do you think it will land on yellow?
3 Spin the paperclip 20 times and record the results in the table below.
Green
Yellow
4 Was your prediction correct?
Explain why.
5 Write your partner’s
Green
Yellow
results in the table.
6 Were the results the same?
Why do you think that happened?
7 What results do you think you might get if you used your spinner
1 000 times?
Unit
20
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Chance (TRB pp. 87–88) Chance MA2-19SP describes and compares chance events in social and experimental contexts
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Chance Machines
DATE:
1 Colour in the balls so it is certain
that you will get a red ball.
2 Colour in the balls so it would be
likely that you would get a green ball.
3 Colour in the balls so it would be
impossible that you will get a yellow ball.
4 Colour in the balls so it is certain that
you have an even chance of getting
a red or blue ball.
5 Mike puts his money into the toy machine.
Do you think he will be happy with
the toy he gets?
Explain why.
6 Jo wants a yo-yo. What advice would you give her about spending her money in the machine?
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20
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Chance (TRB pp. 86–87) Chance MA2-19SP describes and compares chance events in social and experimental contexts
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DATE:
Unit
20
STUDENT ASSESSMENT
1 Write likely, certain, impossible or unlikely to describe
the chance of drawing out a black counter from each bag.
2 Colour the spinners to show the following. It is impossible
It is unlikely to
There is a 3 out
equal chance of to get black but
get red and
of 4 chance of
likely to get red.
likely to get
getting green.
There is an blue and yellow.
yellow.
3 There were 2 blue, 1 green and 2 yellow counters in a bag.
What do you predict will happen after 2 draws from
the bag?
4 After 20 draws, these were the results.
Blue
Green
Yellow
12
3
5
Are the results the same as you predicted? Explain why.
Unit
20
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Unit
18
Decimals to 2 Decimal Places
NUMBER AND ALGEBRA Fractions and decimals: MA2-7NA represents, models and compares commonly used fractions and decimals
ML
decimal, decimal point, hundredths, larger, number line order, place value, smaller, tenths, units, whole number, zero
LESSON PLAN
TUNING IN
1
ORDERING NUMBERS 1–1 000 You will need: A4 paper, scissors Give each student a sheet of A4 paper. Have students fold and cut the paper into quarters. On each quarter, have students write: their favourite number between 1 and 1 000, a number less than 500, a number greater than 800 and a number between 600 and 700. Have students work in pairs to order the eight pieces of paper from smallest to largest. To extend the activity, students could work in groups of four. Note: this can be used as a pre-assessment activity.
WHOLE-CLASS INTRODUCTION EXPLORING PLACE VALUE WITH DECIMAL NUMBERS You will need: an IWB, NTO 4.5 ‘Place-Value Chart’ Generate numbers with either one or two decimal places, and have students place the digits into the relevant place-value columns using NTO 4.5 ‘Place-Value Chart’. Ask, ‘What are each of the columns called? What happens after the decimal point? What happens if there is a zero in the number?’ The activity could be completed on the IWB, by drawing a place-value chart with columns from thousands to hundredths and giving students numbers to write into the chart.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: dice (four for each pair – a different colour for each student in the pair), Excel, Word, Student Book p. 102 ‘Place-Value Chart’
TASK 1:
PLACE-VALUE CHART
Have pairs of students draw a place-value chart with columns from tens to hundredths. Give each pair four dice – allocate two of one colour to one student and two of a different colour to the other student. Have each student roll their dice and create the largest 2-digit number possible. Now have the two students combine their numbers to make a decimal number – one student’s dice represent the whole number, the other’s represent the decimal. Finally, have each student record the number on their place-value chart. Students collect 10 numbers, then swap the roles of whole number and decimal. Extend this activity by using more dice to create larger whole numbers.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets to create a place-value chart in Excel or Word. Give students a set of numbers with up to two decimal places, and have them insert these into the correct columns on the place-value chart.
TASK 3: STUDENT BOOK p. 102 ‘Place-Value chart’
TEACHING GROUP
You will need: three dice for each student who requires support 2-DIGIT NUMBERS • For students who require support, give them two dice and have them roll to create a 2-digit number. Have students repeat this 10 times to make 10 different numbers. Ask students to create a place-value chart, with columns for ones and tens, and record their numbers on their charts. When students are confident,
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give them a third dice, and have them create 2-digit numbers with one decimal place and record their numbers on another place-value chart featuring tens, ones and tenths. ORDER THE NUMBER • For students who require a challenge, give them a set of 10 numbers with two decimal places to order from smallest to largest. Include numbers such as 3.20, 408.63, 408.4. Have students discuss why different numbers are larger or smaller. Students create their own sets of 10 decimal numbers to order, and swap with a partner.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘Why are zeros important in decimal numbers?’ Create a class chart about the importance of the zero in place value. Have students record their different ideas and display. • Using an IWB, have students display the charts they created in Independent Tasks, Task 2, to share with the class. • Revisit NTO 4.5 ‘Place-Value Chart’, and provide students with ‘tricky’ numbers to add to the chart, e.g. 0.42, 1.06, 3.20, 180.40, 293.04. Discuss.
LESSON PLAN
TUNING IN
2
TRAFFIC LIGHTS You will need: sticky notes Draw a place-value chart on the board with columns from hundreds to hundredths. On a sticky note, write a number that would fit into the place-value chart, containing different values for each digit, e.g. 327.14. Invite students to guess the whole number recorded on the sticky note. On the chart, record the number and under each numeral mark with symbols: for correct digit, for incorrect digit, and o for a digit in the number but in the incorrect position. Students keep guessing, and try to beat you in a set number of rounds, e.g. eight. The student who guesses correctly selects the next number to be recorded on the sticky note.
WHOLE-CLASS INTRODUCTION READING AND WRITING DECIMAL NUMBERS You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’ Enlarge and cut up BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’. Give each student a card and have them silently move around the room to find their pair. Then have the class order themselves from smallest to largest. Do this in individual sets, i.e. all the numbers, then all the word forms. Ask, ‘Are the orders the same?’
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’, BLM 42 ‘Symbols’, PowerPoint, Student Book p. 103 ‘Matching Decimal Numbers and Words’
TASK 1: NUMBER CARDS Give groups of students cards from BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’ and the symbols <, > and = from BLM 42 ‘Symbols’. Have students create statements with the cards, e.g. 1.3 > One and three hundredths. When the group agrees, have the students record their statement on a sheet of paper. Each statement needs to include one numeric card and one word card. Note: review the symbols < and > if necessary.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets to create a PowerPoint presentation that has a number of matching decimal numbers and words on each slide. Students should be encouraged to make the slides interactive, e.g. a) the user has to draw a line matching words and numbers or b) select a match from two or three options.
TASK 3: STUDENT BOOK p. 103 ‘Matching Decimal Numbers and Words’
TEACHING GROUP
You will need: 20 blank cards for each student who requires a challenge NUMERIC ORDER • For students who require support, play a comprehension game. Read out decimal numbers (these could be from BLM 33 ‘Decimal Numbers and Words 1’ or BLM 34 ‘Decimal Numbers and Words 2’ ) and have
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students record them in their books in numeric form. Once students are confident, have them record the numbers read out in word form. Provide an incentive, e.g. once a student has 10 correct answers, they become the reader. DECIMAL MEMORY GAME • For students who require a challenge, give them 20 cards and have them develop their own decimal memory game, e.g. where they write the decimal number and matching word on individual cards. Once complete, pairs of students combine two sets and play the game. Earlier finishers from other activities could be invited to play.
REFLECTION Select from the following to suit your class and their learning outcomes: • Cut out cards from BLM 33 ‘Decimal Numbers and Words 1’. Invite three students to sit in front of the whiteboard, with their backs towards it. Attach one card above each student’s head so they can’t see it, and have them take turns to guess the number, using Yes/No questions. For example: ‘Does my number have two decimal places? Is my number greater than 10?’ Play a number of rounds, with different students taking turns to guess. • Invite students to share what they have learned in the Teaching Groups. Students describe the activity and their discoveries. Ask, ‘What was easy? What was challenging?’ • Create a chart of students’ strategies for writing decimal numbers in words. Ask, ‘What little tricks did you use?’ Display the chart in the classroom.
LESSON PLAN
TUNING IN
3
LET’S RUN You will need: a space to run, tape measure/trundle wheel, stopwatches Have students measure a distance of 100 m. Revise with them how to use a stopwatch. Have students time each other running the 100 m length, and to make note of their individual times. Ask, ‘How do we write down/record the time?’
WHOLE-CLASS INTRODUCTION ORDERING DECIMAL NUMBERS You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’ Show students pairs of numbers and have them identify which is the largest decimal number. (You could use BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’ for this.) Play this as a game: show students 10 pairs of numbers, have them silently record the largest in each pair on a piece of paper, and then find who has the most correct.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’, long rolls of paper, glue, LO 2005 ‘Scale Matters: Hundredths’, Student Book p. 104 ‘Ordering Decimal Numbers’
TASK 1:
DECIMAL NUMBERS AND WORDS
Give pairs of students the cards from BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’ and a long roll of paper. Have students create a giant number line to scale, attaching the decimal numbers in the correct order. Leave the task fairly open-ended. Note: this could be used as informal assessment.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using a hundredths scale on LO 2005 ‘Scale Matters: Hundredths’ to locate or place a number on a number line.
TASK 3: STUDENT BOOK p. 104 ‘Ordering Decimal Numbers’
TEACHING GROUP
You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’, a long sheet of paper, times from a sporting event, poster paper SMALLEST TO LARGEST • For students who require support, use level-appropriate numbers from BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’. Have students work as a group to order the decimal numbers from smallest to largest, and then to create a number line. Give support and guidance through questioning as required. Nelson Maths Australian Curriculum NSW
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FASTEST TO SLOWEST • For students who require a challenge, give them a set of times (out of order) from a sporting event, e.g. running, cycling, swimming, car racing. Have students place them in order from fastest to slowest. Have students present this task as a poster. Students could include pictures related to the sport.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students present the number lines they made in Independent Tasks, Task 1. Ask, ‘Why did you place this number first? How did you decide your order? What was tricky about this task?’ • Have students write their running times from ‘Let’s Run’ in Tuning In on a piece of card. Attach these to the whiteboard. Then, as a group, have students order the times from fastest to slowest.
Home Tasks Select from the possible Home Tasks: • Have students look for things around the home that show numbers with two decimal places, e.g. items from the pantry, books, newspapers, measuring equipment. Have them list the item and the decimal. • Have students look at a newspaper (hard copy or online) for examples of decimal numbers, e.g. results of sporting events, news reports or advertisements. Have students cut out/print/save and bring to class to share. These items could be used in some of the activities in Lesson 3.
Assessment • Have students complete Student Assessment p. 105. • Review with students Assessment Task Card 4.18. During the three lessons: • Collect created items e.g. the Excel spreadsheets from Lesson Plan 1, Independent Tasks, Task 2, and number lines from Lesson Plan 3, Independent Tasks, Task 1, as work samples for student portfolios. • Make note of students who completed the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 105; if the student is experiencing difficulty: Q 1 Work with whole numbers, then numbers with only one decimal place. Q 2–3 Use BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’ to revisit matching the numeric form of a number to its word form. Q 4–8 Practise drawing number lines with whole numbers, before moving to numbers with one decimal place. Give the student numbers like 3.1, 5.6 and 7.2. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 4.18 for specific recommendations. 2. Have the student work with whole numbers in any of the listed activities (at their level) before moving to decimal numbers. Scaffold them with the use of a place-value chart to reinforce the values and positioning of the decimal parts. 3. Review Nelson Maths: Australian Curriculum Year 3 Unit 13. If the student has achieved the recommended skills and these skills are firmly established, consider: 4. Moving forward to Nelson Maths: Australian Curriculum Year 5 Unit 18. 5. Having the student complete Nelson Maths Mental Strategies Big Book 4, pp. 8–9, to reinforce mental strategies with decimal numbers. 6. Extending the student in any of the listed activities or tasks by using decimal numbers to three decimal places.
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BLM
33
Decimal Numbers and Words 1
4.3 Four and three tenths
43.3 43.33 43.03 Forty-three and three tenths
Forty-three and thirty three hundredths
Forty-three and three hundredths
40.30 40.33 40.03
6.9
Forty and thirty-three hundredths
Six and nine tenths
Forty and three tenths
69.9 Sixty-nine and nine tenths
Forty and three hundredths
69.99 69.09 60.90 Sixty-nine and ninety-nine hundredths
Sixty-nine and nine hundredths
Sixty and nine tenths
60.99 60.09 17.05 17.50 Sixty and ninety-nine hundredths
Sixty and nine hundredths
Seventeen and five hundredths
Seventeen and five tenths
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution. Unit
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18 27
Fractions and decimals MA2-7NA
Teacher’s Note: This BLM can be enlarged, photocopied, laminated and cut up to make cards.
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BLM
34
Decimal Numbers and Words 2
17.55 17.75 Seventeen and fifty-five hundredths
Seventeen and seventy-five hundredths
17.77 17.57 Seventeen and seventy-seven hundredths
Seventeen and fifty-seven hundredths
17.07 15.07 15.77 15.70 Seventeen and seven hundredths
Fifteen and seven hundredths
Fifteen and seventy-seven hundredths
Fifteen and seven tenths
3.1
3.11
3.01
1.03
Three and one tenth
Three and eleven hundredths
Three and one hundredth
One and three hundredths
1.3
1.33
1.31
3.31
One and three tenths
One and thirty-three hundredths
One and thirty-one hundredths
Three and thirty-one hundredths
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution. Unit
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18 27
Fractions and decimals MA2-7NA
Teacher’s Note: This BLM can be enlarged, photocopied, laminated and cut up to make cards.
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BLM
42
Symbols
<
>
=
+
–
÷
×
≠
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution. Unit
Unit
18 27
Fractions and decimals MA2-7NA
Teacher’s Note: This BLM can be enlarged, photocopied, laminated and cut up to make cards.
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4.18
Year 4: Assessment Task Card Unit
18
Decimals to 2 Decimal Places
1
Give the student a set of decimal numbers, e.g. 2.45, 3.07, 4.6, 3.90, 2.42. Ask them to record the numbers in order from smallest to largest.
2
Have the student select one of the numbers with two decimal places and write it in words.
3
Ask the student to draw a number line and place on all of the listed numbers. Point to the number line and ask questions, e.g. ‘Why did you place 4.6 here? Would 3.4 be smaller or larger than 4.6?’
4
For the student who requires extension, give them a decimal number, e.g. 4.126. Ask them to round the number to the nearest hundredth and add the number to their number line (marked in a different colour).
Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
4.18
Year 4: Assessment Task Card Unit
18
Decimals to 2 Decimal Places
TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Review with the student the ordering of numbers with no decimal places.
Q2
Use the cards from BLM 33 ‘Decimal Numbers and Words 1’. Give the student a number card and have them find the matching word card.
Q3
Using LO 2005 ‘Scale Matters: Hundredths’, have the student review the use of number lines.
If the student has demonstrated an understanding beyond the skills, consider: Having the student order a set of decimal numbers to three decimal places and place them on a number line.
Q4
Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution.
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Place-Value Chart
DATE:
Expand each decimal number by using the correct columns in the place-value chart. a 42.39
b 21.78
c 130.45
d 17.09
e 12.6
f 710.56
g 11.08
h 403.6
Extension: i
five and six tenths
j
seventeen and forty-two hundredths
k
ninety and nine tenths
l
twenty-seven hundredths
m
nine hundred and twenty-five and three tenths
Hundreds
Tens
Ones
Tenths
a
•
b
•
c
•
d
•
e
•
f
•
g
•
h
•
i
•
j
•
k
•
l
•
m
•
102
Unit
18
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Hundredths
Decimals to 2 Decimal Places (TRB pp. 94–95) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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Matching Decimal Numbers and Words
DATE:
Match the words and the decimal numbers. Write the letter that corresponds to the matching words on the line above each decimal number to complete the puzzle. The first one has been done for you. A
ninety-three and five hundredths
S
three and seven tenths
D
one hundred and six and thirty-nine hundredths
P
eighteen and twenty-five hundredths
O
eighty-one and seventy-six hundredths
E
eight and fifty-five hundredths
W
ninety-nine and ninety-nine hundredths
I
two hundred and sixteen and ninety-three hundredths
N
twenty-one and five hundredths
C
eighteen and five hundredths
T
three hundred and forty-two and thirty-nine hundredths
I
sixteen and thirty-nine hundredths
X
two hundred and fifteen
L
eight hundred and twenty-seven and twenty-five hundredths
M
four hundred and twenty-one and five hundredths
F
fifty-one and seven tenths
A
seventy-six and thirty-five hundredths
*
What is small and round? A
93.05
Unit
18
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106.39
8.55
18.05
216.93
421.05
18.25
81.76
16.39
21.05
342.39
76.35
827.25
Decimals to 2 Decimal Paces (TRB pp. 95–96) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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DATE:
Ordering Decimal Numbers 1
2
3
Order each set of decimal numbers from smallest to largest. a
42.39
12.85
15.72 29.46
30.08
b
20.36
25.49
21.39 19.86
23.76
c
8.46
8.59 8.62
d
150.26
150.73
8.73
150.07
8.21
150.54
150.37
Create a number line for each set of decimals. a
16.3
16.5 16.9
b
100.5
100.9
101.3 101.6
101.9
c
3.6
4.7
3.8
4.1
d
126.7
128.9
124.6 123.5
125.8
17.3
17.5
3.3
These times in minutes are from a car race. Place them in order from shortest to longest to find who came 1st, 2nd and 3rd. 9.45
4
9.00 8.45
9.30
9.15
9.27
9.06
8.54
These are the weights in kilograms of 5 elephants. Place them in order from largest to smallest to find the heaviest and the lightest elephant. 3 200.49
5 505.69
4 370.56
5 505.05
4 465.98
104
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Decimals to 2 Decimal Places (TRB pp. 94–95) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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DATE:
Unit
18
STUDENT ASSESSMENT
Look at these numbers:
2.45 3.07 4.6 3.90 3 2.42 4.05 1
Order the numbers from smallest to largest.
2
Select one of the numbers that has 2 decimal places. Write it here:
3
This is your special number.
Write your special number in words.
4
Draw a number line and include all of the numbers in the box.
5
Explain where you placed your special number on the number line and why.
6
Is the number 5.01 smaller or larger than your special number?
How do you know? 7
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Draw a picture of your special number.
Decimals to 2 Decimal Places (TRB pp. 94–95) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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Unit
8
Shape
MEASUREMENT AND GEOMETRY Two-dimensional space: MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
ML
area, centimetres, formal, informal, irregular, regular, shape, units
LESSON PLAN
TUNING IN
1
BLOCKS You will need: shape blocks Give groups of students a pile of blocks to sort by criteria that they determine. Have groups share their sorting criteria and the different groupings they have created.
WHOLE-CLASS INTRODUCTION REGULAR SHAPES You will need: poster paper Write the term ‘shapes’ on the board and have students brainstorm what it means. Then write the term ‘regular shapes’. Ask, ‘What makes a regular shape?’ (A regular shape is a polygon where all sides and all angles are equal.) Have students come up with criteria. Record the criteria on poster paper and display.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: an assortment of regular shapes, blank cards, LO 10736 ‘Shape Sorter: Wand Tool’, Student Book p. 110 ‘Regular Shapes’
TASK 1:
WHAT AM I?
Give students an assortment of regular shapes and blank cards. Have students write ‘Who am I?’ cards for individual shapes. Ask students to focus on features, e.g. whether all angles are equal, the number of equal sides, and so on. Have students include the answer on the back of the card. Have them make a number of these cards and then test them on a friend. An example of text on a card could be: Who am I? I have 4 equal sides and 4 equal angles.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 10736 ‘Shape Sorter: Wand Tool’ to examine examples of single shapes. They use the wand tool to compare the sides, right angles and lines of symmetry for each shape, and to work out its features. Note: there are more Learning Objects in this series, which will cater for different learning abilities.
TASK 3:
STUDENT BOOK p. 110 ‘Regular Shapes’
TEACHING GROUP
You will need: computers/tablets, LO 3547 ‘Tessellations’, rulers, protractors LO 3547 ‘TESSELLATIONS’ • For students who require support, have them work independently on computers/tablets using LO 3547 ‘Tessellations’ to create tessellations with coloured shapes. CREATING SHAPES • For students who require a challenge, have them practise drawing exact regular shapes, building on the features they identify as important. Give students rulers and protractors to help with accuracy.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their cards from Independent Tasks, Task 1, reading out the description to the class and having the group identify the shapes. • Have students share their electronic tessellations from the Teaching Group. Ask, ‘Why did you select that shape? How did you know to place that shape there?’ • Have students share their accurate drawings from ‘Creating Shapes’ in the Teaching Group. Ask them to reflect on the difficulty of the task, and how they used the tools, e.g. the ruler, to help. Display their work.
LESSON PLAN
TUNING IN
DRAWING SHAPES Ask students to draw a regular six-sided shape and an irregular six-sided shape. Have students share their drawings. Ask, ‘Why is this shape regular? How do we know this shape is irregular?’
2
WHOLE-CLASS INTRODUCTION Go over some of the features of regular shapes, i.e. a polygon where all sides and all angles are equal. Extend to examine what makes a shape irregular. Have students draw a number of different irregular shapes on the board.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 15 ‘1 cm Grid Paper’, an assortment of regular shapes (e.g. blocks), Word, Student Book p. 111 ‘Regular or Irregular?’
TASK 1:
FINDING THE AREA
Give students copies of BLM 15 ‘1 cm Grid Paper’ and an assortment of regular shapes. Ask, ‘How could we find the area of the shapes?’ Guide students towards placing the shape on the grid paper and tracing around it, then counting squares to find the area. Have students write the area (in cm2) in the centre of the shape. Have them measure the area of three different regular shapes. Then ask students to find three irregular shapes in the classroom and repeat the process.
TASK 2:
INTERACTIVE TASK
Have pairs of students work on computers/tablets to use the ‘Shape’ function in Word to create irregular shapes. Under each shape they create, have them write why the shape is irregular. Have students create at least five different shapes.
TASK 3:
STUDENT BOOK p. 111 ‘Regular or Irregular?’
TEACHING GROUP
You will need: BLM 16 ‘Regular and Irregular Shapes’, sheet of paper, scissors, glue, BLM 15 ‘1 cm Grid Paper’ SORTING REGULAR AND IRREGULAR • For students who require support, give them copies of BLM 16 ‘Regular and Irregular Shapes’ to cut up into cards. Have students sort the shapes into two piles – regular and irregular. Students then identify the features of each different set. The cards could be pasted onto a sheet of paper under the headings ‘Regular’ and ‘Irregular’, with students writing the features of each group in the relevant section. This activity could be extended by having students find the areas of the shapes, placing them on BLM 15 ‘1 cm Grid Paper’ and tracing around them to find the area. Note: students would need another copy of BLM 16. DESIGN WITH SHAPES • For students who require a challenge, have them play with a design tool, e.g. Google SketchUp (a free Google application). Allow students to explore what they can design and create.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students write a written reflection on the differences in finding the area of regular and irregular shapes in Independent Tasks, Task 1. Ask, ‘Which was easier to measure – this shape or this shape? Why?’ • Invite students to share their electronic creations of irregular shapes from Independent Tasks, Task 2. Have students explain how they created certain aspects of the shapes.
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• Invite students to share their SketchUp designs from ‘Design with Shapes’ in the Teaching Group. Ask, ‘What did you discover about the program?’
LESSON PLAN
TUNING IN
3
COMPARING AREAS OF REGULAR AND IRREGULAR SHAPES You will need: a regular shape and an irregular shape (these could be sourced from BLM 16 ‘Regular and Irregular Shapes’) Show students a regular and an irregular shape. Ask, ‘How could we compare the areas of these two shapes?’ Have students make suggestions and try out ideas. Guide students towards measuring the respective areas on grid paper, and then comparing.
WHOLE-CLASS INTRODUCTION COMPARING AREAS OF REGULAR AND IRREGULAR SHAPES You will need: IWB, a grid to project onto the board Project a large grid onto the whiteboard or IWB. Note: all IWB software comes with a grid option or these can also be found on the internet. Ask a student to draw a regular shape on the projection. Have another student work out the area of the shape. Revisit the most effective methods of doing this. Repeat with an irregular shape. Ask, ‘What are the units of the area? Which shape has the greatest area? How do we know?’ Repeat the activity with different shapes.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 15 ‘1 cm Grid Paper’, Word, Student Book p. 112 ‘Comparing Regular and Irregular’
TASK 1:
COMPARING AREA OF SHAPES
Give each student a copy of BLM 15 ‘1 cm Grid Paper’. Challenge pairs of students to find in the classroom at least two shapes – one regular and one irregular – that have the same area. Students may select anything in the classroom. Have them find as many different pairs as they can and record their findings. As an extension, once an irregular shape has been outlined on the grip paper in pencil, have students change it in some way to make it a regular shape with the same area.
TASK 2:
INTERACTIVE TASK
Have students work individually on computers/tablets to use the ‘Shape’ function in Word to create regular and irregular shapes that have the same area. Students could overlay their work on electronic grid paper, such as that found on IWB software, to aid the construction.
TASK 3:
STUDENT BOOK p. 112 ‘Comparing Regular and Irregular Shapes’
TEACHING GROUP
You will need: BLM 15 ‘1 cm Grid Paper’, flat blocks, computers/tablets, LO 3547 ‘Tessellations’ COMPARING AREAS OF BLOCKS • For students who require support, give them a copy of BLM 15 ‘1 cm Grid Paper’ and some flat blocks. Have the students look at the blocks and estimate two that may be of equal area. Have them record their estimate. Then have students place the blocks on the grid paper, trace around them and then find the areas. Ensure that students count the squares correctly and talk to them about how to accommodate for the partial squares. Have them check their prediction. Repeat the activity. LO 3547 ‘TESSELLATIONS’ • For students who require a challenge, have them work independently on computers/tablets, using LO 3547 ‘Tessellations’ to create tessellations with coloured shapes. Have students complete a tessellation, then identify which tiles are regular and which are irregular. Have students make a comment about whether or not the regularity (or otherwise) of the tiles had an impact on creating tessellating patterns.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their equal area shapes from Independent Tasks, Task 1. Ask, ‘How did you find the two shapes? Did you have a strategy? How did you check that the areas were the same?’
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• Have students share the equal area shapes from Independent Tasks, Task 2. Ask, ‘How did you know the areas were the same? How did you check? Which shape is regular and why?’ Students could show their work electronically. • Invite students from the Teaching Group to share their tessellation patterns. Ask them to comment on whether or not the regularity (or otherwise) of the tiles had an impact on creating tessellating patterns.
Home Tasks Select from the possible Home Tasks: • Have students conduct a shape hunt at home, looking for regular and irregular shapes. Have them list five things from the kitchen that are a regular shape and five that have an irregular shape. Have students bring the items (if possible) or their list to school to share. • Give each student a copy of BLM 15 ‘1 cm Grid Paper’. Have them find three items at home (regular or irregular) that have an area of 10 cm2. Have students trace around the items and label.
Assessment • Have students complete Student Assessment p. 113. • Review with students Assessment Task Card 4.8. During the three lessons: • Collect a copy of students’ designs, e.g. the irregular shapes from Lesson Plan 2, Independent Tasks, Task 2, or the equal area shapes from Lesson Plan 2, Independent Tasks, Tasks 1 and 2, to add to students’ digital portfolios. • Collect students’ written reflections, e.g. the reflection on finding the area of regular and irregular shapes from Lesson Plan 2, Independent Tasks, Task 1. • Make a note of the students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 113; if the student is experiencing difficulty: Q 1–2 Review the difference between shapes. Have the student sort shapes into groups and then identify properties of the particular groups. Repeat, separating regular and irregular shapes. Q 3 Have the student practise tracing shapes and counting squares. Show them strategies for recording the number of squares, e.g. numbering each individual square or colouring in and keeping a tally. Examine how to count partial squares. Talk about the importance of units. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 4.8 for specific recommendations. 2. Work with simple shapes, e.g. squares, rectangles and triangles. Consolidate ideas with these shapes before moving forward. 3. Practise counting squares to determine areas. 4. When making area comparisons, have the student cut out the shapes and try to overlay them to determine which one is larger. 5. Review Nelson Maths: Australian Curriculum Year 3 Unit 13. If the student has achieved the recommended skills and these skills are firmly established, consider: 6. Having the student investigate circles and how they fit into the classification. They may wish to use references. 7. Moving forward to Nelson Maths: Australian Curriculum Year 5 Unit 8. 8. Having the student complete problems that require multiple steps to solve, i.e. nominate an area of x amount, then create both an irregular and a regular shape of this area.
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Regular Shapes
DATE:
Write a description for each regular shape.
1
a
b
c
d
e
f
2
Circle the shape in each set that is the odd one out (not a regular shape).
a
c
c
d
Extension: On another sheet of paper, draw and name each shape from
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Question 2.
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Regular Shapes (TRB pp. 106–107) Two-dimensional space MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
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Regular or Irregular?
DATE:
1
Colour all of the regular shapes.
2
Circle each shape in each set that is the odd one out (not regular). a
3
b
Using the grid paper as a guide, draw 2 different irregular shapes and 2 regular shapes. Label each shape regular or irregular.
4
Find the area of each shape by counting squares. Write the area on your shape in cm2.
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Regular Shapes (TRB pp. 106–107) Two-dimensional space MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
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Comparing Regular and Irregular Shapes 1
DATE:
For each shape, find the area and write it inside the shape.
a
c
b
d
e
f g
2
Shade each regular shape red and each irregular shape green.
3
Find the shapes that have the same areas and list them below.
4
Create an irregular shape that has an area the same as shape g.
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Regular Shapes (TRB pp. 106–107) Two-dimensional space MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
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DATE:
Unit
8 1
STUDENT ASSESSMENT Label each shape regular or irregular.
a
b
2
c
d
e
f
Describe what features make a regular shape, e.g. a pentagon.
3
Find and record the area of each shape.
1
2 3 4
a Which two shapes have the same area?
b Which shape has the largest area? c What is the area of the smallest shape? Extension: Draw an irregular shape that is 4 cm2.
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Unit
1
Place Value
NUMBER AND ALGEBRA Whole numbers: MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
ML
abacus, digits, expanding numbers, hundreds, hundreds of thousands, integers, millions, number expanders, place value, tens, tens of thousands, thousands, units
LESSON PLAN
TUNING IN
1
ORDERING NUMBERS You will need: sticky notes, poster paper Provide each student with a sticky note. Have each student write a 5- to 6-digit number on their sticky note, and then collect the sticky notes. Redistribute the sticky notes, and have students in small groups order their notes from smallest to largest. Then have the whole group arrange the sticky notes on poster paper from smallest to largest. This activity could be varied by setting a range for the numbers according to students’ abilities. Have students share and discuss the different strategies they used to order the numbers.
WHOLE-CLASS INTRODUCTION NUMBER KNOWLEDGE You will need: sticky notes, NTO 5.1 ‘Spike Abacus’, NTO 5.2 ‘Place-Value Chart’ Invite a number of students to write a 3- or 4-digit number on a sticky note. Have students attach their sticky notes to the board. Ask, ‘How could we represent these numbers?’ NTO 5.1 ‘Spike Abacus’ and NTO 5.2 ‘PlaceValue Chart’ could be used. Discuss place value and what it means if there is a zero acting as a place holder. Have students order the numbers from smallest to largest on the sticky notes using either NTO.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: newspapers or magazines, scissors, glue, poster paper, BLM 1 ‘Place-Value Chart’, LO 1999 ‘Scale Matters: Tens of Thousands’, Student Book p. 112 ‘Identifying Place’
TASK 1:
REAL PLACE-VALUE CHARTS
Individually, have students look in newspapers or magazines for different numbers, cut them out and paste them on poster paper. Then have students write the number into a place-value chart, either one they have drawn or a copy of BLM 1 ‘Place-Value Chart’. Set minimum numbers for students to collect or a time limit.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 1999 ‘Scale Matters: Tens of Thousands’ whereby students explore the use of scale on a number line.
TASK 3: STUDENT BOOK p.122 ‘Identifying Place’
TEACHING GROUP
You will need: NTO 5.1 ‘Spike Abacus’, NTO 5.2 ‘Place-Value Chart’, blank cards, a long sheet of paper (optional) ABACUS • For students who require support, display NTO 5.1 ‘Spike Abacus’ and have students take it in turns to display or read a selection of numbers. Review with students what each of the spikes represents. Repeat the activity using NTO 5.2 ‘Place-Value Chart’ with the MAB materials and the same numbers. Ask students to identify what is similar and what is different between the two representations. 7-DIGIT NUMBERS • For students who require a challenge, have each student write a 7-digit number on a piece of card. Have them represent the number three different ways, e.g. in words, as a diagram, on a place-value chart. Then, as a group, have students order the numbers from smallest to largest. This activity could then be extended with students creating a number line of their 7-digit numbers on a long sheet of paper. Nelson Maths Australian Curriculum NSW
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their collected numbers from Independent Tasks, Task 1. Ask, ‘How did you know how to record the number in the place-value chart? Why did you write a zero there?’ • Invite students to share their 7-digit number representations from the Teaching Group. Have them share the number line (if created) and display in the room. • Have students list three strategies that they use when ordering numbers from largest to smallest.
LESSON PLAN
TUNING IN
2
NUMBER EXPANDERS You will need: BLM 2 ‘5-digit Number Expander’, scissors, contact (optional), | NTO 5.3 ‘Number Expander’ Have students create a 5-digit number expander from BLM 2 ‘5-digit Number Expander’. You may wish to use contact with the number expanders so students can write the numbers on the number expander with whiteboard markers and erase. Note: it is difficult to fold the number expanders if they have been laminated. Once complete, have students work in pairs providing each other with 5-digit numbers to explore on the number expander. Use NTO 5.3 ‘Number Expander’ to support and extend the activity.
WHOLE-CLASS INTRODUCTION WRITING IN EXPANDED FORM You will need: NTO 5.4 ‘Expanded Form’ Explore writing numbers in expanded form, e.g. 421 = 400 + 20 + 1, by providing examples on the board. Have students come to the board, show the expanded form and explain how they work it out. This could be supported with NTO 5.4 ‘Expanded Form’. Then provide a number of expanded numbers, and have students write as a set of digits, again having them explain their ideas.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: five different-coloured dice per pair of students, sheets of paper, LO 871 ‘Wishball: Whole Numbers’, Student Book p. 123 ‘Comparing Expanded Form’
TASK 1:
EXPANDING WITH DICE
Provide students in pairs with at least five different-coloured dice. On a sheet of paper, students identify what colour represents each place value, e.g. blue is hundreds. Have students take it in turns rolling the dice to generate 5-digit numbers. Have students record the number and then express it in expanded form. This activity could be altered by the number of dice used.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 871 ‘Wishball: Whole Numbers’. This is where students receive a starting number, such as 3 786, and work towards turning it into a target number, 7 664, based on addition and subtraction with place value. The aim is to reach the target number in the smallest number of goes. Note: this activity could be used as a whole-class activity and is one of a series of Learning Objects.
TASK 3: STUDENT BOOK p. 123 ‘Comparing Expanded Form’
TEACHING GROUP
You will need: sticky notes, sheets of paper, dice (optional), NTO 5 ‘Flipbook’ EXPANDED FORM IN PARTS • For students who require support, provide them with a number, e.g. 421. Have students expand the number with each part of the expansion on a different sticky note, e.g. 400 + 20 + 1. Have students mix up the equation using the sticky notes and record, e.g. 20 + 400 + 1. Then have them swap with a partner. The other student needs to write the number in digits, e.g. 421. Repeat a number of times. Begin with smaller numbers, e.g. 3-digit numbers, and work to 5-digit numbers if possible. EXPANDED NUMBER QUIZ • For students who require a challenge, have them write a number in expanded form but not in order, e.g. 1 + 300 + 50 + 6 000 + 90 000 = . Have them complete 10 different examples on one sheet of paper with the answers on another. Then have students swap and complete each other’s questions. Students can check the answers. Numbers could be randomly produced using dice. To extend this activity, students could write their numbers in expanded form in words.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Using NTO 5.5 ‘Flipbook’, have a discussion with students about internal zeros in numbers and how these are represented using place-value charts and expanded notation. • Have students share their results from ‘Expanding with Dice’, Independent Tasks, Task 1. Ask, ‘What numbers did you have difficulty with? Did the same number come up twice?’ • Provide five digits on the board, e.g. 4 2 5 0 0. Have students form these digits into three diferent 5-digit numbers and represent them on their number expanders made from BLM 2 ‘5-digit Number Expander’. Write all of the different variations on a place-value chart on the board. Note that NTO 5.3 ‘Number Expander’ could be used to support this activity.
LESSON PLAN
TUNING IN
3
IN WORDS You will need: poster paper Read out a set of numbers, and have students write them in words, starting with the smaller numbers, e.g. 45, and moving to the larger numbers, e.g. 45 689. Correct as a group, with students coming to the board to share their work. Collect on poster paper any of the numbers that are tricky to spell, e.g. forty, eighty etc, creating a word chart.
WHOLE-CLASS INTRODUCTION STRATEGIES FOR WORDS You will need: NTO 5.2 ‘Place-Value Chart’ Explore strategies that would help students to write numbers in words. Revisit NTO 5.2 ‘Place-Value Chart’ to look at how knowing the place-value language helps write numbers into words. Expanded notation ideas like the number expander could also aid students’ understanding.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: Student Book p. 124 ‘Which Animal?’
TASK 1:
WHO AM I?
Read out a ‘Who am I?’ problem about a number, e.g. ‘I am a 5-digit number less than 40 000. My tens place is occupied by the digit 2 and the digit in the ones place is 2 more than in the tens place. My hundreds and thousands digits are the same and total 8. All of my digits add up to 17. Who am I?’ (34 424) Have students solve and discuss the different strategies they used to solve the problem. Have students write their own ‘Who am I?’ problems about a number.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using level-appropriate software for the following task. Provide each student with a number according to their ability. Then, have students key in everything they can think of about that number, e.g. in words, expanded form, what it is larger than, less than, if it represents something, if it is odd or even. Allow students to be creative in their presentation.
TASK 3: STUDENT BOOK p. 124 ‘Which Animal?’
TEACHING GROUP
You will need: packs of playing cards MULTIPLYING WITH PLAYING CARDS • For students who require support, use packs of playing cards with the aces, tens and picture cards removed. Provide students with a set of cards. Have them create a 3-digit number by turning over the cards. Have students record the number, and then write the number in words below. Discuss strategies to help students, e.g. identifying the value of each place, being aware of the place such as tens. Have students say the word out loud. If students are still struggling, provide a word list of the first 20 numbers and all of the tens numbers to 100 to support students with their writing. WHO AM I? IN WORDS • For students who require a challenge, have them write ‘Who am I?’ problems for numbers into the millions only using words. Students could type their problems on the computer.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students present their ‘Who am I?’ problems from Independent Tasks, Task 1, and the Teaching Group. Have the student read them out and the rest of the class can solve. • Have students share their number investigation from Independent Tasks, Task 1. Look for interesting and unusual representations. Collect into a class book, either digital or hard copy. • Put students in teams of three or four. Read out a number, e.g. 54 291. Have students write the number out in words in large text on a sheet of paper or on a tablet and hold it up. The first group that does this correctly collects a point. The aim of the activity is accuracy. Play a number of rounds. This activity could be varied by writing numbers in words as well.
Home Tasks Select from the possible Home Tasks: • Have students take home their number expanders and explain to their parents or carers how the expanders work with a number of examples. These examples could be provided on a sticky note according to students’ abilities. • Have students look around at home for five numbers with at least four digits. Have students record the numbers, where they found them and then expand them. Have students bring the numbers into class to share.
Assessment • Have students complete Student Assessment p. 125. • Review with students Assessment Task Card 5.1. During the three lessons: • Collect a copy of students’ ‘Who am I?’ problems from Lesson 3, Independent Tasks, Task 1, as evidence of their understanding of place value. Add the extension activity (Lesson Plan 3, Teaching Group) if completed. • Collect students’ ideas about their number from Lesson 3, Independent Tasks, Task 2, as evidence of their knowledge of place value, how to express the number in different forms and so on. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 125; if the student is experiencing difficulty: Review the use of the place-value chart and what each of the columns represents. NTO 5.2 ‘Place-Value Q 1 Chart’ could be used to aid discussion. Have the student practise inserting numbers into the chart. Review how to expand numbers by breaking them into each of the place values. Practise with the Q 2 student-made number expanders and NTO 5.3 ‘Number Expander’. Q 3–4 Review the writing of numbers in words and vice versa. The student could complete matching activities of words and numbers. The student could also create their own word/number chart to remind them of spelling. Q 5–6 To help the student with comparison of numbers, discuss strategies, e.g. working with the tens of thousands, then thousands etc., essentially the place-value chart backwards. The student could also circle the part of the number that they find to be the largest when comparing. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 5.1 for specific recommendations. 2. Have the student work with 2- and 3-digit numbers before moving to larger numbers. 3. Consolidate ideas by creating a ‘tool box’ for the student including a place-value chart, their number expander, their word/number chart as reference points. 4. Review Nelson Maths: Australian Curriculum Year 4 Units 2–3. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student apply the ideas and concepts to larger numbers in the millions. 2. Moving forward to Nelson Maths: Australian Curriculum Year 6 Unit 1. 3. Have the student complete Nelson Maths Building Mentals Strategies Book 5 Unit 4 ‘Ordering 6-digit Numbers’, Unit 5 ‘Expanding Numbers’ and Unit 6 ‘Less Than and Greater Than’, pp. 10–15. 4. Extending the student in any of the listed activities or task by using decimal numbers.
Unit 1
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BLM
1
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Place-Value Chart M
HTh
TTh
Th
H
T
O
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Whole numbers MA3-4NA
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BLM
2
Ones Tens Thousands Tens of thousands
Hundreds
Ones Tens Thousands Tens of thousands
Hundreds
Thousands Tens of thousands
Hundreds
Tens
Ones
5-digit Number Expander
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 5 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA3-4NA
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5.1
Year 5: Assessment Task Card Unit
1
PLACE VALUE
Resources: a sheet of paper per student, NTO 5.2 ‘Place-Value Chart’, NTO 5.3 ‘Number Expander’, NTO 5.4 ‘Expanded Form’
1
On a sheet of paper, have the student write the number 2 542 368.
2
Have the student write the number in words.
3
Have the student expand 45 807.
4
Have the student write three numbers larger than 9 999 999.
5
For students who require extension, have them write a 7-digit number that has two internal zeros, and then write this number in words.
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
5.1
Year 5: Assessment Task Card Unit
1
PLACE VALUE TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Review writing numbers based on place-value charts. Work with NTO 5.2 ‘Place-Value Chart’ and how this can help with writing numbers. Work with numbers with only three digits.
Q2
Practise writing numbers in words, beginning with numbers less than 100. Have the student develop a word chart to assist with the spelling of the numbers.
Q3
Use NTO 5.3 ‘Number Expander’ and NTO 5.4 ‘Expanded Form’ to revisit number structure and expanding numbers.
Q4
Have the student practise ordering numbers from smallest to largest noting the strategies. When writing numbers that are larger, have the student consider strategies, e.g. counting on.
If the student has demonstrated an understanding beyond the skills, consider: Q5
Having the student work with larger numbers in all forms up to billions and also with decimal numbers.
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 5 may be photocopied for educational use within the purchasing institution.
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Identifying Place
DATE:
1 Write the numeral shown on each abacus. a b
Hth Tth Th H T
Hth Tth Th H T
O
c
O
Hth Tth Th H T
O
2 State the value of the 6 in the following numbers. a 61 432
b 11 056
c 46 161
d 16 528
e 43 601
f 50 116
3 Circle the largest number in each pair. a 29 006
2 998
b 42 119
41 911
c 16 832
17 852
d 60 479
60 794
e 185 609
185 690
f
4 600 142
4 006 142
4 Describe how you worked out which number was largest in Question 3c.
5 Order the following sets of numbers from smallest to largest. a 16 487, 15 058, 17 598, 16 993 b 42 3147, 406 102, 450 328, 44 199, 424 199 c 84 294, 84 105, 84 336, 84 156 d 307 421, 4 714 809, 3 074 456, 37 201, 471 809 6 To turn 9 million into 10 000 000 I would: (Shade the correct bubble.) Add 100 000
Subtract 1 000 000
Add 1 000 000
Subtract 100 000
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Place Value (TRB pp. 20–23) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Comparing Expanded Form
DATE:
1 Write the numeral for the following numbers. a 70 000 + 2 000 + 500 + 20 + 1
b 30 000 + 5 000 + 800 + 90 + 5
c 20 000 + 400 + 50 + 6
d 10 000 + 1 000 + 400 + 30 + 3
2 Express each of the following in expanded form. a 60 419
c 81 403
3 Circle the largest number in each pair. a 21 432
20 000 + 1 000 + 400 + 40 + 1
b 42 119
40 000 + 2 000 + 400 + 20 + 6
c 16 832
10 000 + 5 000 + 700 + 90 + 5
d 60 000 + 4 000 + 300 + 5
64 350
e 10 000 + 8 000 + 900 + 20 + 1
14 922
f 4 000 + 200 + 5
40 205
4 Describe how you worked out which number was largest in 3e.
5 Order the following numbers from smallest to largest. 70 000 + 5 000 + 200 + 80 + 1 70 000 + 5 000 + 400 + 90 + 5 70 000 + 5 000 + 300 + 40 + 6
Extension: Using the digits 4, 8, 7, 6, 5, 1 a Write the smallest number using all of the digits.
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b Write the largest number using all of the digits.
Place Value (TRB pp. 114–115) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Which Animal?
DATE:
Complete the gaps to find the unused number on the animal that will complete the joke. 1 10 658 = ten thousand hundred and fifty-eight 2 25 306 = twenty-five thousand three hundred six 3 61 259 = sixty-
thousand two hundred and fifty-nine
4 89 220 = eighty-nine thousand, two hundred and 5
44 244 =
-four thousand, two hundred and forty-four
6
16 225 =
thousand, two hundred and twenty-five
7 98 178 = ninety-
thousand, one hundred and seventy eight
8 54 115 = fifty-four thousand, one hundred and 9 54 10 11
24 = fifty-four thousand, nine hundred and twenty-four 10 = eleven thousand, one hundred and ten
84 56
11
= eighty-four thousand, five hundred and sixty
12 9 325 = ninety-five thousand, three hundred and twenty-five 13
4 235 = fourteen thousand, two hundred and thirty-five
fift e
eight
en
sixteen
one
forty tw en
and
en
six
e et
9
ty
n
ni
1
1 5
What goes 29-clonk, 29-clonk,
0
29-clonk? A
with
a wooden leg!
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Unit
DATE:
1
STUDENT ASSESSMENT
1 Write the following numbers in the place-value chart. a
54 236
d 4 782 368
TM
b 11 054
c 724 000
e 921
f 31 270 356
M
Hth
TTH
Th
H
T
O
a b c d e f 2 Expand each of the following numbers. a 58 920 b 32 560 3 Write each number in words. a 32 561 b 14 560 4 Write the numeral for each number. a twenty-five thousand, three hundred and eleven b eighty-two thousand, one hundred and three 5 Order the following numbers from smallest to largest. a 56 123, 56 892, 56 741, 56 334
b 2 114 021, 12 114 201, 12 114 210, 2 114 201
6 Circle the largest number of this pair. How did you work it out? 42 631 and 42 813
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Place Value (TRB pp. 20–23) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Unit
14
Perimeter
MEASUREMENT AND GEOMETRY Length: MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
ML
centimetre, length, metre, millimetre, perimeter, rectangle, ruler, square, units, width
1
LESSON PLAN
TUNING IN
MEASURING LENGTH You will need: rectangular objects, rulers Provide each student with a rectangular object, e.g. a tissue box. Have students measure the length of each of the sides with a ruler, and record on a diagram. Check students are measuring correctly using the ruler, and are recording an appropriate diagram with the correct units of measurement. Repeat if necessary and have students share results.
WHOLE-CLASS INTRODUCTION WHAT IS PERIMETER? You will need: recorded measurements and objects from Tuning In, calculators Ask, ‘What is perimeter?’. Brainstorm students’ ideas on the board. Then have students find the perimeter of their object from Tuning In. Ensure they add the perimeter of their object correctly. Have them compare their results with a partner. They may need to use calculators to aid the calculations. If time permits, have students swap objects and find the measurement.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: rulers, sheets of paper, LO 3528 ‘Geoboard’, Student Book p. 130 ‘Perimeter of Rectangles’
TASK 1: MEASURING PERIMETER Provide students with a ruler and a sheet of paper and have them select five rectangular objects (from around the classroom) to measure the perimeter of. Have them record the measurements of each side length on a diagram. Students could be encouraged to collect their information in the form of a table with the following headings.
TASK 2:
Name of object/ where found
Diagram with labels
Perimeter
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 3528 ‘Geoboard’, whereby students can use the virtual geoboard to stretch bands to create shapes and then find the perimeter. Have students record their results.
TASK 3: STUDENT BOOK p. 130 ‘Perimeter of Rectangles’
TEACHING GROUP You will need: rulers
MEASURING RECTANGLES ON THE BOARD • For students who require support, draw some rectangles on the board. Have students use a ruler to take it in turns to measure and label each of the side lengths. Then discuss with students the idea of perimeter being ‘the total distance around the shape’. Repeat with a number of examples. FINDING THE PERIMETER • For students who require a challenge, provide them with the task of finding objects with a set value perimeter, e.g. 10 cm or 50 cm or even 100 cm or 1 m. Have students work in pairs to see how many objects they can find to meet the criteria.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their collected perimeters from Independent Tasks, Task 1. Look for different objects that have the same perimeter. Perhaps they could be listed together. Ask students why they selected particular objects. • Invite students to share the objects they found that met the perimeter requirements in ‘Finding the Perimeter’ from the Teaching Group. Ask students to explain how they solved the task. • As a class, create a perimeter poster with facts, ideas and reminders to be displayed in the classroom.
LESSON PLAN
TUNING IN
2
WORKING WITH GRIDS You will need: NTO 5.6 ‘Grid Paper’ Using NTO 5.6 ‘Grid Paper’, create a rectangle on the board and have students find the length of each side and then the perimeter. Repeat with a number of different examples.
WHOLE-CLASS INTRODUCTION IS THERE A QUICKER WAY? You will need: NTO 5.6 ‘Grid Paper’ Using NTO 5.6 ‘Grid Paper’, have a student create a rectangle on the board. Discuss with students the strategies for finding the perimeter. Ask, ‘Is there a quicker way to find the perimeter?’ Draw out ideas, e.g. ‘length + width × 2 = perimeter’ or ‘2 × Length + 2 × width = perimeter’. Add these to the perimeter poster from the Reflection in Lesson Plan 1. Try the processes (ideas) with a number of examples at the board.
INDEPENDENT TASKS
Note: Choose from Tasks1, 2 or 3. You will need: metre rulers, tape measures, trundle wheels, NTO 5.6 ‘Grid Paper’, Student Book p. 131 ‘Rectangles on Grids’
TASK 1:
PERIMETER OF A LARGE OBJECT
As a class, have students measure the perimeter of a large object, e.g. the basketball court or a school building or playground. Before moving outside, have students brainstorm how, as a group, they will complete the measurement task, e.g. they could divide into smaller groups and each group measures a particular section. Have students consider how they will record this information.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets to explore NTO 5.6 ‘Grid Paper’, whereby they will add a rectangle and find the side lengths and perimeter of the shape. Students could record their work by taking a screen shot or photo of the page. Have students complete a number of measurements. This activity could be extended by providing the perimeter and the students determine the side lengths of the rectangle.
TASK 3: STUDENT BOOK p. 131 ‘Rectangles on Grids’
TEACHING GROUP
You will need: BLM 3 ‘1cm Grid Paper’, rulers, calculators PRACTISING WITH GRIDS • For students who require support, provide them with a copy of BLM 3 ‘1 cm Grid Paper’. Have students draw rectangles to specifications, e.g. length 5 cm, width 3 cm, using rulers. Then have students find the perimeter. Encourage students to consider ‘length + width × 2 = perimeter’ or ‘2 × length + 2 × width = perimeter’, perhaps working through examples of each. Note: students may need to use calculators. SOLVING THE GRID PROBLEM • For students who require a challenge, provide them with a copy of BLM 3 ‘1 cm Grid Paper’. Have them examine the problem: to find the number of rectangles with a perimeter of 24 cm that will fit on their page. Allow students to use any strategies they wish. They must be able to justify the number they arrive at.
REFLECTION Select from the following to suit your class and their learning outcomes: • Draw the ideas and calculations of students finding the perimeter of a large object from Independent Tasks, Task 1. Ask, ‘What was challenging about this task? How do you know the answer is correct? How would grids have aided you to find the answer?’
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• Have students share their discoveries and results from ‘Solving the Grid Problem’ in the Teaching Group. Display NTO 5.6 ‘Grid Paper’ on the board and invite students to share some of their ideas. • Draw a rectangle on the board. Ask students how they could they find the perimeter. Draw out students’ different strategies and calculate the perimeter of the rectangle with each of the strategies. Ask students which strategies they prefer and why.
LESSON PLAN
TUNING IN
3
SQUARES AND RECTANGLES Provide students with a number of squares and rectangles for them to find the perimeter of, including rectangles and squares that have been rotated. Provide these on shapes with the side lengths labelled. Have students find the perimeters of the shapes in pairs.
WHOLE-CLASS INTRODUCTION PERIMETER OF A SQUARE Review the definition of perimeter with students. Then discuss the perimeter of a square. Ask, ‘Do you know a short cut when finding the perimeter of a square?’ i.e. 4 × length = perimeter of a square. Ask, ‘Why is a square a special case?’
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: Student Book p. 132 ‘Perimeter’
TASK 1:
INVESTIGATING PERIMETER
Provide students with a total perimeter, e.g. 24 cm or 48 cm, and have students in pairs investigate all of the different rectangles and squares that could have that total perimeter. Encourage students to be systematic in solving the task. Have them write up their results on poster paper. To extend the activity, provide students with a perimeter measurement featuring decimals.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets. Provide students with the task of designing a garden bed that has a perimeter of 100 m. The garden bed could be rectangular, or it may be an irregular shape, the only stipulation being that the sections of the garden bed are straight.
TASK 3: STUDENT BOOK p. 132 ‘Perimeter’
TEACHING GROUP
You will need: rulers, square-based objects, calculators, rulers, NTO 5.7 ‘Length Convertor’ PERIMETER OF A SQUARE • For students who require support, provide a range of square-based objects and have students measure the side lengths with rulers. Have them record the lengths on a diagram and label it. Ask them to find the perimeter, reminding students about the measuring units to use. Repeat a number of times, then ask students what they notice, and if there are any ‘short cuts’ they may be able to use. Note: students may need to be supported with the use of calculators. CONVERTING UNITS • For students who require a challenge, provide them with a number of different-sized squares with sides labelled in metres, e.g. side length 2 m or 2.5 m, etc. Ask them to find the perimeter and then have them convert their answers into cm and even mm. Students will need access to calculators for this activity. Note: NTO 5.7 ‘Length Convertor’ could be used to assist with this activity.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their findings from Independent Tasks, Task 1. Ask, ‘How did you solve the problem? Did you have a process?’ • Have students share their garden bed designs from Independent Tasks, Task 2, either in hard copy or electronically. Ask, ‘Why did you create your garden bed like that?’ Check students have side lengths recorded and that they total 100 m. • Draw a number of squares and rectangles on the board and have students find the perimeter of each. Ask, ‘What is a quicker method than adding all 4 side lengths with the square? How do we know the value of each side length, if it is not labelled?’ Nelson Maths Australian Curriculum NSW
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Home Tasks Select from the possible Home Tasks: • Have students find the perimeter of two squares and three rectangles from around their home. Have students record the item, its side lengths and perimeter. This could be represented in a table. • Provide students with a value, e.g. 16 m, and have them determine the different perimeters of rectangles and squares that could give that perimeter. Have students record their ideas and share with the rest of the class.
Assessment • Have students complete Student Assessment p. 133. • Review with students Assessment Task Card 5.14. During the three lessons:
• Collect a copy of students’ results from Lesson Plan 3, Independent Tasks, Task 1, for their student portfolio. • Collect a copy of the gardens designed by students from Lesson Plan 3, Independent Tasks, Task 2, for their student portfolio. • Make a note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 133; if the student is experiencing difficulty:
Q 1
Review the concept that opposite sides in a rectangle are equal in length. Review that all four side lengths in a square are equal. Q 2–3 Review how to find perimeter by adding each of the side lengths. When this concept is strong, the student could be encouraged to use strategies such as 4 × side length = perimeter of a square. Q4 Review the finding of perimeter by adding each of the side lengths. Then have the student work out what numbers could add to give 10 cm, e.g. 2 + 2 + 3 + 3 = 10. Then have them add this to a diagram. Remind the student that two pairs of the side lengths need to be the same/equal. If the student has not achieved the recommended skills for this unit:
1. See Assessment Task Card 5.14 for specific recommendations. 2. Have the student continue to work with the physical materials, tracing and then measuring the side lengths with rulers. 3. Review the use of rulers. 4. Have the student work with small numbers and not worry about the measurements units initially. 5. Create a reminder chart about perimeter to display. 6. Review Nelson Maths: Australian Curriculum Year 4 Unit 14. If the student has achieved the recommended skills and these skills are firmly established, consider:
1. Having the student work with larger numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 6 Unit 13. 3. Having the student complete questions with conversions involved. 4. Extending the student to include more word-based problems.
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Perimeter of Rectangles
DATE:
You will need: a ruler 1 Find the length of each of the sides of the rectangles and label the diagrams. 2 By adding the side lengths, find the total perimeter for each of the rectangles
and write this in the centre of the rectangles.
a
b
c
d e
f
Extension: On another sheet of paper, draw two different rectangles that each have a total perimeter of 10 cm.
130
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Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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Rectangles on Grids
DATE:
You will need: a ruler 1 Find the length of each of the sides of the rectangles and label the diagrams. 2 Find the total perimeter for each of the rectangles and write this in the centre of
the rectangles. Use one of these strategies:
• length + width × 2 = perimeter
• 2 × length + 2 × width = perimeter
b
c
a
d
e
3 Which method did you use to find the perimeter of rectangle c?
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Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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Perimeter
DATE:
You will need: a ruler 1 Find the perimeter of each shape and label the diagram. a
c
b
d
2 Find the perimeter of each square and label the diagram. a
c
b
3 Which method did you use to find the perimeter of square c?
4 Complete the table.
Rectangle
Length
Width
a
7 cm
4 cm
b
12 cm
10 cm
c
5m
1m
d
10 m
20 m
Perimeter
Extension: On another sheet of paper, draw an irregular shape with a perimeter of 20 cm.
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Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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DATE:
Unit
14
STUDENT ASSESSMENT
You will need: a ruler 1 Find the missing side lengths on each rectangle and square
and add to the labels. c
a
b
d
2 cm 4 cm
3 cm
1 cm
e 8 cm
2 Find the perimeter of each rectangle and square. Write the perimeter
in each shape.
a
c
d
3 cm
3 cm 6 cm 5 cm
5 cm e
b 2 cm 2 cm
2 cm
4 cm
4 cm 3 Explain how you found the perimeter of the shape c in Question 2.
4 On another sheet of paper, draw a shape that has a total perimeter
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of 10 cm, and label each of the side lengths.
Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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Unit
3
Integers
NUMBER AND ALGEBRA Whole numbers: MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
ML
integers, negative numbers, number line, positive numbers, zero
LESSON PLAN
TUNING IN
1
SORTING INTEGERS You will need: sets of cards made from BLM 1 ‘Integer Cards 1’ Ensure there are enough cards from BLM 1 ‘Integer Cards 1’ for one set between two students. Have students sort the cards into positive and negative numbers. Ask, ‘What is similar about each group? What is different about each groups? What about zero?’
WHOLE-CLASS INTRODUCTION INTEGERS Discuss what makes up the set of integers (whole numbers). Talk about the symbol representing negative numbers, and look at the importance of zero. Introduce the term ‘integers’. Ask students where we see negative numbers in real life, e.g. thermometers, on graphs, etc. Collect ideas and comments on the board.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: newspapers or magazines, scissors, glue, poster paper, calculators, sheets of paper, NTO 6.1 ‘Calculator’, Student Book p. 144 ‘Knights in Maths’
TASK 1:
NEWSPAPER HUNT
Individually, have students look in newspapers or magazines for integers (positive and negative). Have students cut out and collect these on poster paper, explaining the context in which the integers were found. Challenge students with a minimum number of negative numbers and zeros for them to collect or set a time limit.
TASK 2:
INTERACTIVE TASK
Provide each student with a calculator. Have students create different numbers (up to millions) from a starting point. Ask, ‘If I begin with a 5, how can I create 5 million? How do I create negative 5?’ Have students record what they do on a sheet of paper. Repeat with a number of different numbers. Note: NTO 6.1 ‘Calculator’ could be used to support this activity.
TASK 3: STUDENT BOOK p. 144 ‘Knights in Maths’
TEACHING GROUP
You will need: sets of number cards made from BLM 1 ‘Integer Cards 1’ and BLM 2 ‘Number Line’, sheets of paper SORTING INTEGERS • For students who require support, provide them with a set of number cards made from BLM 1 ‘Integer Cards 1’ and a copy of BLM 2 ‘Number Line’ with the numbers from –10 to 10 filled in. Have students match the cards to the numbers on the number line, and then have them sort into piles of positive and negative numbers. Observe how students sort the numbers. LARGER RANGE • For students who require a challenge, ask them to order the number cards made from BLM 1 ‘Integer Cards 1’ from smallest to largest and record these on paper. Ask students to write a comment below their work, articulating the process they used for the sorting. Students could then be encouraged to place these on a number line to scale.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their integers posters from Independent Tasks, Task 1, and explain where they found negative numbers. On the back of their posters, have students write about what they learnt looking for the numbers. • Ask, ‘What is the difference between a negative number and a decimal?’ Explore ideas and comments on the board. • Give each student a number card from BLM 1 ‘Integer Cards 1’ and have students sort themselves into groups of positive and negative numbers. Give the zero card to one of the stronger students. Ask students from the different groups, ‘How do you know you are in the right group?’
LESSON PLAN
TUNING IN
2
ORDERING INTEGERS You will need: BLM 1 ‘Integer Cards 1’, BLM 3 ‘Integer Cards 2’ Provide each student with an integer card made from BLM 1 ‘Integer Cards 1’ or BLM 3 ‘Integer Cards 2’. Have students order themselves from smallest to largest. Note that these numbers may be sequential the first time the activity is completed, but it could be repeated with non-sequential numbers.
WHOLE-CLASS INTRODUCTION CONVERTING TO A NUMBER LINE You will need: number cards made from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’, Blu Tack, NTO 6.2 ‘Number Line’ Using the cards made from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’, have students add Blu Tack to their card and place it on a number line on the board. Note that NTO 6.2 ‘Number Line’ could be used for this activity. Discuss with students the importance of zero. Look at the way the 1 and –1 sit on either side of the zero. This activity could be expanded by having students complete counting patterns on the number line, including negative numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of number cards made from BLM 1 ‘Integer Cards 1’ and BLM 3’ Integer Cards 2’, long sheets of paper, LO 2001 ‘Scale Matters Negatives’, Student Book p. 145 ‘Ordering Integers’
TASK 1:
NUMBER LINES
Provide pairs of students with a range of number cards made from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’, e.g. from –20 to 20, and have them represent these numbers on a number line on a long sheet of paper. Have students explore a number sequence, e.g. counting backwards by 2s starting at 20. Adjust the activity based on students’ abilities. Repeat this activity, if required, either using the same number line with a different number sequence to explore or a new set of numbers represented on a number line.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 2001 ‘Scale Matters Negatives’, whereby students explore the use of scale on a number line including negative numbers.
TASK 3: STUDENT BOOK p. 145 ‘Ordering Integers’
TEACHING GROUP
You will need: BLM 1 ‘Integer Cards 1’, BLM 3 ‘Integer Cards 2’, paper, glue, long sheets of paper ORDERING GROUPS OF INTEGERS • For students who require support, provide them with the positive numbers and zero from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’. Have students order these numbers from smallest to largest and discuss how they worked this out. Repeat the activity with the set of negative numbers and zero. If students are ready, move them to combining the two sets. Students could then paste these to a long sheet of paper in order. LARGER NUMBER LINES • For students who require a challenge, have them create a number line between –30 and 30 on long sheets of paper. Have them write in all of the numbers and then include some decimal numbers and fractions. Determine which extra numbers students include according to their ability.
REFLECTION Select from the following to suit your class and their learning outcomes:
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• Using NTO 6.2 ‘Number Line’, place numbers –10 to 10 on the number line. Ask, ‘Where would a decimal such as 1.5 or 0.5 go on the number line? What about ½ and ¼?’ Have students locate these numbers on the number line. Explore the difference between these numbers and negative numbers. Have students who completed ‘Larger Range’ in the Teaching Group share their number lines. • Go through students’ responses to Student Book p. 141. Note any students who seem to be struggling with the numbers. • Create on a large piece of card a < or > sign. Have one student hold the card. Then provide two other students with a number card made from BLM 1 ‘Integer Cards 1’ or BLM 3 ‘Integer Cards 2’. Have students arrange themselves in order to create a correct number sentence. Note that it may be necessary to revise what < and > mean.
LESSON PLAN
TUNING IN
3
LOOK AT TEMPERATURE You will need: NTO 6.3 ‘Thermometer’ Show students NTO 6.3 ‘Thermometer’, and have them identify the positive numbers, the negative numbers and integers. Ask students to come to the board and represent different temperatures on the thermometer, including negative temperatures, and perhaps relate to locations where the temperature is –5ºC, e.g. snowfields.
WHOLE-CLASS INTRODUCTION ADDITION You will need: NTO 6.3 ‘Thermometer’, NTO 6.2 ‘Number Line’ Continuing with NTO 6.3 ‘Thermometer’, create scenarios for students to find the final temperature, e.g. ‘It was –1ºC when I woke up, but the temperature increased by 3 degrees. What is the temperature now?’ Have students use the thermometer to determine the answer, then have students write an equation. Repeat a number of times. Then move to a horizontal number line, completing similar equations. Note that NTO 6.2 ‘Number Line’ could be used with this activity.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 4 ‘Plotting Points’, NTO 6.4 ‘Grid Paper’, BLM 5 ‘1 cm Grid Paper’, Excel, Student Book p. 146 ‘Addition with Negative Numbers’
TASK 1:
PLOTTING POINTS
Have students complete BLM 4 ‘Plotting Points’. It may be necessary to review the process of plotting points, and NTO 6.4 ‘Grid Paper’ could be used to assist with this. To extend the activity, provide students with a copy of BLM 5 ‘1 cm Grid Paper’ and have them create their own tracing to solve.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using level-appropriate spreadsheet software, e.g. Excel. Have students create lists or grids of equations to explore the addition of negative numbers, e.g. 1 + –1 = 0, 1 + –2 = –1 and then –1 + 1 = 0, –1 + 2 = 1 and so on. As they are exploring, have students record comments about their findings.
TASK 3: STUDENT BOOK p. 146 ‘Addition with Negative Numbers’
TEACHING GROUP
You will need: NTO 6.2 ‘Number Line’, counters ON NUMBER LINES • For students who require support, use either NTO 6.2 ‘Number Line’ or counters and a drawn number line. Have students place their token at a starting place and then move it so many units forwards or backwards. Have students record this as an equation, e.g. 5 – 7 = –2. Repeat. Then provide students with a selection of equations (according to their ability) and have them work out the answers using the number line. EXTENDING EQUATIONS • For students who require a challenge, provide them with more challenging equations either containing 2-digit positive and negative numbers or equations that would require multiple steps, e.g. 3 – 8 + 2 – 10 = ?. Spend time discussing with students the appropriate layout and organisation of their work.
REFLECTION Select from the following to suit your class and their learning outcomes:
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• Revisit NTO 6.3 ‘Thermometer’ and provide students with different temperatures. Ask, ‘What would the temperature be if it dropped 5ºC?’ Have students show this using the thermometer. • Have students share their work from Independent Tasks, Task 1. Ask, ‘What is important about negative numbers on the grid? Where does this mean points will be plotted?’ Have students share tracings they may have created. Point out the use of negative numbers. • As a group, have a discussion about the general observations students may have made with what happens when two signs are next to each other in an equation, e.g. 3 + –4 = ?. Ask, ‘What does it mean? Is 3 – 4 = the same thing?’ If possible, extend the discussion to include equations like 3 + + 4 = ? and 3 – –4 = ?. Check to see whether or not students can make generalisations.
Home Tasks Select from the possible Home Tasks: • Have students explore at home to find positive and negative integers. Have students note where these integers are located. Have them bring samples to school and share with the group. • Have students create a number line from –10 to + 10. Have them write five equations that could be solved using the number line. Criteria could be set, e.g. two of the equations must include negative numbers.
Assessment • Have students complete Student Assessment p. 147. • Review with students Assessment Task Card 6.3. During the three lessons: • Note students who are experiencing difficulties with positive and negative numbers through reflection activities, e.g. using NTO 6.3 ‘Thermometer’ in Lesson Plan 3. • Keep a copy of students’ home task of creating a number line and writing five related equations as evidence of their understanding of integers. • Keep copies of students’ work examining the addition of negative numbers from Lesson Plan 3, Independent Tasks, Task 2. • Make a note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 147; if the student is experiencing difficulty: Review the difference between positive and negative numbers. Also review the writing of such numbers. Q 1 Q 2–3 Review how to order positive and negative numbers on a number line. This could be completed with the student drawing a number line and adding in values, or by using NTO 6.2 ‘Number Line’. Review the structure of the number line before and after the zero and the importance of zero in its construction. Q 4–5 Review the addition of numbers. First have the student work with positive numbers and then use either NTO 6.2 ‘Number Line’ or NTO 6.3 ‘Thermometer’ to explore the addition of positive and negative numbers. When the student is more confident, they could move away from the number line to complete equations. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 6.3 for specific recommendations. 2. Have the student work with only positive numbers for both order-type activities and addition-based activities, using a number line as support. Move to ordering activities and the addition of positive and negative numbers supported by a number line. 3. Review Nelson Maths: Australian Curriculum Year 5 Unit 1. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student apply the ideas and concepts to larger numbers. 2. Moving forwards to Nelson Maths: Australian Curriculum Year 6 Plus Unit 2. 3. Having the student complete Nelson Maths Building Mentals Strategies Big Book 6 Unit 7, pp. 16–17. 4. Extending the student in any of the listed activities or tasks by creating equations with multiple steps, e.g. 15 – 16 + 17 – 3 = ?. 5. Extending the student to consider the effect of negative numbers on multiplication and division equations. This could be explored through the use of calculators and spreadsheets.
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BLM
1
Integer Cards 1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
Teacher’s Note: This BLM can be enlarged, photocopied and cut up to use as number cards.
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BLM
2
Number Line
Paste here
Paste here
Paste here
Paste here
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
Teacher’s Note: This BLM can be cut out and individual sections used or a number of sections pasted together.
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BLM
3
Integer Cards 2
14
15
16
17
18
19
20
21
22
23
24
–23
–11
–12
–13
–14
–15
–16
–17
–18
–19
–20
–21
–22
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
Teacher’s Note: This BLM can be enlarged, photocopied and cut up to use as number cards.
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BLM
4
Plotting Points
Plot the following points on the grid. The first one has been done for you. (0, 4), (0, 0), (2, –3), (3, –4), (4, –3), (5, 0), (6, 4), (7, 5), (9, 4), (10, 0), (10, –3), (9, –5) When you have finished, turn the page on its side to find the letter. Remember in the reference (3, 2), the first number (3) is the one read on the x (horizontal) axis. The second number (2) is the one read on the y (vertical) axis. Where these meet is where the dot is drawn. When all the dots are on the grid, draw the line.
y 5 4 3 2 1 0 -1
x 1
2
3
4
5
6
7
8
9
10 11 12
-2 -3 -4 -5
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
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BLM
5
1 cm Grid Paper
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
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Year 6: Assessment Task Card
6.3
INTEGERS
Unit
3
Resources: a piece of paper per student
1
On a sheet of paper, have the student write three positive numbers and three negative numbers.
2
Have the student order the numbers from smallest to largest on a number line.
3
Have the student write and solve three addition equations related to their numbers, which contain the use of negative numbers.
4
Have the student draw a thermometer showing the temperature 5ºC.
5
Have the student use the thermometer to show what the temperature would be if it decreased by 7oC.
6
For the student who requires extension, have them find the answer to 10 + 16 – 23 = ?.
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
Year 6: Assessment Task Card
6.3
Unit
3
INTEGERS TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Review the difference between positive and negative numbers. This could be supported with the use of a number line using NTO 6.2 ‘Number Line’.
Q2
Use the number line in NTO 6.2 ‘Number Line’ to help the student organise the numbers. Examine the numbers that are the closest to zero and how they increase in size as they move away.
Q3
Use a tool like a number line to aid the student in developing equations. ‘On Number Lines’ in the Teaching Group in Lesson Plan 3 could be revisited.
Q4–5
Use NTO 6.3 ‘Thermometer’ to revisit thermometers and where to locate numbers, as well as how to move up and down the scale to find the answer.
If the student has demonstrated an understanding beyond the skills, consider: The student could be encouraged to work with larger numbers, including 2- and 3-digit numbers, and both processes of addition and subtraction of positive and negative numbers.
Q6
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution.
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Knights in Maths
DATE:
Why did the knight run about shouting for a tin opener? Match the numbers and words, and then write the letters below to find the answer. The first one has been done for you.
1
negative eight
H
4
four
I
–3
two
E
3
negative nine
F
5
ten
B
7
negative six
T
–8
negative three
N
–6
seven
S
–10
zero
U
–9
three
R
2
negative ten
D
–1
eight
Y
0
five
A
8
negative one
M
10
one
O
–2
negative two
W
–8
2
–8
5
–10
5
10
2
2
4
–3
–8
4
7
7
0
4
–6
–1
1
0
3
O
1
–9
5
3
Extension: On another sheet of paper, create your own puzzle.
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Integers (TRB pp. 134–135) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Ordering Integers
DATE:
1 Order each set of numbers from smallest to largest. a 2, 3, 5, 0, –1, –2
b 2, 4, 0, –2, 6, –4
c –1, –3, 5, 0, 3, –5, 1
d 19, 14, 0, –10, 15, –9, –13
2 Show the following numbers on a number line. a 2, –3, 0, 5, –4, 3
b –8, 7, –6, 5, 0, 1, 4
c 3, –10, 5, –8, –6, 0, 2
d –9, 5, 7, 8, –6, –4, –2
3 Circle the largest number in each pair. a –2 6
d 5 2
g –3 –1
b –7 –8
e 2 –5
h
c –2 3
f 0 –4
2 –5
4 Describe how you worked out which number was largest in Question 3e.
Extension: Using all of the digits 5, 6, 2, 1 a Write the smallest number. b Write the largest number. c What might the smallest negative number be?
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Integers (TRB pp. 134–135) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Addition with Negative Numbers
DATE:
1 During winter, the temperature was 5ºC. What would the temperature be if it was: a 4 degrees warmer?
b 5 degrees cooler?
c 7 degrees warmer?
d 10 degrees cooler?
2 Use the number line to solve each equation. a 10 + –6 =
b 2 + –5 =
c 3 + –8 =
d –2 + –3 =
3 Complete each equation. a 6 + –4 =
b –7 + –8 =
c –2 + 3 =
d 2 + –5 =
e 0 + –4 =
f 0 + –4 =
g 5 + 2 =
h 2 + –5 =
4 Describe any patterns you notice when adding negative numbers.
Extension: Use the graph to describe what is happening to the temperature
during the day.
temp oC
9 8 7 6 5 4 3 2 1 0 5am 6am 7am 8am 9am 10am 11am Noon 1pm 2pm 3pm -1 time -2 -3
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3
DATE:
Unit
STUDENT ASSESSMENT
1 Draw lines to match the numbers and words. –3
negative six
15
negative eighteen
0
twenty–one
–18
negative three
21
zero
–6
fifteen
2 Draw each set of numbers on a number line. a –5, 2, 0, 4, 8, –3
b –7, –1, 0, 5, –2, 8, 4
3 Circle the largest number in each pair. a 3 –5
b 1
c –7
0
–5
d 9
11
4 Use a number line to solve each equation. a –7 + –3 = b 4 + –5 = c 0 – 4 = d –1 – 3 = 5 Complete the equations. a 3 + –4 =
b –5 + 3 =
6 Circle the largest number:
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c –1+ –3 =
42 631
d 6 + –7 =
42 813
Describe how you worked this out.
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11
Cartesian System
NUMBER AND ALGEBRA Patterns and Algebra: MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
ML
Cartesian plane, coordinates, location, mapping, quadrant
LESSON PLAN
TUNING IN
PLOTTING POINTS You will need: BLM 5 ‘1 cm Grid Paper’, rulers Provide each student with a copy of BLM 5 ‘1 cm Grid Paper’. Have them rule an xy axis on the paper, labelling 0 to 10 on each axis. Then provide students with a series of points to plot. Use only use positive whole numbers. Review with students which number is plotted first (x, y).
y
1 x
WHOLE-CLASS INTRODUCTION CHECKING THE ANSWERS You will need: plotted points from the Tuning In activity, NTO 6.5 ‘Coordinates Grid’ Using NTO 6.5 ‘Coordinates Grid’, invite students to the board to plot the different points from the Tuning In activity. As students are plotting the points, ask, ‘How did you know to place the point there? Why is the zero important? If there is a zero in the coordinate pair, what does that mean?’ Have students check their answers. You can extend this activity by having students plot additional points.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: coloured chalk, A4 paper, a digital camera, Student Book p. 152 ‘Plot to Create’
TASK LARGEAXIS AXIS TASK 1: 1: LARGE Using a large space, e.g. a basketball court and chalk, create a large xy axis. Discuss with students the importance of putting arrows on the end of the axis as well labelling. Once created, provide different students with a coordinate and have them plot themselves onto the graph. The plotted points may create a line or a shape. Provide each student with at least one opportunity to be plotted. This activity could be varied by having students write their coordinates in large print on a sheet of A4 paper, and then they could hold it up once plotted and a digital photo taken.
TASK INTERACTIVE TASK TASK 2: 2: INTERACTIVE TASK GRID ACTIVITY Have students work independently on computers/tablets, using an online grid plotting activity, e.g. http://www. oswego.org/ocsd-web/games/BillyBug/bugcoord.html, to practise plotting coordinate points.
TASK 3: 3: SB p.XXX ‘Plot to Cr TASK STUDENT BOOK p. 152 ‘Plot to Create’
TEACHING GROUP
You will need: BLM 5 ‘1 cm Grid Paper’, sheets of poster paper, sticky-tape POSTER PAPER • For students who require support, draw an xy axis on large sheets of poster paper taped together and work in the number range from 0 to 10. Provide students with a grid reference and have them stand or place an object in the correct location. Talk about which number is first, e.g. (x, y). An easy way for students to recall x is plotted first followed by y is to say to them, ‘Go across the floor and up the stairs’. Provide students with a number of examples so they can practise plotting. WORKING BACKWARDS • For students who require a challenge, provide them with a copy of BLM 5 ‘1 cm Grid Paper’ and have them rule up an xy axis. Students create a drawing for which they will list the coordinates and swap with
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another student to draw (as with Student Book p. 148). Have students record the list of coordinates on a different sheet of paper.
REFLECTION Select from the following to suit your class and their learning outcomes: • If taken, provide students with a copy of the digital photo from Independent Tasks, Task 1. Have students write a reflection about what they learnt through completing the activity. • Give students some points that are already plotted. You could use NTO 6.5 ‘Coordinates Grid’. Have students identify the coordinates of each of the points. • Using the instructions created by one of the students from ‘Working Backwards’ in the Teaching Group, read out the coordinates and have students plot onto their own copy of BLM 5 ‘1 cm Grid Paper’. Ask, ‘Did you all get the same answer?’
LESSON PLAN
TUNING IN
2
POSITIVE AND NEGATIVE NUMBERS You will need: sheets of paper, rulers Have students rule and draw a number line with zero in the middle on a sheet of paper. Call out numbers and have students locate them on the number line, e.g. 4, –6, 1, –10. Check to see that students have the numbers in y the correct position. Spend some time reviewing the construction with negative and positive numbers and their order in relation to the zero.
WHOLE-CLASS INTRODUCTION
x
x
EXTENDING THE AXIS You will need: BLM 5 ‘1 cm Grid Paper’, rulers y Provide students with a copy of BLM 5 ‘1 cm Grid Paper’. Have them draw an axis that has all four quadrants in the middle of the page. Have them label each of the axis from –10 to 10. Discuss with students where the negative numbers lie, building on the Tuning In activity, and have students think about a thermometer when considering the y axis. Label each of the axis, x and y, and discuss the term ‘Cartesian System’.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: created grid from Whole-Class Introduction activity, LO 352 ‘Rainforest: Make a Walking Track’, Student Book p. 153 ‘Plotting on the Cartesian Axis’
TASK TASK 1: 1: PLOTTING ON THE CARTESIAN SYSTEM Have students use their axis created from the Whole-Class Introduction activity. Read out a series of coordinates and have students plot them onto the axis. These may or may not form a shape, but should include points from all four quadrants, e.g. (1, 5), (–2, 6), (–6, –4), (3, –1). Discuss with students which number is plotted first (x) and discuss the importance of the sign (+/–) in locating the point.
TASK 2: 2: INTERACTIVE TASK: TASK TASK LO 352 ‘RAINFOREST: MAKE A WALKING TRACK’ Have students work independently on computers/tablets using LO 352 ‘Rainforest: Make a Walking Track’. Students mark the route for a walking track on a map of a rainforest. Choose a section of track based on instructions about distances, compass directions and grid references.
TASK3: 3: SB STUDENT BOOK p.on 153 ‘Plotting on the Cartesian Axis’ TASK p.XXX ‘Plotting e Cartesian Axis’
TEACHING GROUP
y
You will need: BLM 5 ‘1 cm Grid Paper’, rulers PRACTISING WITH GRIDS • For students who require support, provide them with a copy of BLM 5 ‘1 cm Grid Paper’. Have them draw an axis just looking at positive numbers of the x axis and both positive and negative numbers of the y axis. Provide students with a number of coordinates and have them y plot them onto the axis. Check that students are locating the positions correctly. Then have students draw a number of points onto their grids and write the coordinates under each point.
x
MORE DETAIL • For students who require a challenge, provide them with a copy of BLM 5 ‘1 cm Grid Paper’. Either have them create their own picture and list the coordinates, or provide them with a set of coordinates. Ensure the coordinate sets include halves, e.g. (3½, 4).
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REFLECTION Select from the following to suit your class and their learning outcomes: • Using NTO 6.6 ‘Coordinates Grid’, review student answers from Independent Tasks, Task 1. Invite students to the board to plot the points, and ask, ‘Why did you place that point there?’ • Have students share their result from Student Book p. 149 ‘Plotting on the Cartesian Axis’. Ask, ‘What shape did you find? What other features did you add?’ • Show students a local map with an axis from a street directory and have them locate points using the coordinates, e.g. the coordinate for the school. Extend the activity by asking students to locate a feature and give the related coordinates. Discuss with students what happens if the feature goes across a number of grids.
LESSON PLAN
TUNING IN
3
BATTLESHIPS You will need: BLM 5 ‘1 cm Grid Paper’, NTO 6.5 ‘Coordinates Grid’ Have students draw up a –10 to 10 xy axis. On your grid, draw several ‘ships’ that are of varying line lengths. Write a list of these on the board, e.g. 3 cm ships × 4, 5 cm ship × 1 and so on. The aim of the game is for students to find and sink all of your ships in a set number of goes by calling out the coordinates, e.g. this may be 48 goes, so two guesses per student. You could use NTO 6.5 ‘Coordinates Grid’ to keep a record of the guesses.
WHOLE-CLASS INTRODUCTION GIVING THE COORDINATES You will need: NTO 6.5 ‘Coordinates Grid’, sheets of paper Using NTO 6.5 ‘Coordinates Grid’, construct a shape. Have students record on a sheet of paper the coordinates of each corner or main feature of the shape. Delete the shape, and using a student’s coordinates, recreate the shape using the NTO. Repeat a number of times, checking that students are recording the coordinates correctly.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3 You will need: a copy of a local map with a grid reference system or one overlaid, sheets of paper, Turtle Geometry, Student Book p. 154 ‘Listing the Coordinates’
TASK ONMAPS MAPS TASK 1: 1: ON Provide students with a copy of a local map with a grid reference system, e.g. from a street directory, or alternatively Google Maps can be used and a grid overlaid onto it. Have students create a pathway around the map between several locations, e.g. the school, local shops, the sportsground and home. Have students list the coordinates of the pathway on another sheet of paper. You can vary this activity by providing students with a number of coordinates and having them identify the feature at that location.
TASK 2: 2: INTERACTIVE TASK: TURTLE GEOMETRY TASK INTERACTIVE TASK Have students work independently on computers/tablets using Turtle Geometry to program a turtle around the page or through a maze. The program can be found at http://nlvm.usu.edu/en/nav/frames_asid_178_g_3_t_1. html?open=activities
TASK 3: 3: SB p.XXX ‘List the p. Coo4inates’ TASK STUDENT BOOK 154 ‘List the Coordinates’
TEACHING GROUP
You will need: BLM 5 ‘1 cm Grid Paper’ SQUARES AND RECTANGLES • For students who require support, provide them with a copy of BLM 5 ‘1 cm Grid Paper’ and have them draw an axis of –5 to 5. Have students draw a number of squares on the axis, and then list the coordinates of each square. Ask, ‘What do you notice?’ Students should notice common values between coordinate sets. Repeat with rectangles, again drawing out commonalities. LARGE-SCALE TURTLES • For students who require a challenge, say: ‘Imagine you have a large turtle to program, and the screen is the classroom floor. 1 move = 1 m. Program your turtle to move around the room without crashing into the furniture’. Set a number of destinations, e.g. from the student’s seat to the door, etc.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students do the Battleships activity from Tuning In in pairs, trying to guess the location of each Nelson Maths Australian Curriculum NSW
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other’s ships. It may be best to allocate the size and number of ships for the class for consistency. • Have students share the pathway they created on the local map from Independent Tasks, Task 1. Students could read out the coordinates and have other students follow on their own maps. • Have students share what they discovered from ‘Squares and Rectangles’ in the Teaching Group. • Have students share their large-scale turtle programing from ‘Large-Scale Turtles’ in the Teaching Group.
Home Tasks Select from the possible Home Tasks: • Provide students with a copy of BLM 5 ‘1 cm Grid Paper’ and have them create a basic map of their house or backyard on the grid. Have them create an axis over this, and then list coordinates of the important features of their room, house or yard. • Provide students with a copy of BLM 5 ‘1 cm Grid Paper’ with a –10 to 10 axis drawn on. Have students use this to create a set of instructions of coordinates to create a shape or picture of a rocket. Have students bring to class to share.
Assessment • Have students complete Student Assessment p. 155. • Review with students Assessment Task Card 6.11. During the three lessons: • Collect student work from ‘Working Backwards’ in the Teaching Group from Lesson Plan 1, as evidence of students’ understanding of using coordinates to create a picture. • Collect a copy of student work from Lesson Plan 3, Independent Tasks, Task 1, to provide evidence of students’ understanding of coordinates on a map system and how they relate to locating features. • Collect a copy of the rocket instructions created by students in Home Tasks as evidence of their understanding of coordinates. • Make notes of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of difficult areas.
Recommendations for Future Learning Specific to Student Assessment p. 155; if the student is experiencing difficulty: Q 1 Review the process of finding coordinates on an axis. Ask, ‘What value is read and written first?’ Review how to write a coordinate pair (2, 4). Review plotting of coordinates on a grid, e.g. the x is plotted, then the y. Review the process of reading the scale. Q 2 Q3 Practise looking at maps, having the student locate and identify features and then giving coordinates for the features. The student can practise reading coordinates to find a feature. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 6.11 for specific recommendations. 2. Have the student work with an axis, where they need to plot themselves at coordinate locations. 3. Provide laminated grids with an axis and have the student practise plotting coordinates with whiteboard markers. 4. Provided laminated grids with a drawn shape, and have the student identify the coordinates of the corners of the shape. 5. Have the student practise creating their own axis on grid paper using rulers and developing the scale. 6. Review Nelson Maths: Australian Curriculum Year 5 Unit 12. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student work with larger scales. 2. Having the student work with scales that are not 1:1, e.g. scales of 5 or 10. 3. Moving forward to Nelson Maths: Australian Curriculum Year 6 Plus Unit 10. 4. Having the student complete more complex plotting. 5. Having the student develop pathways on maps, using the coordinate system.
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Plot to Create
DATE:
1 Plot the following coordinates. Complete each set as a separate part of the
drawing, joining the points together.
a
Part A: (1, 5), (4, 1), (12, 1), (15, 5), (1, 5)
b
Part B: (12, 5), (12, 14), (5, 6), (12, 8)
c
Part C: (3, 5), (3, 15), (1, 13), (3, 13)
2 When completed, colour your picture. 3 Then add some of your own features and give the coordinates.
y 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
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2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 x
Cartesian System (TRB pp. 148–149) Patterns and algebra MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
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Plotting on the Cartesian Axis
DATE:
1 Plot the following coordinates. Join the points together in order.
a
(3, 0)
b
(6, 4)
c
(2, 4)
d
(0, 7)
e
(–2, 4)
f
(–6, 4)
g
(–3, 0)
h
(–6, –5)
i
(–3, –4)
j
(0, –3)
k
(3, –4)
l
(6, –5)
m
(3, 0)
2 What shape have you made? 3 Add features to your picture and list the relevant coordinates.
y 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 –8 –7 –6 –5 –4 –3 –2 –1
x
-1 -2 -3 -4 -5 -6 -7 -8
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List the Coordinates
DATE:
1 List the coordinates of each of the points indicated on the image.
y 8 B
C
F
G
7J
K
N
O
D
E
H
6 I
L
M
P
Q
5 4 b
c
a
z
x
y
3 2 1
e d 0 U –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 V –2
x
T
–3 –4 –5 A
W –6
S
R
–7 –8
154
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DATE:
Unit
11
STUDENT ASSESSMENT 3
1 List the coordinates for
B
each of the corners of
y A
2
the shape.
1 –4 –3 –2 –1 1 2 3 4 0 –1
C
x
D
–2 –3 2 Plot the following points. What shape
a (0, 2)
b (1, 1)
c (2, 0)
f (–4, –2) g (–3, –1) h (–2, 0)
do they make?
d (3, –1)
e (4, –2)
i (–1, 1)
3 y 2 1 0 –4 –3 –2 –1 1 2 3 4
x
–1 –2 –3 3 Give the central coordinates for the following features: a the school
b the oval
c the shop
d the playground 4 y 3 2 1
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 0
x
–1 –2 –3 –4 Unit
11
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Scope and Sequence
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Kindergarten
Addition and subtraction
Unit 17 Beginning Addition Unit 19 More About Addition Unit 27 Subtraction Unit 28 More About Subtraction Unit 30 Addition, Subtraction and Money
Number and Algebra Unit 1 Numbers to 5 Whole numbers Unit 2 Counting to 5 Unit 3 Groups of Things Unit 5 More Counting Unit 6 Dot Patterns Unit 8 Numbers to 10 Unit 9 Counting with Numbers to 10 Unit 10 Ten Frames Unit 11 Counting and Comparing Groups Unit 13 Ordinal Number Unit 16 Understanding More About Numbers to 10 Unit 22 Numbers Beyond 10 Unit 24 More About Numbers to 20
NSW Mathematics K–10 Syllabus strand and substrand
Unit 12 Developing Mental Strategies for Addition Unit 25 Subtraction Unit 26 More About Subtraction Unit 30 Addition and Subtraction
Unit 1 Recognising Numbers to 20 Unit 2 Counting to 20 Unit 5 Modelling Numbers Unit 6 Number Lines Unit 8 Numbers Beyond 20 Unit 15 2-digit Numbers Unit 16 More About 2-digit Numbers Unit 20 Money Unit 21 More About Money Unit 28 Place Value
Year 1
Unit 4 Numbers Up Unit 5 Strategies for Addition Unit 6 More Strategies for Addition Unit 9 Solving Problems with Addition Unit 11 Strategies for Subtraction Unit 12 Subtraction Unit 15 More About Subtraction Unit 16 Addition and Subtraction
Unit 1 Counting Unit 2 Modelling Numbers Unit 4 Numbers up to 1000 Unit 17 Money
Year 2
Unit 1 Odd and Even Numbers Unit 2 Numbers to Tens of Thousands Unit 3 Place Value Unit 31 Money
Year 4
Unit 5 Mental Unit 13 Addition and Strategies for Subtraction Addition Unit 31 Money Unit 6 Addition Unit 8 Place Value Unit 12 Mental Strategies for Subtraction Unit 13 Subtraction Unit 14 Connections Between Addition and Subtraction Unit 15 Solving Addition and Subtraction Problems
Unit 1 Numbers! Numbers! Numbers! Unit 2 Numbers to 10 000 Unit 3 More About Numbers to 10 000 Unit 8 Place Value Unit 9 More About Place Value Unit 32 Money
Year 3
Unit 1 Place Value and BODMAS Unit 3 Integers Unit 6 Prime Numbers Unit 7 Composite Numbers Unit 18 Problems with Positive and Negative Numbers
Year 6
Unit 2 Addition and Unit 2 All Four Subtraction Operations Unit 6 Estimation Unit 31 Financial Plans
Unit 1 Place Value and BODMAS Unit 3 Factors and Multiples Unit 6 Estimation
Year 5
Note: the Working Mathematically outcomes of Communicating, Problem Solving and Reasoning are integrated throughout the activities and tasks in the program.
Nelson Maths: Australian Curriculum NSW Scope and Sequence across the Year Levels
Nelson Maths Australian Curriculum NSW
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Year 2
157
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Kindergarten
Patterns and algebra
Unit 14 Patterns
Fractions and decimals Unit 23 Halves
Number and Algebra Unit 20 Grouping and Multiplication and Sharing division
NSW Mathematics K–10 Syllabus strand and substrand
Unit 18 Patterns Unit 19 Number Patterns
Unit 13 Halves and Quarters
Unit 3 Skip Counting Unit 9 Grouping and Sharing
Year 1
Unit 26 Fractions Unit 27 More About Fractions Unit 28 Decimals
Unit 18 Mental Strategies for Multiplication Unit 19 More About Mental Strategies for Multiplication Unit 22 Multiplication Unit 24 Division Unit 25 More About Division
Year 3
Unit 18 Number Unit 21 Patterns Patterns Unit 19 More Number Patterns
Unit 7 Fractions Unit 30 More About Fractions
Unit 23 Multiplication Unit 24 More About Multiplication Unit 27 Division Unit 28 More About Division
Year 2
Unit 21 Number Patterns Unit 28 Number Sentences Unit 32 Word Problems
Unit 18 Decimals to 2 Decimal Places Unit 23 Equivalent Fractions Unit 24 Counting with Fractions Unit 27 Fractions and Decimals
Unit 6 Number Sequences: 3s, 6s and 9s Unit 7 Number Sequences 4s, 8s and 7s Unit 10 Multiplication Facts (Times Tables) Unit 11 Multiplication Facts and Related Division Facts Unit 15 Multiplication and Division Strategies Unit 16 More Multiplication and Division Strategies
Year 4
Year 6
Unit 21 Number Patterns Unit 28 Number Sentences
Unit 13 Addition and Subtraction of Decimals Unit 17 Fractions Unit 18 Decimals to Three Places Unit 23 Addition of Fractions Unit 24 Subtraction of Fractions Unit 27 Fractions and Decimals
Unit 11 Cartesian System Unit 21 Number Sequences
Unit 12 Decimal Representations of the Metric System Unit 14 Addition and Subtraction of Decimals Unit 15 Multiplication of Decimals Unit 17 Fractions Unit 23 Addition of Fractions Unit 24 Subtraction of Fractions Unit 27 Fractions of a Quantity Unit 28 Fractions, Decimals and Percentages Unit 31 Percentage Discounts
Unit 2 All Four Unit 3 Factors and Operations Multiples Unit 7 Multiplication of Large Numbers A Unit 10 Multiplication of Large Numbers B Unit 11 Division with Remainders Unit 15 Mental Strategies
Year 5
158
Scope and Sequence
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Unit 22 Data
Unit 11 Our Community – Data
Unit 27 Data
Data
Unit 25 Our Class
Unit 20 Chance
Unit 29 Chance
Unit 7 Position
Unit 24 Chance
Unit 10 Position
Unit 29 Symmetry
Unit 31 3D Objects
Unit 16 Time
Unit 30 Capacity Unit 10 Mass
Unit 4 Length Unit 23 Area
Year 3
Statistics and Probability Chance
Unit 7 Position
Unit 8 Transformation with 2D Shapes
Unit 26 3D Objects
Unit 14 Telling the Time Unit 21 More About Time
Unit 20 Capacity Unit 13 Mass
Unit 3 Length Unit 25 Area
Year 2
Unit 17 Angles
Unit 4 Position
Position
Unit 4 2D Shapes
Unit 17 3D Objects
Unit 14 Time Unit 22 More AboutTime
Unit 29 Capacity Unit 23 Mass
Unit 10 Length and Area
Year 1
Angles
Unit 12 2D Shapes
Unit 18 More About Shapes and Objects
3D Space
2D Space
Unit 15 Time Unit 29 More About Time
Unit 26 How Much Does It Hold? Unit 21 Mass
Unit 7 Length and Area
Kindergarten
Time
Volume and capacity Mass
Measurement and Geometry Length Area
NSW Mathematics K–10 Syllabus strand and substrand
Unit 16 Volume and Capacity Unit 5 Mass and Capacity
Unit 9 3D Objects
Unit 19 Chance
Unit 22 Angles Unit 33 Angle Applications
Unit 12 Grid References
Unit 20 Collecting Data Unit 20 Collecting Data Unit 29 Displaying Data Unit 29 Data Displays Unit 30 Interpreting Unit 30 Interpreting Data Data
Unit 19 Chance
Unit 22 Angles
Unit 12 Mapping
Unit 8 Regular Shapes Unit 8 Shapes Unit 33 Patterns Unit 32 Transformations
Unit 9 Drawings of 3D Objects
Unit 20 Collecting Data Unit 29 Data Displays Unit 30 Interpreting Data
Unit 19 Chance
Unit 22 Angles
Unit 10 Mapping/Grid References
Unit 8 2D Shapes and 3D Objects Unit 9 Prisms and Pyramids Unit 8 2 Shapes and 3D Objects Unit 32 Transformations Unit 33 Use of Transformations
Unit 25 Time Unit 25 Time Unit 25 Time Unit 26 Time Problems Unit 26 Time Problems Unit 26 Timetables and Timelines
Unit 5 Mass and Capacity
Unit 17 Volume Unit 5 Mass and Capacity
Year 6
Unit 4 Area and Perimeter Unit 13 Length and Area Problems
Year 5
Unit 4 Length, Area Unit 4 Length and and Volume Temperature Unit 14 Perimeter and Unit 14 Perimeter Area Unit 16 Area
Year 4
Notes
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Notes
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K– 6
NSW 1
2
3
4
5
6
9780170352864
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9780170352970
9780170352987
9780170352994
9780170353007
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9780170251525
9780170251532
9780170131858
9780170131841
9780170131865
9780170131872
STUDENT BOOKS
TEACHER’S RESOURCE BOOK WITH NELSON TEACHING OBJECTS CD & REPRODUCIBLE RESOURCES CD
BUILDING MENTAL STRATEGIES BIG BOOKS
BUILDING MENTAL STRATEGIES SKILL BOOKS NSW
NELSON MATHS FACTS STUDENT HANDBOOK 9780170127684
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STUDENT BOOK AND TEACHER’S RESOURCE SAMPLER
K
LEVEL
NELSON MATHS Australian Curriculum NSW
AUSTRALIAN CURRICULUM
AUSTRALIAN CURRICULUM
NSW
K– 6
o o k B a t n n e d d u t S her ’s Resour c c e a Te SAMPLER
STUDENT BOOK AND TEACHER’S RESOURCE SAMPLER
Written for the NSW Mathematics K–6 Syllabus for the Australian Curriculum Glenda Bradley, Pauline Rogers, Yale Mercieca, Lauren White & Aaron Tait PRI 8368 NMAC NSW Sampler Cover.indd 3
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Nelson Maths: Australian Curriculum NSW Sampler
Text: Glenda Bradley, Pauline Rogers and Brian Murray Series consultant and co-author: Jay Dale Series consultant (NSW): Brian Murray Editor: Sarah Russell Designers: Mark Sanders and Stella Vassiliou Cover designer: Ivana Tendean Cover illustration: Ned Culic Text illustrations: Mary Ann Furness, Colby Heppell, Rob Mancini, Joe Sciglitano Production controller: Renee Cusmano Acknowledgements The authors and publisher would like to acknowledge permission to reproduce material from the following source: NSW Mathematics K–10 Syllabus © Board of Studies, NSW for and on behalf of the Crown in right of the state of New South Wales, 2013 The Board of Studies takes no responsibility for errors in the reproduction of the Material supplied by the Board of Studies to the Publisher.
ACARA Copyright Notice All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2014.
For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum. Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors. Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au. This material is reproduced with the permission of ACARA.
Every effort has been made to trace and acknowledge copyright. However, if any infringement has occurred, the publishers tender their apologies and invite the copyright holders to contact them.
Text © 2014 Cengage Learning Australia Pty Limited Illustrations © 2014 Cengage Learning Australia Pty Limited
Copyright Notice This Work is copyright. No part of this Work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without prior written permission of the Publisher. Except as permitted under the Copyright Act 1968, for example any fair dealing for the purposes of private study, research, criticism or review, subject to certain limitations. These limitations include: Restricting the copying to a maximum of one chapter or 10% of this book, whichever is greater; Providing an appropriate notice and warning with the copies of the Work disseminated; Taking all reasonable steps to limit access to these copies to people authorised to receive these copies; Ensuring you hold the appropriate Licences issued by the Copyright Agency Limited (“CAL”), supply a remuneration notice to CAL and pay any required fees.
Cengage Learning Australia Level 7, 80 Dorcas Street South Melbourne, Victoria Australia 3205 Phone: 1300 790 853 Cengage Learning New Zealand Unit 4B Rosedale Office Park 331 Rosedale Road, Albany, North Shore NZ 0632 Phone: 0800 449 725 For learning solutions, visit cengage.com.au Printed in Australia by RR Donnelley Asia Printing Solutions Limited 1 2 3 4 5 6 7 18 17 16 15 14
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K– 6
o o k B a t n n e d d u t S her ’s Resour c c e a Te SAMPLER Glenda Bradley, Pauline Rogers, Yale Mercieca, Lauren White & Aaron Tait
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Contents Introduction Kindergarten
3
Lesson Plan BLM 8 ‘Blank Cards’ BLM 15 ‘Dot Patterns to 6’ BLM 16 ‘Make a Dice’ BLM 17 ‘Number Fan: Numerals’ BLM 20 ‘In the Pond’ BLM 21 ‘Speckled Frogs’ Assessment Task Card Student Book
6 6 10 11 12 13 14 15 16 18
Lesson Plan Student Book
22 22 26
Year 1 Lesson Plan BLM 6 ‘Blank Number Line’ BLM 14 ‘100 Chart’ BLM 15 ‘Make Your Own 100 Chart’ Assessment Task Card Student Book
30 30 34 35 36 37 38
Lesson Plan Student Book
Statistics and Probability Unit 20 Chance Lesson Plan Student Book
Number and Algebra Unit 18 Decimals to 2 Decimal Places Lesson Plan BLM 34 ‘Decimal Numbers and Words 2’ BLM 42 ‘Symbols’ Assessment Task Card Student Book
Unit 8 Shape Lesson Plan Student Book
42 42 46
Unit 1 Place Value Lesson Plan BLM 2 ‘5-digit Number Expander’ Assessment Task Card
Student Book
Number and Algebra
Unit 14 Perimeter
BLM 1 ‘Number Cards’ BLM 2 ‘Arrow Cards 1’ BLM 3 ‘Arrow Cards 2’ BLM 4 ‘Number Stairs’ Assessment Task Card Student Book
50 50 54 55 56 57 58 60
Measurement and Geometry Unit 10 Position Lesson Plan Student Book
Year 3 Lesson Plan BLM 1 ‘Number Cards 1’
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Student Book
114 114 118 119 120 122 126 126 130
Year 6 Number and Algebra Unit 3 Integers Lesson Plan BLM 1 ‘Integer Cards 1’ BLM 2 ‘Number Line’ BLM 4 ‘Plotting Points’ BLM 5 ‘1 cm Grid Paper’ Assessment Task Card Student Book
134 134 138 139 140 141 142 143 144
Number and Algebra
Number and Algebra Unit 1 Numbers, Numbers, Numbers
Lesson Plan
BLM 3 ‘Integer Cards 2’
64 64 68
106 106 110
Number and Algebra
Measurement and Geometry
Lesson Plan
94 94 98 99 100 101 102
Year 5
Year 2 Unit 4 Numbers Up to 1000
86 86 90
Year 4
BLM 1 ‘Place-Value Chart’
Measurement and Geometry Unit 10 Length and Area
Student Book
77 78 79 80 82
Measurement and Geometry
Number and Algebra Unit 8 Numbers Beyond 20
Assessment Task Card
BLM 33 ‘Decimal Numbers and Words 1’
Measurement and Geometry Unit 12 2D Shapes
BLM 3 ‘Blank Chart’ BLM 4 ‘Blank Cards’
Number and Algebra Unit 6 Dot Patterns
BLM 2 ‘Number Cards 2’
72 72 76
Unit 11 Cartesian System Lesson Plan Student Book
Scope and Sequence
148 148 152 156
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Introduction This Sampler presents units from the new primary mathematics program – Nelson Maths: Australian Curriculum NSW – available for implementation in 2015. This exciting new mathematics program supports the Australian Curriculum content strands of Number and Algebra, Measurement and Geometry, and Statistics and Probability from Kindergarten to Year 6. The program also integrates the Working Mathematically outcomes of Communicating, Problem Solving and Reasoning throughout the activities and tasks for each year level. Assessment is an essential part of Nelson Maths: Australian Curriculum NSW, providing teachers with a variety of opportunities to assess their students’ learning for future planning.
6
Two units from each year level from Kindergarten to Year 6 are included in this Sampler. One of the units for each year level is from the strand of Number and Algebra, to showcase the sequential development of this content throughout the year levels.
6
Teachers can be assured that Nelson Maths: Australian Curriculum NSW NSW continues the tradition of offering teachers choice when selecting tasks to suit the needs of their students. AUSTRALIAN CURRICULUM
AUSTRALIAN CURRICULUM
General Overview
NSW
er’ Teacrhce Bs
Nelson Maths: Australian Curriculum NSW supports the implementation of the NSW Syllabus for the Australian Curriculum: Mathematics K-10. The units cover the content strands of Number and Algebra, Measurement and Geometry and Statistics and Probability K–6, and integrate the Working Mathematically strands of Communicating, Problem Solving and Reasoning throughout the activities and tasks.
sou Re
This edition of Nelson Maths provides: • up to 33 units of work, specifically written to match the Australian Curriculum • extensive assessment opportunities including 30+ Assessment Task Cards, Student Assessment pages and Mid- and End-of-Year Tests • numerous hands-on tasks and investigative activities where teachers have the opportunity to choose tasks that best suit the needs of their students
• interactive activities in every unit, incorporating ICT and utilising classroom computers and interactive whiteboards
Nelson Maths: Australian Curriculum NSW is based on between 30 and 35 units of work for each year level. Each unit of work is divided into three 6 teaching 2 Lesson Plans. A Lesson Plan can be taught over one or more 5 sessions depending on the needs of students. While the Lessons Plans% 8 5.. 6 are sequential and should be taught in the order they appear in7the63 unit, teachers have the flexibility to complete a number of activities from a Lesson Plan over a number of days – to cater for the learning requirements of their class.
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Pauline Rogers
• an extensive range of interactive Nelson Teaching Objects and reference to Learning Objects from Education Services Australia • specific recommendations for future learning experiences, including both scaffolded and extension activities • over 50 unit, resource, assessment and planning BLMs.
YEAR 6
NSW
NELSON MATHS Australian Curriculum
AUSTRALIAN CURRICULUM
NSW
6
dent Book Stu
guide a consolidated invaluable Facts is It is an Maths Nelson student years Mathematics. to middle resource for students,and is fully and parents, up-to-date on CD-ROM. teachers materials teachers, by interactive headings supported under topic is arranged Mathematics the current The handbook through follow the that closelyThis format is carriednt learning curriculum. and skill-developme interactive on the CD-ROM. yet featured objects a compact Facts is that will Maths resource facts Nelson practical mathematical comprehensive with basic and CD-ROM students sequential provide The handbook nitions. an easy-to-follow and defi consolidate provide that will materials of concepts understanding. summary mathematical students’
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AUSTRALIAN CURRICULUM
Nelson Maths: Australian Curriculum NSW supports the implementation of the NSW Syllabus for the Australian Curriculum: Mathematics K-10. The units cover the content strands of Number and Algebra, Measurement and Geometry and Statistics and Probability K–6, and integrates the Working Mathematically strands of Communicating, Problem Solving and Reasoning throughout the activities and tasks.
The Nelson Maths: Australian Curriculum NSW Edition Student Books feature: • engaging tasks that students can complete independently or in groups • three Student Book pages per unit • one Student Assessment page per unit • the linking NSW Syllabus for the Australian Curriculum - Mathematics K-10 content sub-strand, outcome and code for each unit • a Glossary of mathematical terms.
Nelson Maths Facts CVR.indd 1
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Unit
6
1 to 6, using small paper plates and dot stickers. Get them to arrange the plates in a random order in front, and using NTO K.20 ‘Dice’ roll a number and get them to point to a plate with the same number of dots. Repeat, gradually rolling the dice more quickly.
Dot Patterns
Whole numbers: MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
ML
LESSON PLAN
TUNING IN HOW MANY CAN YOU SEE?
1
FIVE LITTLE SPECKLED FROGS
Give the student a set of cards made from BLM 15 ‘Dot Patterns to 6’. Present NTO K.4 ‘Numbers’ and randomly generate a number from 0 to 6. Have them read the number and find the matching number card.
3
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is more than the dot pattern displayed.
4
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is less than the dot pattern displayed.
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, a large number fan and one for each student made from BLM 17 ‘Number Fan: Numerals’ Ask students how many speckled frogs were sitting on the log. Show students large cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns and invite a student to find a dot plate that shows five. Show students the enlarged number fan made from BLM 17 ‘Number Fan: Numerals’ and all the numbers that are on it. Tell students that you will hold up each number, and when you get to the number that matches the plate, students put up their hand. Select another dot plate and then ask a student to find the corresponding number on the number fan. Give a number fan to each student, and hold up various dot plates, getting students to find the matching number on their number fan.
Note: Choose from Tasks 1, 2 or 3. You will need: NTO K.20 ‘Dice’ or a large dice, BLM 16 ‘Make a Dice’, counters, NTO K.19 ‘How Many Dots?’, Student Book p. 18 ‘Dot Plates’
6
You will need: BLM 20 ‘In the Pond’, counters, a dice, NTO K.22 ‘What Number Is This?’, Student Book p. 19 ‘Glub! Glub!’
IN THE POND
Give a copy of BLM 20 ‘In the Pond’ to pairs of students. Each student will need about 20 counters that are the same colour but different from their partner’s. Students take it in turns to roll a dice and then place one counter on a lily pad that matches the dice. The counter can be placed on a word, numeral or dot pattern that matches the dice. If they cannot find a lily pad to match the dice, they miss that turn. The student who places the most counters on the board is the winner.
INTERACTIVE TASK
Have students use NTO K.19 ‘How Many Dots?’.
STUDENT BOOK p. 18 ‘Dot Plates’
TASK 2:
TEACHING GROUP
DOT PATTERNS
TARGETED ASSESSMENT
If the student is experiencing difficulty:
Note: Choose from Tasks 1, 2 or 3.
TASK 1:
K.6
Kindergarten: Assessment Task Card Unit
INDEPENDENT TASKS
SAME, SAME
Ask students what they can see on the sides of a dot dice on NTO K.20 ‘Dice’ or a large dice. Explain that they are going to make their own dice using BLM 16 ‘Make a Dice’. In one of the squares students draw one dot. In the next square they draw two dots and so on until each side has been filled with dots for each number from 1 to 6. Students cut out the dice net and assemble. Note: students may need teacher, older peer or parent support to assemble. Have students play ‘Same, Same’ with a partner. Students roll their dice, and when the numbers rolled are the same, they collect a counter. The first pair to collect six counters is the winner.
Q1
Have the student practise reading dot patterns by playing board games, e.g. ‘Number Game Board’ in Nelson Maths Building Mental Strategies Big Book 1, pp. 12–13.
Q2
Have the student use NTO K.19 ‘How Many Dots?’ set to numbers from 0 to 6 and randomly generate either dot patterns or numerals for recognisation.
Q3
Give the student the set of cards made from BLM 15. Using NTO K.19 to generate a number between 0 and 6, have the student find a card with the same dot pattern. Then have them find the cards that show more and show less.
Q4
Select a card from BLM 15, and have the student guess the card by asking ‘Is it less?’ questions, e.g. ‘Is it less than 3?’
INTERACTIVE TASK
Have students use NTO K.22 ‘What Number Is This?’. Vary the range of numbers to suit the abilities of students.
You will need: a set of paper plates with dot patterns or a set of enlarged cards made from BLM 15 ‘Dot Patterns to 6’, round counters, paper plates, stickers, NTO K.20 ‘Dice’, poster paper
TASK 3:
MAKING DOT PLATES • For students who require support, you may need to allow more time for them to view dot patterns and provide many experiences to view common arrangements of dots. Show students a paper plate or card, and ask them how many dots they can see. Get them to select that many counters and then make the arrangement on a paper plate. Continue showing them a plate or card and they select that amount of counters to make the same arrangement. Students can make their own set of dot plates for numbers
Teacher’s Resource
2
DOTS AND NUMBERS
INDEPENDENT TASKS
Nelson Maths Australian Curriculum NSW
Present NTO K.19 ‘How Many Dots?’ and check if the student can automatically recognise how many dots.
WHOLE-CLASS INTRODUCTION
You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, paper plates, round counters Hold up a card made from BLM 15 ‘Dot Patterns to 6’ or a plate for a few seconds and ask, ‘What did you see?’ Hold up the card or plate again to check. Repeat. When students are comfortable identifying the number of dots, give each student a paper plate and counters. Hold up a card or plate with three dots for a few seconds. Ask students how many dots they can see and have them make the arrangement of dots with their counters. Ask, ‘Can you make three another way?’ Explore different arrangements. Repeat for other numbers.
6
K.6
DOT PATTERNS
Resources: NTO K.19 ‘How Many Dots?’, BLM 15 ‘Dot Patterns to 6’, NTO K.4 ‘Numbers’
1
2
You will need: NTO K.21 ‘Five Little Speckled Frogs’, enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Present NTO K.21 ‘Five Little Speckled Frogs’, and while singing, hold up fingers matching the number of frogs in each verse. Next, display dot plates with the numbers 1 to 5 represented. This time, as students sing, invite a student to hold up a dot plate to match the number of frogs.
DOT PATTERNS
TASK 3:
LESSON PLAN
TUNING IN
WHOLE-CLASS INTRODUCTION
TASK 2:
6
Select from the following to suit your class and their learning outcomes: • Ask students to show all the different ways they made five on Student Book p. 17. Make a ‘Fabulous Five’ poster recording the different ways students found to represent five. • Ask students how they were able to recognise the numbers quickly. Discuss what they see when they look at arrangements for five and six. Ask which numbers are easy to recognise and discuss why.
You will need: NTO K.7 ‘Can You Count?’ Present NTO K.7 ‘Can You Count?’ showing a collection of objects, and ask, ‘How many can you see?’. Invite a student to point to each item while counting aloud to check if the response is correct. Repeat. This is a good time to identify students who may still be having difficulty counting collections.
TASK 1:
Unit
REFLECTION
five, four, less, more, one, same, six, three, two, zero
9 780170 353007
Kindergarten: Assessment Task Card
DOT PATTERN POSTER • For students who require a challenge, have them work with a greater range of numbers. Get them to choose a number, and using a paper plate and counters, have them explore different ways they can represent the number. Students can record their findings by making a poster.
NUMBER AND ALGEBRA
CD-ROMs inside
ISBN: 978-0170353007
For learning solutions, visit cengage.com.au
STUDENT BOOK p. 19 ‘Glub! Glub!’
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
TEACHING GROUP You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, BLM 21 ‘Speckled Frogs’, scissors, BLM 8 ‘Blank Cards’ © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution.
Unit 6
Kindergarten
Nelson Maths Australian Curriculum NSW
7
Dot Patterns
16
Teacher’s Resource
Kindergarten
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Dot Plates
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Glub! Glub!
DATE:
*
Show 5 in different ways. Use a paper plate and some counters.
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DATE:
BLM
15
Draw dots on each frog to match the number of bugs it will eat. One has been done for you.
BLM
20
Dot Patterns to 6
In the Pond
Draw some of the ways you found.
4
5
3
the lily pad, write the matching number word. * On One has been done for you.
2
*
three
1
two
five
Play a game.
six
Draw a line matching each frog to a lily pad and a bug. One has been done for you.
You will need:
• a partner
one
five
6
• a dice
How to play:
four
• In turn, roll a dice. • Each time you roll 5, cover one of the paper plates above with a piece of paper.
five
• The first player to cover all their plates wins.
six
one
two © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution.
18
Unit
6
Unit
Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
19 06/05/14 2:06 PM
Unit
Unit
6 16
Whole numbers MAe-4NA
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
Teacher’s Note: Patterns can be made on paper plates or printed, laminated and made into sets of cards.
6
Unit
9
Whole numbers MAe-4NA
11
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Teacher’s Note: This BLM can be printed and laminated to use for other number activities.
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Units in the Sampler For each Number and Algebra unit in this Sampler, there are: • three Lesson Plans, which include Tuning In, Whole-Class Introduction, Independent Tasks, Teaching Group tasks, Reflection, Home Tasks, Assessment and Recommendations for Future Learning • accompanying unit and resource BLMs • an Assessment Task Card • three Student Book pages and one Student Assessment page that accompanies each unit. Also included in this Sampler are the Lesson Plans, Student Book and Student Assessment pages from an additional unit for each year level.
Components The following components are available in 2015 for each year level from Kindergarten to Year 6.
Teacher’s Resource The Teacher’s Resource Book provides: • three Lesson Plans for each unit • an Assessment Task Card with a linking Targeted Assessment Task Card • Tests A and B • assessment and planning BLMs • a CD-ROM containing all Nelson Teaching Objects (NTOs) • a CD-ROM containing all BLMs, tests, answers and Assessment Task Cards as printable PDFs.
Pauline Rogers
7
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CD-ROMs inside
If you experience difficulties using this product, email: [email protected]
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ISBN: 978-0170352987
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The Student Book provides: • three Student Book pages for each unit (there is one Student Book page for each Lesson Plan) • one Student Assessment page for each unit (this page enables both student and teacher to monitor and assess the student’s mathematical understandings throughout the unit of work) • a link to the strand, sub strand and outcome of the NSW Mathematics K-10 Syllabus for the Australian Curriculum
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Student Book and Teacher’s Resource Sampler
07/05/14 3:23 PM
Nelson Teaching Objects and Learning Objects Nelson Maths: Australian Curriculum NSW is committed to integrating Information and Communication Technology (ICT) into the classroom. The program provides a large number of Nelson Teaching Objects (NTOs) available for use on interactive whiteboards (IWBs) and individual computers. The NTOs: • illustrate mathematical concepts explicitly • engage students actively in their learning • scaffold student learning • require students to use their mathematical understandings in an engaging and meaningful context. Also available are pedagogically sound, interactive Learning Objects (LOs) from Education Services Australia.
An example of a Nelson Teaching Object DATE:
Unit
6
STUDENT ASSESSMENT
Tommy Turtle get to the letter box. * Help Colour in the stepping stones that show 5.
Assessment Resources The assessment for each unit consists of: • one Student Assessment page per unit that links to Recommendations for Future Learning in the Teacher’s Resource Book
5
3
4
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* more dots than Tommy.
Draw a friend for Tommy Turtle who has
a friend for Tommy Turtle who has * Draw less dots than Tommy.
• one Assessment Task Card that has been designed to be used with individual students, small groups or as a whole-class assessment task. Each Assessment Task Card has a linking Targeting Assessment Task Card with specific recommendations for future learning • two pen-and-paper tests (Test A and Test B) for mid- and end-of-year assessment and report writing.
Draw a friend with the same number of dots as Tommy Turtle. Use a different pattern.
Unit
6
Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
Marketing Sampler.indb 21
21 06/05/14 2:06 PM
We hope you and your class enjoy and benefit from the sample units provided in this Sampler. We feel proud to say that Nelson Maths: Australian Curriculum NSW continues to provide teachers with choice by featuring an array of hands-on tasks and investigative activities. Teachers have the opportunity to tailor a program for their students based on their different learning styles and their diverse needs. Each unit provides ideas on how to scaffold students’ learning and also provides learning tasks to extend more able students.
Introduction
Marketing Sampler.indb 5
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07/05/14 3:23 PM
Unit
6
Dot Patterns
NUMBER AND ALGEBRA Whole numbers: MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
ML
five, four, less, more, one, same, six, three, two, zero
LESSON PLAN
TUNING IN HOW MANY CAN YOU SEE?
1
You will need: NTO K.7 ‘Can You Count?’ Present NTO K.7 ‘Can You Count?’ showing a collection of objects, and ask, ‘How many can you see?’. Invite a student to point to each item while counting aloud to check if the response is correct. Repeat. This is a good time to identify students who may still be having difficulty counting collections.
WHOLE-CLASS INTRODUCTION DOT PATTERNS You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, paper plates, round counters Hold up a card made from BLM 15 ‘Dot Patterns to 6’ or a plate for a few seconds and ask, ‘What did you see?’ Hold up the card or plate again to check. Repeat. When students are comfortable identifying the number of dots, give each student a paper plate and counters. Hold up a card or plate with three dots for a few seconds. Ask students how many dots they can see and have them make the arrangement of dots with their counters. Ask, ‘Can you make three another way?’ Explore different arrangements. Repeat for other numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: NTO K.20 ‘Dice’ or a large dice, BLM 16 ‘Make a Dice’, counters, NTO K.19 ‘How Many Dots?’, Student Book p. 18 ‘Dot Plates’
TASK 1:
SAME, SAME
Ask students what they can see on the sides of a dot dice on NTO K.20 ‘Dice’ or a large dice. Explain that they are going to make their own dice using BLM 16 ‘Make a Dice’. In one of the squares students draw one dot. In the next square they draw two dots and so on until each side has been filled with dots for each number from 1 to 6. Students cut out the dice net and assemble. Note: students may need teacher, older peer or parent support to assemble. Have students play ‘Same, Same’ with a partner. Students roll their dice, and when the numbers rolled are the same, they collect a counter. The first pair to collect six counters is the winner.
TASK 2:
INTERACTIVE TASK
Have students use NTO K.19 ‘How Many Dots?’.
TASK 3:
STUDENT BOOK p. 18 ‘Dot Plates’
TEACHING GROUP You will need: a set of paper plates with dot patterns or a set of enlarged cards made from BLM 15 ‘Dot Patterns to 6’, round counters, paper plates, stickers, NTO K.20 ‘Dice’, poster paper MAKING DOT PLATES • For students who require support, you may need to allow more time for them to view dot patterns and provide many experiences to view common arrangements of dots. Show students a paper plate or card, and ask them how many dots they can see. Get them to select that many counters and then make the arrangement on a paper plate. Continue showing them a plate or card and they select that amount of counters to make the same arrangement. Students can make their own set of dot plates for numbers
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1 to 6, using small paper plates and dot stickers. Get them to arrange the plates in a random order in front, and using NTO K.20 ‘Dice’ roll a number and get them to point to a plate with the same number of dots. Repeat, gradually rolling the dice more quickly. DOT PATTERN POSTER • For students who require a challenge, have them work with a greater range of numbers. Get them to choose a number, and using a paper plate and counters, have them explore different ways they can represent the number. Students can record their findings by making a poster.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask students to show all the different ways they made five on Student Book p. 17. Make a ‘Fabulous Five’ poster recording the different ways students found to represent five. • Ask students how they were able to recognise the numbers quickly. Discuss what they see when they look at arrangements for five and six. Ask which numbers are easy to recognise and discuss why.
LESSON PLAN
TUNING IN FIVE LITTLE SPECKLED FROGS
2
You will need: NTO K.21 ‘Five Little Speckled Frogs’, enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Present NTO K.21 ‘Five Little Speckled Frogs’, and while singing, hold up fingers matching the number of frogs in each verse. Next, display dot plates with the numbers 1 to 5 represented. This time, as students sing, invite a student to hold up a dot plate to match the number of frogs.
WHOLE-CLASS INTRODUCTION DOTS AND NUMBERS You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, a large number fan and one for each student made from BLM 17 ‘Number Fan: Numerals’ Ask students how many speckled frogs were sitting on the log. Show students large cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns and invite a student to find a dot plate that shows five. Show students the enlarged number fan made from BLM 17 ‘Number Fan: Numerals’ and all the numbers that are on it. Tell students that you will hold up each number, and when you get to the number that matches the plate, students put up their hand. Select another dot plate and then ask a student to find the corresponding number on the number fan. Give a number fan to each student, and hold up various dot plates, getting students to find the matching number on their number fan.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 20 ‘In the Pond’, counters, a dice, NTO K.22 ‘What Number Is This?’, Student Book p. 19 ‘Glub! Glub!’
TASK 1:
IN THE POND
Give a copy of BLM 20 ‘In the Pond’ to pairs of students. Each student will need about 20 counters that are the same colour but different from their partner’s. Students take it in turns to roll a dice and then place one counter on a lily pad that matches the dice. The counter can be placed on a word, numeral or dot pattern that matches the dice. If they cannot find a lily pad to match the dice, they miss that turn. The student who places the most counters on the board is the winner.
TASK 2:
INTERACTIVE TASK
Have students use NTO K.22 ‘What Number Is This?’. Vary the range of numbers to suit the abilities of students.
TASK 3:
STUDENT BOOK p. 19 ‘Glub! Glub!’
TEACHING GROUP You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns, BLM 21 ‘Speckled Frogs’, scissors, BLM 8 ‘Blank Cards’
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FROG JUMP • For students who require support, practise identifying the dot patterns by making a trail of cards from BLM 15 ‘Dot Patterns to 6’ and getting students to jump onto the first card, call out the number, and if correct, jump to the next and so on. Then give pairs of students a copy of BLM 21 ‘Speckled Frogs’ and have them cut out each item (these could be prepared before the lesson). Get students to match the frogs, lily pads and bugs. Then get students to place the items face-down and take it in turns to turn over a frog, a lily pad and a bug to see if they get a match. MORE DOT CARDS • For students who require a challenge, they can work with greater range of numbers. Give them a copy of BLM 8 ‘Blank Cards’ and have them make a set of cards by the writing the numerals for the numbers they want to work with. Then they can make matching cards with the words for the numbers and also a set of dot pattern cards. Students can play ‘Snap’ or ‘Memory’ with a partner.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘When you played “In the Pond” (Independent Tasks, Task 1), what did you cover first? Was it the numeral, word or dot pattern?’ Also ask, ‘Was it difficult to find a match to the dice all of the time? Why?’ • Ask, ‘When you look at dot patterns, do you recognise the number instantly? Which patterns are easiest to recognise? Why?’
LESSON PLAN
TUNING IN PUT THE PLATES IN ORDER
3
You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Revisit the dot patterns by holding up a dot pattern card made from BLM 15 ‘Dot Patterns to 6’ (or a paper plate with dot patterns) for a few seconds and have students call out how many. Place all of the dot pattern cards on the floor and ask a student to find a card or plate that has three dots. When the student has identified the card or plate, ask, ‘Can you find another plate/card that shows the same number?’ Repeat for a few other numbers. Tell students that you would like their help to pack the plates (or cards) up in order starting from zero. Make sure all of the plates showing the same number are picked up.
WHOLE-CLASS INTRODUCTION MORE OR LESS DOTS You will need: enlarged cards made from BLM 15 ‘Dot Patterns to 6’ or paper plates with dot patterns Hold up a dot pattern card (or plate) that shows three dots and ask students how many dots they can see. Invite a student to come and find a card or plate that has less dots. Ask, ‘How do you know it has less dots?’ Then ask if anyone can find a card that has more dots. Again ask, ‘How do you know that the dot pattern has more dots?’ Repeat for other number patterns. Next, hold a card in each hand and ask students to indicate which has more by holding out the same arm. Repeat for other numbers. Give out number fans and hold up a dot plate (or dot card) and ask students to show a number on their fan that is more and less. Repeat.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: a set of cards for each student made from BLM 15 ‘Dot Patterns to 6’, NTO K.20 ‘Dice’, Student Book p. 20 ‘Hungry Frogs’
TASK 1:
MORE DOTS
From their set of cards made from BLM 15 ‘Dot Patterns to 6’, each student turns over a card. Students compare cards and the student who has the card that shows more takes both cards and adds them to the bottom of their pile of cards. The game continues until one student has won all of the cards.
TASK 2:
INTERACTIVE TASK
In pairs with their sets of cards made from BLM 15, students take it in turns to generate a number using NTO K.20 ‘Dice’. However, before they select a card, they predict if the number on their card will be more, less or the same than the number generated. If they are correct, they keep the card. The student with the most cards wins.
TASK 3:
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STUDENT BOOK p. 20 ‘Hungry Frogs’
Nelson Maths Australian Curriculum NSW
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Kindergarten
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TEACHING GROUP You will need: paper plates with dot patterns as in BLM 15 ‘Dot Patterns to 6’, paper plates, counters MAKE MORE OR LESS • For students who require support, give them a dot paper plate with a number of dots on it that they can identify, e.g. 3. Have them place the plate in front, and in front of their dot pattern plate, have them place an empty plate and another empty plate after it. On the first plate they make a dot pattern that is less and on the last plate they make a dot pattern that is more. Ask them how they know that the number is less or more. Repeat with other number dot plates. MORE OR LESS CHALLENGE • For students who require a challenge, have them use the dot pattern cards made from BLM 15 that they made in Lesson Plan 2. In pairs, one student puts down one of their cards. Their partner turns over one of their cards, but before they do, they must say if their number will be more, less or the same. If their choice is correct, then they keep the pair of cards, but if not, their partner wins the cards. The students then take it in turns deciding if the card they turn over is more, less or the same. The student with the most cards at the end wins.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘How did you recognise the patterns that were more or less?’ Discuss if it was easy to tell which numbers were more or less and why. • Hold up a dot pattern plate and ask, ‘If I were to show another plate, do you think it would be a number that is more, less or the same?’ Ask students to explain their choice.
Assessment • Have students complete Student Assessment p. 21. • Review with students Assessment Task Card K.6. During the three lessons: • Observe which students were able to quickly recognise dot patterns during Lesson Plan 1, Independent Tasks, Task 2 and Lesson Plan 2, Independent Tasks, Task 1, and mark on a class list. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty. • Make a note of students’ responses to reflection questions.
Recommendations for Future Learning Specific to Student Assessment p. 21; if the student is experiencing difficulty: Continue working with recognition of dot patterns beginning with patterns for 1, 2 and 3 and then Q 1 gradually increasing. Q 2–3 Use NTO K.20 ‘Dice’ to randomly generate numbers and have the student copy and then add or subtract one counter to make more or less. Provide the student with paper plates and counters to explore different possible arrangements for each Q 4 number from 2 to 6. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card K.6 for specific recommendations. 2. Give more exposure to dot patterns by playing games, e.g. ‘Snap’ and ‘Concentration’. 3. Continue to work with dot patterns in the context of other number work. 4. Review Nelson Maths Building Mental Strategies Big Book 1, p. 6. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 1 Unit xx, pp. xx–xx. 2. Extending the student in any of the listed activities or tasks by using larger numbers.
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Dot Patterns
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BLM
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Blank Cards
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit Unit
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9 10 11 24
Whole numbers MAe-4NA
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BLM
15
Dot Patterns to 6
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
Unit
6 16
Whole numbers MAe-4NA
Teacher’s Note: Patterns can be made on paper plates or printed, laminated and made into sets of cards.
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BLM
16
Make a Dice
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Whole numbers MAe-4NA
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BLM
17
Number Fan: Numerals
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1
3
7
6
4
5
0
9
10
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© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Unit
Unit
Unit
Unit
Unit
8 10 11 20 30
Whole numbers MAe-4NA
Teacher’s Note: This BLM can be photocopied onto card, laminated, cut out and made into a fan by joining with a binder ring split pin. Enlarge and make a fan for teacher modelling.
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BLM
20
In the Pond
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six
3 2
three
1
two
one
five
6 four
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Unit
9
Whole numbers MAe-4NA
Teacher’s Note: This BLM can be printed and laminated to use for other number activities.
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BLM
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Speckled Frogs
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution. Unit
6
Whole numbers MAe-4NA
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K.6
Kindergarten: Assessment Task Card Unit
6
DOT PATTERNS
Resources: NTO K.19 ‘How Many Dots?’, BLM 15 ‘Dot Patterns to 6’, NTO K.4 ‘Numbers’
1
Present NTO K.19 ‘How Many Dots?’ and check if the student can automatically recognise how many dots.
2
Give the student a set of cards made from BLM 15 ‘Dot Patterns to 6’. Present NTO K.4 ‘Numbers’ and randomly generate a number from 0 to 6. Have them read the number and find the matching number card.
3
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is more than the dot pattern displayed.
4
Give the student a set of cards made from BLM 15. Show them a card from BLM 15 and have them select a card that is less than the dot pattern displayed.
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
K.6
Kindergarten: Assessment Task Card Unit
6
DOT PATTERNS TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Have the student practise reading dot patterns by playing board games, e.g. ‘Number Game Board’ in Nelson Maths Building Mental Strategies Big Book 1, pp. 12–13.
Q2
Have the student use NTO K.19 ‘How Many Dots?’ set to numbers from 0 to 6 and randomly generate either dot patterns or numerals for recognisation.
Q3
Give the student the set of cards made from BLM 15. Using NTO K.19 to generate a number between 0 and 6, have the student find a card with the same dot pattern. Then have them find the cards that show more and show less.
Q4
Select a card from BLM 15, and have the student guess the card by asking ‘Is it less?’ questions, e.g. ‘Is it less than 3?’
Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Kindergarten may be photocopied for educational use within the purchasing institution.
Nelson Maths Australian Curriculum NSW
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Teacher’s Resource
Kindergarten
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Dot Plates
DATE:
**
Show 5 in different ways. Use a paper plate and some counters. Draw some of the ways you found.
5 Play a game. You will need: •• a dice •• a partner How to play: •• In turn, roll a dice. •• Each time you roll 5, cover one of the paper plates above with a piece of paper. •• The first player to cover all their plates wins.
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Unit
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Glub! Glub!
DATE:
**
Draw dots on each frog to match the number of bugs it will eat. One has been done for you.
**
On the lily pad, write the matching number word. One has been done for you.
five a line matching each frog to a lily pad **Draw and a bug. One has been done for you.
five Unit
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six
one
two
Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Hungry Frogs
DATE:
You will need: • a partner • one set of cards for each player made from BLM 15 ‘Dot Patterns to 6’ How to play: • Choose a frog. Turn over all your cards and place them in a pile. • Take a card from your pile. Your partner needs to do this, too. • The player who has more dots on their card can colour their first lily pad. • Keep turning over cards. The player with more dots each time colours a lily pad. • The first player to reach the fly wins.
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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DATE:
Unit
6
STUDENT ASSESSMENT
**
Help Tommy Turtle get to the letter box. Colour in the stepping stones that show 5.
5
3
4
5
6 5
a friend for Tommy Turtle who has **Draw more dots than Tommy.
a friend for Tommy Turtle who has **Draw less dots than Tommy.
Draw a friend with the same number of dots as Tommy Turtle. Use a different pattern.
Unit
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Dot Patterns (TRB pp. 42–45) Whole numbers MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20
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Unit
12
2D Shapes
U
MEASUREMENT AND GEOMETRY Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
ML
circle, corners, edges, rectangle, square, triangle
LESSON PLAN
TUNING IN BLOCKS
You will need: pattern blocks, attribute blocks and other sets of blocks containing a variety of shapes
1
Provide students with different sets of blocks, e.g. pattern blocks, attribute blocks or any that have a variety of flat shapes. Have students make pictures using the different-shaped blocks. Give students the opportunity to see one another’s pictures. Have students put the shapes back into their containers. Observe which students have difficulty matching shapes to the holding space as this will help determine which students may need support.
WHOLE-CLASS INTRODUCTION SHAPES IN THE CLASSROOM You will need: NTO K.38 ‘What Shape Is This?’ Using NTO K.38 ‘What Shape Is This?’, select a shape, e.g. circle, and ask students to look around the room to see if they can find something that has the same shape in it. It is not necessary at this stage to name the shape as a circle; however, some students may know the name of the shape. If possible, let students bring to the front of the class the objects they find that contain a circle. Have them trace the circle shape with their finger to make it clear to the class where the circle is located. Continue until most objects containing circles have been identified. Repeat for other shapes, e.g. square, rectangle and any others that can be found in the classroom. Prior to the lesson, you may need to make sure that there are a range of objects in the classroom to match the different shapes explored.
INDEPENDENT TASKS Note: Choose from Tasks 1, 2 or 3. You will need: BLM 30 ‘I Can Find’, NTO K.39 ‘Match This Shape’, Student Book p. 26 ‘Shapes You Can See’
TASK 1:
SHAPES I CAN FIND
Give each student a copy of BLM 30 ‘I Can Find’ and explain that they need to find an object or objects in the classroom for each shape and draw it. So that each BLM can be made into a book, have students fold their page in half horizontally and then vertically.
TASK 2:
INTERACTIVE TASK
Using NTO K.39 ‘Match This Shape’, students work independently on computers to select the same shape from five alternatives.
TASK 3:
STUDENT BOOK p. 26 ‘Shapes You Can See’
TEACHING GROUP You will need: a set of cards made from BLM 31 ‘Shape Cards 1’ and BLM 32 ‘Shape Cards 2’ WHERE IS THE SHAPE? • For students who require support, show them a card with a rectangle made from BLM 31 ‘Shape Cards 1’. Have them trace the shape with their finger and imagine what the rectangle could be. Draw the suggestions students give. Students may need to go on a walk around the classroom while you hold up the shape card and then identify particular shapes in objects. Repeat with another shape, e.g. circle. Give students either a rectangle or a circle to trace onto a piece of paper or a small whiteboard, and have them draw an object in the classroom that contains that shape.
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FIND MY SHAPE • For students who require a challenge, expose them to a greater range of shapes, e.g. shapes included in BLM 32 ‘Shape Cards 2’. Have two sets of cards made from BLMs 31 and 32 ‘Shape Cards’. Place one set where they are visible to all. Invite a student to select a card from the second set (making sure the other students do not know the shape they selected). Have them describe their shape and invite other students to find it. Encourage students to describe their shape in terms of features, e.g. number of sides and corners.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their ‘I Can Find’ books they made using BLM 30 ‘I Can Find’ in Independent Tasks, Task 1. Ask, ‘What other objects contain the same shape?’ As students share their drawings, make a chart of what the students drew for each shape. • Have students share their completed Student Book p. 25 with a partner, and then select some students to come and explain how they were able to find the shapes. Ask, ‘How did you know that you were correct?’ • For students from the Teaching Groups, have them share their work and ask, ‘How were you able to find the objects with that shape? How did you know it was the same shape?’
LESSON PLAN
TUNING IN SHAPES IN OUR SCHOOL You will need: BLM 31 ‘Shape Cards 1’
2
Enlarge a number of BLM 31 ‘Shape Cards 1’ and make these into cards. Give each student a card and take students on a walk around the school to see if they can see their shape somewhere in the school environment. Take digital photos of students finding their shape in the school environment for display or to put into a class Maths Journal.
WHOLE-CLASS INTRODUCTION NAMING SHAPES You will need: NTO K.38 ‘What Shape Is This?’, cards made from BLM 31 ‘Shape Cards 1’ Present NTO K.38 ‘What Shape Is This?’ to students or alternatively use a card made from BLM 31 ‘Shape Cards 1’. Ask students to look carefully at the shape and provide words to describe it. Encourage students to look at number of edges and corners, colour and size. Ask, ‘Does anyone know the name of the shape?’ If necessary, tell students the name of the shape. Repeat for other shapes.
INDEPENDENT TASKS Note: Choose from Tasks 1, 2 or 3. You will need: BLM 31 ‘Shape Cards 1’, BLM 32 ‘Shape Cards 2’, scissors, glue, sheets of paper, coloured pencils, NTO K.40 ‘Shape Express’, Student Book p. 27 ‘Find the Shape’
TASK 1:
SHAPE PICTURES
For this task each student will select a card from BLM 31 ‘Shape Cards 1’ or for more able students a card from BLM 32 ‘Shape Cards 2’. To find out which students know the names of some shapes, ask them to name the shape they would like to use. Students then need to cut out the shape and paste it onto a sheet of paper. Using coloured pencils, students make the shape into a picture.
TASK 2:
INTERACTIVE TASK
Have students use NTO K.40 ‘Shape Express’ where they need to complete the train by finding the matching shape.
TASK 3:
STUDENT BOOK p. 27 ‘Find the Shape’
TEACHING GROUP You will need: BLM 31 ‘Shape Cards 1’, scissors, glue, sheets of paper, BLM 32 ‘Shape Cards 2’ RECTANGLES • For students who require support, work with them in a small group and have them cut out a rectangle from BLM 31 ‘Shape Cards 1’. Before they paste the rectangle onto a sheet of paper and use coloured pencils to make it into a picture, have them explore the features of the shape. They can do this by folding
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the rectangle to find that the four corners are the same and that the opposite sides are the same, but that there is a pair of long sides and a pair of short sides. As a group, brainstorm things that could be rectangular in shape, e.g. a book, a laptop, a tabletop, and have students complete their picture. LOTS OF SHAPES • For students who require a challenge, have them select a number of shapes from BLM 31 ‘Shape Cards 1’ or BLM 32 ‘Shape Cards 2’. Then they need to plan and draw a picture where these shapes might be found.
REFLECTION Select from the following to suit your class and their learning outcomes: • Select students to come to the front and name the shape and how they used it to make a picture in Independent Tasks, Task 1. Record what students say, e.g. ‘I used a square to make a picture of a house’, and make a display or a book of students’ work. • Get students to show where they put a rectangle in their picture ‘Rectangles’ in the Teaching Group. Ask them to explain how they knew the shape was a rectangle and not another shape. Ask students to identify and name the other shapes that they can see.
LESSON PLAN
TUNING IN I SPY SOMETHING IN THE CLASSROOM
3
Select an object in the classroom that has a particular shape, e.g. the door. Say, ‘I spy something in the classroom that is a big rectangle.’ Select students to go and point to an object that might be the object you are thinking about. Once a student points to the door, select another object in the shape of another shape, e.g. square, triangle or circle, and repeat the activity. This is a good time to identify students who cannot recognise shapes and need support in the Teaching Group.
WHOLE-CLASS INTRODUCTION MATCHING SHAPES You will need: a large hoop (or draw a circle on the floor with chalk that can be removed later), attribute blocks Tip the attribute blocks onto the floor so that all students can see them. Select a block, e.g. a rectangle, and have students describe the shape by describing its colour, number of sides, size and thickness. Place the block into a hoop on the floor and say, ‘I like rectangles. Can anyone find another block that is a rectangle?’ Select students to find other blocks with rectangles and get them to place them inside the hoop or circle. Continue until all of the rectangles have been placed into the hoop or circle. Ask students to name the shapes in the hoop or circle and tell them that the shapes outside the hoop or circle are not rectangles. Repeat for other shapes and attributes, making sure that students understand which shapes have a common attribute and which do not.
INDEPENDENT TASKS Note: Choose from Tasks 1, 2 or 3. You will need: BLM 33 ‘Shape Bingo’, attribute blocks, a bag, counters, NTO K.41 ‘Make a Picture’, Student Book p. 28 ‘Shape Caterpillars’
TASK 1:
SHAPE BINGO
Model the following tasks before students work in pairs or small groups. Provide students with one of the four bingo templates from BLM 33 ‘Shape Bingo’. (Note that the one in the top left-hand corner is the easiest and the one in the bottom right-hand corner is more difficult). Ask students to colour two of their shapes red, then another two blue and another two yellow. Tell students that they can colour the remaining shapes red, blue or yellow. Place the circles, squares, triangles and rectangles from the attribute blocks in a container or bag. Select a shape and hold up for students to see. Tell them to look at their bingo board, and if they have the same shape in the same colour, they can cover it with a counter. Continue selecting shapes from the container or bag until a student has covered either a row or all of the bingo board.
TASK 2:
INTERACTIVE TASK
Have some students use NTO K.41 ‘Make a Picture’ to recreate a picture by selecting the correct shapes.
TASK 3:
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STUDENT BOOK p. 28 ‘Shape Caterpillars’
Nelson Maths Australian Curriculum NSW
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Teacher’s Resource
Kindergarten
07/05/14 3:23 PM
TEACHING GROUP You will need: NTO K.39 ‘Match This Shape’, BLM 31 ‘Shape Cards 1’, BLM 32 ‘Shape Cards 2’, a bag, green, red, blue and yellow counters MATCH THE SHAPE • For students who require support, present NTO K.39 ‘Match This Shape’. When a shape appears on the screen, ask students to look carefully at the shape and ask questions about its features, e.g. ‘How many sides does this shape have? Are the sides the same length? How many corners does the shape have? What colour is the shape?’ Invite a student to come to the board and explain which shape they think has the same number of sides, corners and colour, and then get them to test their prediction by selecting the shape. Reset and repeat so that students continue to identify features of the shape to help find the match. BINGO CHALLENGE • For students who require a challenge, have them fold a piece of paper in half and half again and then turn the paper 90 degrees and fold in half and in half again so that their paper is a 4 x 4 grid. Give them BLMs 31 and 32 ‘Shape Cards’ to create their own bingo board. Have students colour their shapes red, blue, green or yellow. In a bag place a set of cards made from BLMs 31 and 32 ‘Shape Cards’ and a red, blue, green and yellow counter. Have one student select a card and counter from the bag, while the others look for the shape in that colour on their bingo board. If a student has that shape in that colour, they cover it with a counter. Continue until one student has ‘bingo’ by getting four counters in a row.
REFLECTION Select from the following to suit your class and their learning outcomes: • Put a selection of attribute blocks in front of students and then ask them to look at the shapes and see if they can find a given shape, e.g. a triangle. Ask, ‘How do you know that the shape is a triangle? How do you know that it is not a circle?’. Repeat. • Get students to show the caterpillars they designed in Independent Tasks, Task 3. Have students explain the shapes they chose and why.
Assessment • Have students complete Student Assessment p. 29. • Review with students Assessment Task Card K.12. During the three lessons: • Note on a class list which students in Lesson Plan 2, Independent Tasks, Task 1, were able to name the shape they wished to use. • Make a note of students completing the scaffolding tasks or more challenging activities in the Teaching Group. • Review Student Book pages and make notes on which students are experiencing difficulties and those able to complete the tasks. • Note students’ responses to Reflection questions.
Recommendations for Future Learning Specific to Student Assessment p. 29; if the student is experiencing difficulty: Q 1 Provide more experiences for the student to explore the features of shapes. Make sets of laminated shapes from BLM 31 ‘Shape Cards 1’. Have the student outline the shapes and then describe what they see. Make a set of cards from BLM 31 ‘Shape Cards 1’ and play flashcard games so the student can recognise and name the shapes. Give the student cards made from BLM 31 ‘Shape Cards 1’ and have them identify objects that contain Q 2 that shape in the classroom and school environment. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card K.12 for specific recommendations. 2. Have the student explore NTO K.39 ‘Match This Shape’ and NTO K.40 ‘Shape Express’. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 1 Unit xx, pp. xx–xx. 2. Extending the student in any of the listed activities or tasks by using more shapes, e.g. semi-circle, trapezium, hexagon, pentagon, rhombus and kite.
Unit 12
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2D Shapes
25
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Shapes You Can See
DATE:
at each shape. Draw something from your **Look classroom that has the same shape.
Find another shape in the classroom and draw it.
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Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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Find the Shape
DATE:
**
Look at the picture below. Colour all the rectangles blue.
**How many rectangles are in the picture? What other shapes can you see? **
Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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Shape Caterpillars
DATE:
**Finish the patterns on the caterpillars.
**Draw your own shapes on the caterpillar.
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Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
07/05/14 3:23 PM
DATE:
Unit
12
STUDENT ASSESSMENT
**Look at all the shapes. Colour the triangles red.
**This is a rectangle.
Draw something from your classroom that has
a rectangle.
Unit
12
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2D Shapes (TRB pp. 22–23) Two-dimensional space MAe-15MG manipulates, sorts and describes representations of two dimensional shapes, including circles, triangles, squares and rectangles, using everyday language
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Unit
8
Numbers Beyond 20
NUMBER AND ALGEBRA Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
ML
consecutive, eighty, fifty, forty, ninety, one hundred, ones, seventy, sixty, tens, thirty, twenty
LESSON PLAN
TUNING IN
HOW FAR CAN YOU COUNT? Have students sit or stand in a circle and designate someone to begin counting by ones from zero, with each student counting the next consecutive number. See how far students can go before making a mistake. Write down the last correct number. Have students try again to see if they can count further.
1
WHOLE-CLASS INTRODUCTION WRITING NUMBERS On the board, write the numerals from 1 to 10 and underneath from 11 to 20 and have students read them. Point to the 20 and say, ‘This is how we write 20. Can anyone write the other numbers in the 20s?’ Invite a student to write the numbers 21 to 29. Then ask, ‘What number comes after 29?’, and as students answer, write 30 on the board. Ask, ‘Do you notice anything about the numbers?’ Draw students’ attention to the repeating nature of the final digit pattern. Continue by asking a student to write the other numbers in the 30s. Then ask what comes next and write 40 on the board. Continue having students write the numbers up to 100. Point to different numbers and see if students can read them.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 6 ‘Blank Number Line’, scissors, Word, Student Book p. 38 ‘Number Bingo’
TASK 1: NUMBERS TO 100 Have students work in a group of three to make a number line to 100. Give each student a copy of BLM 6 ‘Blank Number Line’. Have them cut out the sections and work out which numbers individual students will write. Note: number lines go up to 120 – have students cut off the number line at 100. Remind students that the numbers are on the board for support. Have students make number lines to 100 beginning at zero.
TASK 2:
INTERACTIVE TASK
Using Word, students make a 10 x 10 table and have them fill in the numbers from 1 to 100 to make a 100 chart.
TASK 3:
STUDENT BOOK p. 38 ‘Number Bingo’
TEACHING GROUP You will need: NTO 1.1 ‘Number Cards’, number tiles made by cutting up BLM 14 ‘100 Chart’ MAKING A NUMBER LIST • For students who require support, begin revising numbers that students know and gradually introduce larger numbers. Set NTO 1.1 ‘Number Cards’ to show numerals to 20, and have students read numbers as they appear. Then increase the range of numbers to 30 for students to practise reading. Have a number race whereby students form a starting line and the first student to recognise the number takes one step forward. Ask students to write down the numbers to 30. Introduce the next ten numbers, writing them on the board and saying them and getting students to repeat. Randomly point to the numbers and have students say them. Have students add the next ten numbers to their list. Once students have written down the numbers to 50, call out random numbers and have students point to them. Keep the number lists to add to in later lessons.
Nelson Maths Australian Curriculum NSW
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PUT THEM IN ORDER • For students who require a challenge, give them a set of number tiles made from BLM 14 ‘100 Chart’ and have them put the numbers in order either in a 10 x 10 grid pattern or as a long line. Have students work with a partner.
REFLECTION Select from the following to suit your class and their learning outcomes: • Write numbers on the board, e.g. 68, 33, 92, and have students read the numbers. Ask, ‘How did you know what the numbers were? What helps you to read the numbers?’ • Ask, ‘When you write all the numbers to 100, how can you make sure that you have not missed any? What strategies do you use?’
LESSON PLAN
TUNING IN AROUND THE WORLD
2
You will need: a set of number cards from 1 to 100 made from an enlarged copy of BLM 14 ‘100 Chart’ Hold up number cards in random order and have students read them. Play ‘Around the World’ whereby students sit in a circle and two students sitting next to one another are selected to stand and see who can read the number the quickest. The student who reads the number the quickest remains standing and the next student in the circle competes. The game continues until every student has had a turn.
WHOLE-CLASS INTRODUCTION A CHART OF NUMBERS You will need: NTO 1.21 ‘Numbers to 100’ Present NTO 1.21 ‘Number to 100’ and point to the 1 and 100. Have students read the numbers. Tell students that you need their help to make a 100 chart. Ask, ‘What number comes after 1?’ When students have answered, click onto the first blank space to reveal the number. Continue asking for the next number and invite students to come and click on the space to reveal the next number until all the numbers on the chart are revealed.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 15 ‘Make Your Own 100 Chart’, number tiles made by cutting up BLM 14 ‘100 Chart’, NTO 1.21 ‘Numbers to 100’, counters, a dice, Student Book p. 39 ‘Lucky Slides’
TASK 1:
TIC TAC TOE
Give students a copy of BLM 15 ‘Make Your Own 100 Chart’ and have them fill in the numbers from 1 to 100. If students need support, display NTO ‘Numbers to 100’ with the numbers revealed. Once students have filled in the numbers, have them play ‘Tic Tac Toe’.
TASK 2:
INTERACTIVE TASK
Have students work in pairs. Give each pair a set of number tiles made from BLM 14 ‘100 Chart’. One student from each pair selects a number for the other student to locate on NTO 1.21 ‘Numbers to 100’. Continue until all of the numbers from 1 to 100 have been located.
TASK 3:
STUDENT BOOK p. 39 ‘Lucky Slides’
TEACHING GROUP You will need: BLM 15 ‘Make Your Own 100 Chart’, number tiles made from BLM 14 ‘100 Chart’ A FEW MORE NUMBERS • For students who require support, continue to revise numbers that they know. Have students read through the number list they made in ‘Making a Number List’ in Lesson Plan 1, Teaching Group. Have students stand in a circle and throw or roll a ball across the circle to each other and the student who catches the ball says the next consecutive number. Support students to count past 50 to 80. Have students add the numbers they have counted to their number list. BURIED TREASURE • For students who require a challenge, have them complete a 100 chart using BLM 15 ‘Make Your Own 100 Chart’. Next, have pairs of students use their 100 charts to play a strategy game. One student selects a number tile (these can be made from BLM 14 ‘100 Chart’). The number on the tile must be used as part of a row of three adjacent numbers on the student’s 100 chart, e.g. if number tile 25 is chosen, the row of three numbers – or ‘bars of buried treasure’ – could be 24, 25, 26 or 25, 15, 5 or 25, 36, 47. (Note: numbers
Unit 8
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Numbers Beyond 20
31
07/05/14 3:23 PM
may be diagonally adjacent on the 100 chart). The first student colours in their bars of treasure on the 100 chart, without showing their partner. The second student tries to ‘find’ the bars of buried treasure by guessing any number that forms part of the treasure. For example, students ask: ‘Is number 25 in your bar of buried treasure?’ Pairs swap roles when the bars of buried treasure have been guessed correctly.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share the 100 charts they completed in Independent Tasks, Task 1, and ask, ‘When you wrote the numbers, what were you thinking that helped you write the correct number?’ • Ask in relation to ‘Buried Treasure’ in the Teaching Group, ‘What strategies did you use to win?‘
LESSON PLAN
TUNING IN POINT TO THE NUMBER
3
You will need: NTO 1.21 ‘Numbers to 100’ Present NTO 1.21 ‘Numbers to 100’ with numbers showing and the pointer selected. Ask, ‘Can anyone point to the number that tells us how many students are in the class?’ Continue to ask students to point to numbers that are significant to them, e.g. their classroom number, the number in their address and so on.
WHOLE-CLASS INTRODUCTION HOW THE NUMBERS ARE ARRANGED You will need: NTO 1.21 ‘Numbers to 100’ Present NTO 1.21 ‘Numbers to 100’ with the numbers showing and ask, ‘Have you noticed anything about the way that the numbers on a 100 chart are arranged?’ Discuss that the numbers are in consecutive order, the final digit pattern is repeated in each row and that, as you move down a column, there is an increase of one in the ‘tens’ number. Hide the numbers on the NTO 1.21 ‘Numbers to 100’, click one number and have students read the number. Then point to the next space and ask, ‘What number will come next?’ Have students uncover the next space to check their answer. Point to the first number uncovered and ask, ‘What number will come before this number?’ Again have students check their answer by uncovering the space. Continue selecting numbers and asking students to name the numbers that comes after and before.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: Sets of number tiles made from BLM 14 ‘100 Chart’, NTO 1.21 ‘Numbers to 100’, Student Book p. 40 ‘What’s the Number?’
TASK 1:
CONSECUTIVE NUMBERS
Have students work in small groups. Give them a set of number tiles made from BLM 14 ‘100 Chart’ and have them spread the tiles out, face-down, on the floor or tabletop. Explain to students that they are going to try to get two number tiles that are consecutive numbers. So, they turn over one tile and then turn over another one. The second tile needs to be the number that comes before or after the number on the first tile for them to keep the tiles and have another turn. Otherwise they have to turn the tiles back over and it is the next person’s turn.
TASK 2:
INTERACTIVE TASK
Have students use NTO 1.21 ‘Numbers to 100’ to explore consecutive numbers. Randomly click on a number. Students write it down and then write down the number that comes after and the number that comes before, using the NTO to check their answers.
TASK 3:
STUDENT BOOK p. 40 ‘What’s the Number?’
TEACHING GROUP You will need: NTO 1.21 ‘Numbers to 100’, a set of number tiles made from BLM 14 ‘100 Chart’, a copy of BLM 14 ‘100 Chart’
MAKE IT TO 100 • For students who require support, have them continue to complete their number list from ‘A Few More Numbers’ in Lesson Plan 2, Teaching Group. Present NTO 1.21 ‘Numbers to 100’ with the numbers hidden. Begin clicking the numbers in order from 1 to 80, having the students recite the numbers as you do. Ask, ‘We know that the last number was 80, so what will the next number be?’ Check students’ prediction by revealing it on the NTO. Have students continue predicting the numbers to 89 and then ask them to write them on their number list. Tell students to look at the last column, have them read the Nelson Maths Australian Curriculum NSW
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numbers 10, 20, 30, 40 50, 60, 70, 80 and ask, ‘What do you think the next number will be? How do you write that?’ Have students add 90 to their list and then have them check on the NTO that they are correct. Have students write the remaining numbers to 100 and then check on the NTO. WHAT COMES NEXT? • For students who require a challenge, put them into small groups and give each group a set of number tiles made from an enlarged copy of BLM 14 ‘100 Chart’. Have them shuffle the tiles, and then each student takes five. The remaining number tiles are placed in a pile face-down. One tile from the pile is turned over and placed on a 100 chart (use another copy of BLM 14 ‘100 Chart’). The aim of the game is to be the first student to get rid of their number tiles, which they do by taking it in turns to place a tile on the 100 chart. They can only place a tile if it is the number that comes before or after or would appear above or below the number/s on the 100 chart. If students are unable to place a number tile, they must pick up another tile from the pile.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘When exploring a 100 chart, was it always easy to work out the numbers that come before and after another number? What strategies do you use to help you work it out?’ • Ask, ‘Are there some numbers that come after each other that are more difficult to remember than others? Why?’
Assessment • Have students complete Student Assessment p. 41. • Review with students Assessment Task Card 1.8. During the three lessons: • Collect created items, e.g. completed number lines and 100 charts, as work samples for student portfolios. • Observe students as they complete ‘Consecutive Numbers’ in Lesson Plan 3, Independent Tasks, Task 1, and mark on a class list students who are able to identify pairs of consecutive numbers. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 41; if the student is experiencing difficulty: Q 1 Provide more practice with oral counting. Look for opportunities within the school environment, e.g. classroom numbers, classroom charts that list numbers of books borrowed, for them to read numbers up to 100. Q 2 Have the student complete 100 charts and use as game boards and to play games, e.g. ‘Tic Tac Toe’, which will reinforce understanding of how the numbers are organised. Q 3 Have the student use NTO 1.21 ‘Numbers to 100’ whereby they can explore numbers that come before and after. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 1.8 for specific recommendations. 2. Review Nelson Maths: Australian Curriculum Year 1 Units 22 and 23. 3. Have the student complete Nelson Maths Building Mental Strategies Big Book 2, p. 6. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Completing Nelson Maths Building Mental Strategies Big Book 3, p. 3, to explore larger numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 2 Unit xx, pp. xx–xx. 3. Extending the student in any of the listed activities or tasks by using larger numbers.
Unit 8
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Numbers Beyond 20
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BLM
6
Blank Number Line
Paste here
Paste here
Paste here
Paste here
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution. Unit
8
Whole numbers MA1-4NA
Teacher’s Note: This BLM can be cut out and individual sections used or a number of sections pasted together.
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BLM
14
100 Chart
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution. Unit
1 8
Whole numbers MA1-4NA
Teacher’s Note: This BLM can be photocopied and laminated for re-use in the classroom. Make sets of number tiles from 1 to 100 by enlarging, copying each set on different-coloured paper and cutting into number tiles.
35
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Unit
15
Make Your Own 100 Chart
Fill in the numbers from 1 to 100.
1
10
14 43
27
35
59
62 86
78 100
Tic Tac Toe You will need: a partner, a completed 100 chart, a different-coloured pencil from your partner • Take it in turns to tell your partner which number to colour in for you. • If your partner has coloured three numbers in a row for you, then you score a point. © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution. Unit
1 8
Whole numbers MA1-4NA
36
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1.8 F.1
Year Foundation: 1: Assessment Assessment Task Card Task Card Unit
NUMBERS BEYOND 20
8 1
Resources: NTO 1.21 ‘Numbers to 100’, a set of number tiles made by cutting up a copy of BLM 14 ‘100 Chart’
1
Present NTO 1.21 ‘Numbers to 100’ set to show the numbers. Randomly point to different numbers and have the student read them.
2
Have the student write the following numbers as you say them:
89, 13, 48, 72, 31, 50
3
Give the student a copy of BLM 14 ‘100 Chart’ and a matching set of number tiles made from BLM 14 ‘100 Chart’. Have them randomly select number tiles and place them on the corresponding number on the 100 chart.
4
Have the student select number tiles and name the number that comes before and after the number they have selected.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
1.8 F.1
Year Foundation: 1: Assessment Assessment Task Card Task Card Unit
8 1
NUMBERS BEYOND 20
TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Continue to provide practice in reading numbers by playing races involving who can read the number first or playing ‘Around the World’ in Lesson Plan 2, Tuning In.
Q2
Look for opportunities for the student to read numbers in the school environment, e.g. team or sporting scores.
Q3
If the student takes a while to place number tiles on a 100 chart and appears to be going through numbers from 1 onwards to find a number, then they have not demonstrated an understanding of how the numbers are placed. Have them complete a blank 10 x 10 grid writing the numbers to 99 or 100. Ask them to point to a particular number and read all the numbers in that column and row, and discuss what is common to all the numbers in that column and row.
Q4
Initially, have the student point to numbers on NTO 1.21 ‘Numbers to 100’ and name the number that comes before and after. Then ask them to visualise a 100 chart and think about where a number would be and what numbers they would see either side of it. Play ‘Consecutive Numbers’ in Lesson Plan 3, Independent Tasks, Task 1, whereby the student places number tiles side by side to see if they look like consecutive numbers.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 1 may be photocopied for educational use within the purchasing institution.
Unit 8
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Decimals to 2 Decimal Places
37
Teacher’s Resource
Year 1
07/05/14 3:23 PM
Number Bingo
DATE:
You will need: a partner, a copy of BLM 14 ‘100 Chart’, scissors, a paper bag 1
Choose numbers between 1 and 100.
Write each number in the grid below.
2
Cut up BLM 14 ‘100 Chart’ to make number tiles.
Place the number tiles in a paper bag.
3
With a partner, take it in turns to pull a number
tile from the paper bag. Read the number.
4
If you have that number in your grid, cross it off.
5
The first person to cross off all of their numbers wins.
6
Use the grid below to play again.
38
Unit
8
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Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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Lucky Slides
DATE:
You will need: a dice, small counters 1
Fill in the missing numbers to complete the game board.
0
1
2
10
13 21
22
30
4
5
14
15
52
71
90
64
46
66
91
85
39
47 57
58
67
68
76
72 84
19
38
55
80
9
27
45
63
17
35
40
60
16
24 33
51
8
78
79
98
99
86 97
2 To play a game with a partner, put your counters on 0. 3 In turn, roll the dice and move that many spaces.
4 Look carefully so you follow the numbers in the correct order.
If you do not follow the correct order, you have to go back to 0.
5 If you land on a number at the top of the slide, ‘slide’ down
to the number at the bottom.
6 The first to 99 wins!
Unit
8
Marketing Sampler.indb 39
Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
39 07/05/14 3:23 PM
What’s the Number?
DATE:
You will need: a set of number tiles made BLM 14 ‘100 Chart’
for each table, glue
1
Select a number card. Paste it in the space below. Think about
a 100 chart. Now write the number that comes before and
after. Do this 3 more times.
2
Three groups of children played a game.
Work out who came 1st , 2nd and 3rd for each group.
Their scores were: a Abdul: 78
Jake: 79 2nd
1st b Lucy: 84
Iman: 86 2nd
1st
c Carlos: 39 Nat: 41 2nd
1st
Lee: 76 3rd Maria: 85 3rd Tom: 40 3rd
one more than Jack, Jo scored
3
Jack scored 79. Jan scored
one less than Jack and Jed scored one more than Jan.
What were their scores? Write them in order.
40
Unit
8
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Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
07/05/14 3:23 PM
DATE:
Unit
8
STUDENT ASSESSMENT
You will need: a set of number tiles made from BLM 14 ‘100 Chart’
1
Have your teacher or a partner select 8 number tiles.
As they read them to you, write down each number.
2
Fill in the missing numbers in the 100 chart.
1 19 24
50 53
75
100 3
Unit
8
Marketing Sampler.indb 41
Write the number that comes after each number. 71
17
39
63
Numbers Beyond 20 (TRB pp. 30–31) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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Unit
10
Length and Area
Measurement and Geometry Length: MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres Area: MA1-10MG measures, records, compares and estimates areas using uniform informal units
ML
estimating, long, longer, longest, measuring, tall, taller, tallest, area, surface, cover
LESSON PLAN
TUNING IN
HOW CAN YOU MEASURE? Present a problem to students about wanting to find out which is the longer of two things that cannot be moved. Select something within the classroom or school environment, e.g. your desk and an upright cupboard, and ask, ‘How can we work out which is longer – my desk or the cupboard – when we cannot place them side by side?’ Discuss with students their ideas, including the idea of using some sort of units that are the same size to measure the objects.
1
WHOLE-CLASS INTRODUCTION MAKING A GOOD ESTIMATE You will need: footprints cut out from BLM 18 ‘Dinosaur Footprints’ Show students the dinosaur footprints cut out from BLM 18 ‘Dinosaur Footprints’ and tell them that these will be used to measure the desk and the cupboard. Tell students you would like them to think about how many footprints long the desk and cupboard might be and write students’ estimates on a class list. Invite two students to measure the desk and two students to measure the cupboard. Ask, ‘Which is longer? How do we know?’ Look at the class list and find the students whose estimates were closest and ask, ‘How did you make your estimation?’ Discuss the idea of estimating by thinking about how many of the footprints would fit along the desk or cupboard.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 18 ‘Dinosaur Footprints’, scissors, chalk, Student Book p. 40 ‘Two Footprints Long’
TASK 1:
ESTIMATE AND MEASURE
Have students work with a partner or small group. Give each pair or small group a copy of BLM 18 ‘Dinosaur Footprints’ and have them cut out the footprints. Students then choose two objects in the classroom to measure. Before they measure, they need to record an estimate of how many footprints long they think each object will be and then work together to measure. When students have finished measuring, they need to write about what they did and a statement about which object was the longest and how they know.
TASK 2:
DRAW A DINOSAUR
Have students work with a partner or small group to draw a dinosaur that is five or 10 footprints long or tall using chalk outside the classroom on a concrete or asphalted area.
TASK 3:
STUDENT BOOK p. 40 ‘Two Footprints Long’
TEACHING GROUP
You will need: BLM 18 ‘Dinosaur Footprints’, scissors MORE OR LESS THAN A FOOTPRINT • For students who require support, continue to have them compare individual classroom objects to decide if they are more or less than a dinosaur’s footprint. Have students cut out a footprint from BLM 19 ‘Dinosaur Footprints’, and then holding the footprint in their hand, have them look around the classroom to find something they think will be more than the footprint. Have students collect the object and make a direct comparison. Then ask students to find something in the classroom they think will be less than the footprint and directly compare the object. Have students write about their findings. Nelson Maths Australian Curriculum NSW
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FIVE THINGS • For students who require a challenge, have them work with a partner or small group to cut out a footprint from BLM 18 and look for things in the classroom that might be at least as long as three footprints. Have students select up to five objects and measure them with the footprints and then order the five objects from longest to shortest. Have students record their findings.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from Independent Tasks, Tasks 1 and 2, or from the Teaching Groups, and ask, ‘Was it easier to measure some things than others? Why?’ • Ask, ‘What did you do when you were measuring and the footprint went past the end of the object? How did you count that?’
LESSON PLAN
TUNING IN
2
MEASURING DINOSAUR FOOTPRINTS You will need: three pieces of string 5 cm, 27 cm and 75 cm long or drawings of dinosaur footprints (of these lengths) on paper or on the floor using chalk Prior to the lesson, make sure that all rulers are out of sight. Hold up the pieces of string or point to the footprints, explaining to students that dinosaur footprints were discovered at Lake Quarry in Winton, Queensland, that the footprints belonged to three different types of dinosaurs and that the string (or the drawings) show the average size of the footprints. Ask, ‘What do we have in the classroom that we can use to measure the footprints?’ During discussions of possible objects, stress that whatever is to be used to measure needs to be of uniform size.
WHOLE-CLASS INTRODUCTION MEASURE IT You will need: NTO 1.24 ‘Measure It’ Present NTO 1.24 ‘Measure It’ and select an object, e.g. a shoe, to measure. Choose between the paperclip, craft stick or square counter. Have students estimate how many of each item will be needed to measure the shoe, and then invite a student to measure using the unit of choice and students counting the units. Counting the units presents a good chance to discuss what to do if the units are more than the object.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3 You will need: three pieces of string 5 cm, 27 cm and 75 cm long, paperclips, craft sticks, counters, playing cards, NTO 1.24 ‘Measure It’, Student Book p. 41 ‘Paperclips or Counters?’
TASK 1:
MEASURING WITH THINGS
Have students work with a partner and choose two of the dinosaur footprints (or pieces of string) to measure. Have them record an estimate first and then measure, choosing from a range of informal uniform units, e.g. paperclips, counters, craft sticks, playing cards. Have students record their results.
TASK 2:
INTERACTIVE TASK
Have students explore NTO 1.24 ‘Measure It’ choosing different informal units to measure objects.
TASK 3: STUDENT BOOK p. 41 ‘Paperclips or Counters?’
TEACHING GROUP
You will need: paperclips, craft sticks, playing cards HOW LONG IS A TABLE? • For students who require support, have them focus on one object and the skills involved in using uniform units to measure its length. As a group, decide on an object in the classroom to measure, e.g. a tabletop. Explain to students that they are to measure the length of the tabletop using paperclips. Give each student a paperclip and ask, ‘How many paperclips do you think will fit end to end from one edge of the tabletop to the other?’ Have students write down their estimates. Then have them work in pairs or small groups to measure the tabletop. Have students compare results and discuss reasons for any discrepancies.
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Length and Area
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MEASURING WITH DIFFERENT UNITS • For students who require a challenge, have them explore using different uniform units. As a group, decide on a number of things in the classroom that can be measured, e.g. the width of the doorway, the shortest side of your desk, the width of a computer keyboard. Have each pair of students use something different to measure with, e.g. paperclips, craft sticks or playing cards. Have students record estimates before they measure. When students have finished measuring, have them share results. Record the different results and ask, ‘Were the results the same? Why not?’
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their results from Independent Tasks, Tasks 1 and 2, or from the Teaching Groups, and ask, ‘Did everyone get the same results? Why not?’ • Have the students who estimated well explain what strategies they used. • Have students explain how they measured and record a list of the key things they need to remember on the board or poster paper.
LESSON PLAN
TUNING IN
3
WHAT DO WE MEAN BY AREA? You will need: a normal classroom table In order to ensure that students understand the difference between length and area, have students trace along the edge of a classroom table with their index fingers and identify this as the ‘length’ of the table top. Next, ask them to start at one corner of the table top and to pretend that they are cleaning the whole surface of it with the palms of their hands. Identify this as the surface of the table top and that they have rubbed their hands over the whole of the area of the table top.
WHOLE-CLASS INTRODUCTION THE AREA OF A TABLE TOP You will need: Several books of the same type/size or sheets of A4 paper.’ Remind students of the Tuning In activity in order to ensure that they understand what is meant by the area of something. Say something like, ‘We are going to put the books (sheets of paper) side-by-side on the table top so that they cover the whole area. How many do you think we will need?’ Carry out the activity and identify the area as ** books/sheets of paper.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: counters/blocks, the cover of a book, NTO 1.53 ‘Larger or smaller area?’ 10 cm x 10 cm squares of coloured paper, a piece of card 30 cm x 20 cm divided into 10 cm x 10 cm squares, Student Book p. 42 ‘Area’
TASK 1:
WHAT’S THE AREA?
Working with a partner, students estimate the number of counters that will be needed to cover the front of a book. They could record their guesses and then carry out the activity. Afterwards they record the actvitiy by writing something like, ‘It took 20 counters to cover my book. The area of my book is 20 counters.’
TASK 2:
INTERACTIVE TASK
Have students explore the comparison of two areas area using NTO 1.53 ‘Larger or smaller area?’
TASK 3: STUDENT BOOK p. 42 ‘Area’
TEACHING GROUP
You will need: 10 cm x 10 cm squares of coloured paper, a piece of card 30 cm x 20 cm divided into 10 cm x 10 cm squares, BLM 52 ‘Two-centimetre Grids’ LET’S COVER IT • For students who require support, work with a small number of uniform, informal units (10 cm x 10 cm squares) and a piece of card 30 cm x 20 cm divided into 10 cm x 10 cm squares. Identify what is meant by the area of the card by rubbing a hand over the whole surface (see Tuning In). Ask the students how many of the coloured squares they think will be needed to cover the card. Carry out the activity by placing
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the squares on the card side-by-side, one at a time. Identfy the area of the card as 6 squares. Also use BLM 52 ‘Two-centimetre Grids’. Students estimate how many (2 cm) counters will be needed to cover the rectangles and then carry out the activity and complete Student Book, page 42, ‘Area’. USING DIFFERENT UNIFORM, INFORMAL UNITS • For students who require a challenge, have them explore using various uniform, informal units to find the area of a 10 cm x 10 cm sheet of paper. Ask, ‘Is the total number of counters the same as the total number of blocks, for example? Why or why not?’ Subsequent discussion could lead to the understanding why the use of a formal unit for finding area would be advantageous.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their results from Lesson Plans 1 and 2 Independent Tasks, Task 1, or from the Teaching Groups, and ask, ‘Did everyone get the same results? Why not?’ • Have students who estimated well explain what strategies they used. • Have students explain the difference bewteen what we mean by the length of something and the area of something.
Assessment • Have students complete Student Assessment p. 43. • Review with students Assessment Task Card 1.10. During the three lessons: • Collect created items from Lesson Plan 1, Independent Tasks, Task 1, and Lesson Plan 2, Independent Tasks, Task 1, as work samples for student portfolios. • Observe students as they complete Lesson Plan 1, Independent Tasks, Task 1, and Lesson Plan 2, Independent Tasks, Task 1, and mark off on a class list students who are able to make reasonable estimates and measure the length of objects reasonably accurately. • Make note of the way that students estimate area in Lesson Plan 3. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future learning Specific to Student Assessment p. 43; if the student is experiencing difficulty: Q 1–2 Provide more experiences in the classroom for the student to measure and compare two objects according to length, e.g. finding who has the longest shoe. Q 3 Have the students use a variety of informal units to find the area of the same object. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 1.10 for specific recommendations. 2. Have the student directly compare objects and determine the longest prior to using uniform informal units. 3. Review Nelson Maths: Australian Curriculum Kindergarten Unit 7. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 2 Unit 3. 2. Extending the student in any of the listed activities or tasks by using more than two objects to measure the length and compare using uniform informal units. Discuss the advantage of using uniform, formal units for measurement.
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Length and Area
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Two Footprints Long
DATE:
You will need: a copy of BLM 18 ‘Dinosaur Footprints’, scissors 1
Cut out your dinosaur footprints.
2
Look around your classroom. Draw 3 objects that might be
2 footprints long.
3
Now measure the objects and record what you found out.
Objects (Draw here)
4
46
How many footprints long?
Write what you found out when you measured
How did you decide which objects might be
Unit
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long?
Length and Area (TRB pp. 58–61) Length MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres
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Paperclips or Counters?
DATE:
You will need: paperclips, counters 1
Choose what you are going to use to measure the length
of each object. Write it here:
2
First estimate how long you think each object will be.
3
Now measure each object.
Object
Estimate
How many?
Book
Strap on school bag
4
Which object is longer?
How do you know?
5
Check with a partner. Did they get the same results as you?
How do you think that happened?
Unit
Length and Area (TRB pp. 58–61) Length MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres
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Area
DATE:
1
Use counters to find the area of each shape.
How many counters for each shape?
Colour the shape with the largest area red.
Colour the shape with the smallest area blue.
2
Count the squares to find the area of each letter.
Which has the largest area?
Which has an area that is 1 square bigger than “T”?
Which have the same area?
Draw a letter “L” that has an area of 7 squares.
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Length and Area (TRB pp. 58–61) Area MA1-10MG measures, records, compares and estimates areas using uniform informal units
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DATE:
Unit
10
STUDENT ASSESSMENT
You will need: counters • Look at the snakes. Estimate how long you think each snake might be if you measured it with counters. • Now measure the snakes with counters.
Estimate
Number of counters long
Sammy
Sid
• W hich two letters have the same area? Use counters to find out.
Unit
10
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The letters with the same area are
and
Length and Area (TRB pp. 58–61) Length MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres Area MA1-10MG measures, records, compares and estimates areas using uniform informal units
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Unit
4
Numbers Up to 1 000
NUMBER AND ALGEBRA Whole numbers: MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
ML
digit, hundreds, ones, number cards, MAB blocks, spike abacus, tens
LESSON PLAN
TUNING IN
1
READING NUMBERS You will need: NTO 2.1 ‘Numbers’ Present NTO 2.1 ‘Numbers’ set to show three cards with numbers from 0 to 9. Place the cards close together and have students read the 3-digit number. Rearrange the cards and have students read the new number formed. Continue having students practise reading 3-digit numbers by using the NTO to generate cards that can be arranged to form the numbers.
WHOLE-CLASS INTRODUCTION USING NUMBER CARDS You will need: NTO 2.xx ‘Number Cards’ Present NTO 2.xx ‘Number Cards’. Select a random number and have students read the number. Then ask them to say the number aloud and ask, ‘How many hundreds did you say?’ Invite a student to select the number card for that many hundreds. Have students say the number again. Invite a student to select the tens card and have them say the number again. Finally, have a student select the ones card and have the class say the number again. Generate more numbers, inviting students to say the number and then show it using the number cards.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of arrow cards made from BLM 2 ‘Arrow Cards 1’, BLM 3 ‘Arrow Cards 2’, a set of cards made from BLM 1 ‘Number Cards’, NTO 2.xx ‘Number Cards’, Student Book p. 60 ‘Arrow Cards’
TASK 1:
MATCH THE NUMBER
Have students work in pairs. Give each pair a set of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’ and a set of number cards made from BLM 1 ‘Number Cards’. One student selects a number card (their partner is not allowed to see it) and reads the number aloud while their partner forms that number using arrow cards. This student can then check their arrow card by looking at the number card, and if they are correct, they keep the number card. Students then reverse roles. The student with the most number cards wins.
TASK 2:
INTERACTIVE TASK
Have students explore NTO 2.xx ‘Number Cards’ by randomly generating a number and using the number cards to show the number.
TASK 3: STUDENT BOOK p. 60 ‘Arrow Cards’
TEACHING GROUP
You will need: sets of arrow cards made from BLM 2 ‘Arrow Cards 1’, BLM 3 ‘Arrow Cards 2’ (100 card only), NTO 2.xx ‘Number Cards’ 100 MORE • For students who require support, begin by having them make 2-digit numbers using a set of arrow cards made from BLM 2 ‘Arrow Cards 1’. Working with a partner, have them sort their cards into columns of ones and tens. Have students show 2-digit numbers. Say the number and have students repeat the number and find the two cards to show the number. Continue having students make 2-digit numbers, and when they are ready, have them show 28 and then ask then to place the 100 card (from BLM 3 ‘Arrow
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Cards 2’) underneath and read the number. Continue having students make 2-digit numbers and then placing the 100 card underneath and reading the number. USING THE 1 000S CARDS • For students who require a challenge, have them work with higher numbers. Present NTO 2.xx ‘Number Cards’ and select the 1 000s cards. Point to different cards and have students read them out. Select a 1 000s card, hundreds card, tens cards and a ones card and have students read the number. Double click on the hundreds card to remove it and have students read the number. Double click on the tens card and have students read the number. Repeat a few more times, showing a number and having students read the number aloud. Have students randomly generate a number and then make the number.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask students ‘When you make a number with arrow cards or on the computer, what are you thinking? • Tell students that you want them to show the number 942 (either using arrow cards or NTO 2.1 ‘Numbers’) and have them explain how they would do it. Ask, ‘How do you know you are correct?’ • Present NTO 2.xx ‘Number Cards’ and randomly generate a number, but ask students to show a number that is 100 more or less.
LESSON PLAN
TUNING IN
2
DOES ANYONE HAVE? You will need: a set of number cards made from an enlarged copy of BLM 1 ‘Number Cards’ Give a number card to each student and ask, ‘Does anyone have a number with six tens?’ Have those students stand up and show their cards. Ask, ‘Does anyone have a card with more than five hundreds?’ Continue asking questions about place-value components and note any students who are having difficulty and may need support in the Teaching Groups.
WHOLE-CLASS INTRODUCTION SPIKE ABACUS You will need: NTO 2.xx ‘Spike Abacus’, a set of number cards made from an enlarged copy of BLM xx ‘Number Cards’, small whiteboards Present NTO 2.xx ‘Spike Abacus’ and explain to students that they can use a spike abacus to model numbers. Place one bead on the hundreds spike, two beads on the tens spike and three beads on the ones spike. Ask, ‘What number has one hundred, two tens and three ones?’ Invite a student to write the number on the board. Make another three-digit number with seven beads on the hundreds spike, four beads on the tens spike and six beads on the ones spike, and ask, ‘What number has seven hundreds, four tens and six ones?’ Continue making numbers and asking students to write down the number on small whiteboards. Next, select a number card made from BLM xx ‘Number Cards’ and ask, ‘Can anyone show this number on the spike abacus?’ Invite a student to show the number and then check the number of beads for each place-value component and check against the number card. Continue inviting students to select a number card and show the number on the spike abacus.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’, a spike abacus and beads, BLM 1 ‘Number Cards’, NTO 2.xx ‘Spike Abacus’, Student Book p. 61 ‘Numbers on a Spike Abacus’
TASK 1:
SPIKE ABACUS AND ARROW CARDS
Have students work with a partner whereby one student shows a number on the spike abacus and their partner must show that number using arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’. Then have the student with the arrow cards show a number and their partner must show that number on the spike abacus. Have students alternate roles using the modelling equipment.
TASK 2: INTERACTIVE TASK Give students a set of number cards made from BLM 1 ‘Number Cards’, and have them use NTO 2.xx ‘Spike Abacus’ to model a selected number. They can check they are correct by selecting the ‘show number’ button.
TASK 3:
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STUDENT BOOK p. 61 ‘Numbers on a Spike Abacus’
Numbers Up to 1 000
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TEACHING GROUP
• You will need: small whiteboards, Blu Tack or playdough, wooden skewers (with sharp ends cut off), beads (can be made from playdough), NTO 2.xx ‘Spike Abacus’ MAKING A SPIKE ABACUS • Give each student a small whiteboard and enough Blu Tack so that two skewers can stand upright on the board. Have students label the skewer on the right ‘Ones’ and the skewer on the left ‘Tens’. Say a 2-digit number, e.g. 32, and ask, ‘How many tens?’ Have students place that many beads on the tens skewer and ask, ‘How many ones?’ Have students place that many beads on the ones skewer. Continue. FOUR SPIKES • For students who require a challenge, have them use a spike abacus to make 4-digit numbers. Present NTO 2.xx ‘Spike Abacus’ and select the ‘show thousands’ button to reveal the fourth spike. Place some beads on the spikes, and have students write the number shown on small whiteboards. Invite a student to read their number and ask, ‘How did you work that out?’ Repeat a few more times, displaying numbers and having students write down what number is shown. Next, invite a student to write a 4-digit number on their whiteboard and show that number on the NTO. Have the student reveal the number on the whiteboard and the group determine if it matches the number shown on the spike abacus.
REFLECTION Select from the following to suit your class and their learning outcomes: • Present NTO 2.xx ‘Spike Abacus’ showing 438. Ask, ‘What number is shown? How do you know?’ • Ask, ‘I placed five beads on a three-spike abacus. What number could I have shown?’ Using a spike abacus, discuss possible answers and have students explain how they worked out the problem.
LESSON PLAN
TUNING IN
3
WHAT NUMBERS CAN YOU MAKE? You will need: NTO 2.1 ‘Numbers’ Present NTO 2.1 ‘Numbers’ set to show three number cards between 0 and 9. Have students look at the numbers, and move three of the numbers close to one another and say the 3-digit number. Ask, ‘What other numbers can we make using the three numbers displayed?’ Have students come to the board and rearrange the cards to make other 3-digit numbers. Ask, ‘What is the largest number you can make? What is the smallest number you can make?’
WHOLE-CLASS INTRODUCTION WHAT’S MY NUMBER? You will need: NTO 2.xx ‘Number Cards’ Write a 3-digit number on a piece of paper and keep it hidden. Present NTO 2.xx ‘Number Cards’ and ask, ‘What do you think my number is?’ Instead of saying the number, invite a student to show what they think the number could be. If any of the components are correct, leave the card displayed, but if they are not part of the number, double click to remove the incorrect cards. Continue to invite students to show their guesses, leaving the correct components and removing the incorrect components until the mystery number is worked out.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of 3 dice, BLM 4 ‘Number Stairs’, NTO 2.xx ‘Playing Cards’, Student Book p. 62 ‘Climbing Up the Ladder’
TASK 1:
NUMBER STAIRS
Have students play with a partner whereby they take it in turns to roll the three dice to form a 3-digit number. Students place the number in any space on BLM 4 ‘Number Stairs’, provided the numbers decrease as they go down the stairs. If students cannot make a number that will fit, they forfeit their turn. The first student to complete their stairs with the numbers in order from highest to lowest wins.
TASK 2: INTERACTIVE TASK Have students work with a partner to use NTO 2.xx ‘Playing Cards’ to deal three cards and rearrange the digits to make the largest number they can. Their partner draws three cards to see if they can make a larger number.
TASK 3:
STUDENT BOOK p. 62 ‘Climbing Up the Ladder’
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TEACHING GROUP
You will need: a deck of playing cards with the tens and picture cards removed, a dice BEAT IT • For students who require support, work with 2-digit numbers until they are able to extend their place- value understanding to hundreds. Have students play with a partner whereby the first player draws two playing cards from the deck and forms the largest number they can. Their partner then draws two cards to make a number that will ‘beat it’. The student who has formed the highest number keeps all four cards. The student with the most cards wins. CLOSEST TO 999 • For students who require a challenge, have them draw up a table or grid with three columns in which they write the headings ‘Hundreds’, ‘Tens’ and ‘Ones’. The object of the game is to get a score as close to 999 without going past it. The dice is rolled six times, and for each roll, students will decide if it is to be a hundred, ten or one. After six rolls of the dice, students add up their score and the score that is closest to 999 wins, but if the total is more than 999 they have lost.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask in relation to Independent Tasks, Tasks 1 and 2, ‘When you rolled the dice or drew the cards, how did you decide what was the best number to make?’ • Ask in relation to the Independent Tasks and the Teaching Groups, ‘What strategies did you use to win the game?’
Assessment • Have students complete Student Assessment p. 63. • Review with students Assessment Task Card 2.4. During the three lessons: • Observe students in Lesson Plan 2, Independent Tasks, Task 1, and mark on a class list students who are able to represent 3-digit numbers with arrow cards and on a spike abacus. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 63; if the student is experiencing difficulty: Q 1 Have the student work with a range of materials to model 2-digit and then 3-digit numbers, e.g. craft sticks, Unifix blocks, MAB blocks, and use arrow cards to label models. Q 2–3 Have the student model 2-digit numbers on a spike abacus before moving to 3-digit numbers. Q 4 Provide opportunities for the student to explore making 2-digit numbers by drawing playing cards or rolling dice. Q 5 Look for opportunities in the classroom where the student needs to order numbers, e.g. scores in games, team points and so on. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 2.4 for specific recommendations. 2. Have the student work with 2-digit numbers in any of the listed activities or tasks prior to moving to 3-digit numbers. 3. Review Nelson Maths: Australian Curriculum Year 1 Unit 15. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Completing Nelson Maths Building Mental Strategies Big Book 3, pp. 14–15, to reinforce mental strategies involved in ordering numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 3 Unit xx, pp. xx–xx. 3. Extending the student in any of the listed activities or tasks by using 4-digit numbers.
Unit 4
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Numbers Up to 1 000
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BLM
1
Number Cards
237
73
615
516
948
840
909
217
643
821
395
781
702
372
515
416
489
94
150
634
803
362
123
468
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
Teacher’s Note: This BLM can be photocopied, laminated and cut up to make cards to use for modelling and sorting activities.
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BLM
2
Arrow Cards 1
1 2
7
5
3
6
4
8 0 6
9
8 0
4 0
7 0
3 0
6 0
2 0
5 0
1 0
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
Teacher’s Note: To make the cards, cut around the outside borders and along the dotted diagonal lines. Place cards one on top of the other, aligning the arrows, to build combinations of numbers with hundreds, tens and ones.
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BLM
4 0 0
7 0 0
8 0 0
2 0 0
3 0 0
1 0 0
6 0 0
Arrow Cards 2
5 0 0
3
9 0 0 © Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
Teacher’s Note: To make the cards, cut around the outside borders and along the dotted diagonal lines. Place cards one on top of the other, aligning the arrows, to build combinations of numbers with hundreds, tens and ones.
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BLM
4
Number Stairs
1 000
1 000
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution. Unit
4
Whole numbers MA1-4NA
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2.4
Year 2: Assessment Task Card Unit
4
NUMBERS UP TO 1 000
Resources: BLM 2 ‘Arrow Cards 1’, BLM 3 ‘Arrow Cards 2’, a spike abacus, NTO 2.xx ‘Dice’
1
Say the following numbers and have the student show using arrow cards:
472, 967, 214, 504, 370
2
Show the following numbers on a spike abacus and ask the student what number is shown:
274, 856, 247, 201, 960
3
Have the student show the following numbers on a spike abacus:
324, 178, 670, 302
4
Using NTO 2.xx ‘Dice’, show three dice. Ask the student what is the smallest 3-digit number they can make from those numbers. Ask the student what is the largest 3-digit number they can make from those numbers.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
2.4
Year 2: Assessment Task Card Unit
1
NUMBERS UP TO 1 000 TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Provide opportunities for the student to show 2-digit numbers using arrow cards or NTO 2.xx ‘Number Cards’ before moving to 3-digit numbers.
Q2–3 Have the student model numbers using MAB blocks, and then have them show the same numbers modelled with arrow cards. Have the student show the same numbers on a spike abacus. Q3–4 Provide opportunities for the student to play games, e.g. BLM 4 ‘Number Stairs’ or ‘Ladder Games’, similar to ‘Climbing Up the Ladder’ (Student Book p. 62), whereby the student uses their place-value understandings, and the number of cards or dice used can also match the student’s level of place-value understanding.
Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 2 may be photocopied for educational use within the purchasing institution.
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Arrow Cards
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You will need: a set of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’ 1 Using your arrow cards, make numbers to match the MAB models. Write your numbers beside each model. a
b
c
d
2 Use your arrow cards to make the numbers below. Write your number in the box. a A number that is more than 700 but has no tens b A number that is less than 700 but has no ones c A number that is between 700 and 900
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Numbers Up to 1000 (TRB pp. 50–51) Whole numbers MA1-4NA applies place value, informally, to count, order, read and represent two-and three-digit numbers
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Numbers on a Spike Abacus
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1 Write the numbers that are shown on the abacus.
H
T
O
H
H
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T
O
O
H
H
T
O
T
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H
H
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T
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2 Show the following numbers on the abacus.
905 227 69
562
H
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H
380
H
T
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H
631
H
T
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T
O
H
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454
713
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3 Show the following numbers on the abacus. Write the number beside the abacus. a 10 less than 256
H
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b 100 less than 789
H
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Climbing Up the Ladder You will need:
DATE:
a partner, 3 dice
1 In turn, roll the dice and make a 3-digit number. Write your
number on a rung of the first ladder. The numbers need to get
bigger as you go up the ladder.
2 Once you have written a number, it must stay on that rung. 3 Keep rolling the dice and placing your numbers until each player has filled their ladder.
4 You score 1 point if the numbers are in order from smallest
to largest.
5 The person with the most points after 8 rounds wins.
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DATE:
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STUDENT ASSESSMENT
You will need: a set of arrow cards made from BLM 2 ‘Arrow Cards 1’ and BLM 3 ‘Arrow Cards 2’, a dice 1 Use the arrow cards to make the numbers. Write them.
H
T
O
H
T
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2 Write the numbers that are shown on the abacus.
H
T
O
H
T
O
H
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H
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3 Show the following numbers on the abacus. 147 302 415
562
H
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H
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H
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H
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4 Roll a dice 3 times. Write each number in a box.
Use the numbers to write as many 3-digit numbers as you can. 5 Order your numbers from smallest to largest.
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Position
MEASUREMENT AND GEOMETRY Position: IMA1-16MG represents and describes the positions of objects in everyday situations and on maps
ML
above, back to back, backwards, behind, below, between, centre, forwards, half turn, in front of, left, middle, near, next to, right, quarter turn, side by side, top, towards, under, underneath, upside-down
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LESSON PLAN
TUNING IN
MIME IT Have students work with a partner or in small groups. Explain to students that they are going to mime – actions without speaking – words that are used to give directions. Ask students, ‘What words might you use if you were going to explain to someone how to get from one place to another?’ Record their suggestions. Whisper a word to each group so that no one else can hear and have students mime the word for the class to guess.
WHOLE-CLASS INTRODUCTION ROBOTS Tell students someone is going to be a ‘robot’ and they will move around the room. Explain that the robot cannot think for itself and needs to be programmed so that it can move around the room. Inform students that you are the robot and that they will need to tell you how to move from one place to another in the classroom. Pick two classroom objects to move between that will require at least one turn. Invite different students to give instructions and follow them. If you are instructed to turn, complete a 360 turn unless the students tell you otherwise. At that point, discuss with students the need for more specific language, e.g. quarter turn or half turn. Continue until you have reached your destination. Next, invite a student to be the ‘robot’ and another student to give the instructions to move from place to place, e.g. from the door to your desk, from the board to the bookshelf, from the sink to the computers, and so on.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: disposable or plastic plates of varying sizes, cups, bowls, cutlery, toy food items, LO 1074 ‘Direct a Robot: Which Way?’, Student Book p. 68 ‘Pattern Block Pictures’
TASK 1:
DINNER TIME
Have students work in pairs, each with a variety of the materials above. Have a student make an arrangement using plates or bowls, cups and cutlery, and placing different food on the plates. This arrangement can be covered with a cloth or a barrier placed between so that it is hidden from their partner. The student then explains what they have done and the position of items in relation to one another so that their partner can draw the arrangement as they have laid it out. When they have finished, they check to see which things are in the correct position and which are not, and discuss why this might have happened. Students then change roles.
TASK 2:
INTERACTIVE TASK
Have students explore LO 1074 ‘Direct a Robot: Which Way?’ whereby they need to select the direction the robot turns in order to take the shortest route to collect samples before returning to their spaceship.
TASK 3:
STUDENT BOOK p. 68 ‘Pattern Block Pictures’
TEACHING GROUP
You will need: NTO 2.xx ‘Pattern Blocks’, a set of pattern blocks, a digital camera ARRANGING BLOCKS • For students who require support, have them follow step by step as an arrangement is made on NTO 2.xx ‘Pattern Blocks’ and discuss positional language. Present NTO 2.xx ‘Pattern Blocks’, and explain that as
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an arrangement of shapes is made on the NTO, students will make the same arrangement with pattern blocks. Select a shape, e.g. a square, place it in the centre of the board and ask, ‘How can we describe where we put the square?’ Have students find a square and place it in the centre of the space in front of them. Then select another shape, e.g. a hexagon, place it under and touching the square and ask, ‘How can we describe where we put the hexagon?’ Have students place the hexagon in their own arrangement. Select another shape, e.g. a trapezium, place it above and touching the square and ask, ‘How can we describe where we put the trapezium?’ Have students place the trapezium. Continue placing shapes and have students use directional language to describe the position of each shape as they place in their own arrangement. CAN YOU MAKE A MATCH? • For students who require a challenge, have them create an arrangement of shapes and write a description for a partner to follow to create the same arrangement. Take digital photos of original arrangements, and after instructions have been followed by a partner, pairs can check the photo to see if they are correct. If a matching arrangement has not been made, have students determine why and modify their instructions.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students show their work from Independent Tasks, Tasks 1 and 3, and ask, ‘Why do you think that the pictures were not identical?’ Discuss why some things may have been different sizes and maybe things may not have been placed in the correct place. • Ask in relation to ‘Can You Make a Match?’ in the Teaching Group, ‘What was the first instruction you gave? Why did you choose that?’
LESSON PLAN
TUNING IN
2
BIRD’S-EYE VIEW You will need: a box, a large can, a large ball, NTO 2.xx ‘Bird’s-Eye View’ Pass a box to students and ask them to look down on the box and think about the shape that they can see. Ask, ‘If you could fly and look down on this, what shape do you think you would see?’ Continue to pass the other objects (can and ball) to students. Have them look down on these objects and ask them what shape they think they might see if they were a bird flying over it. Present NTO 2.xx ‘Bird’s-Eye View’ and explain to students that the shape that they see on screen is what a bird would see if it was flying high above an object. Ask, ‘What do you think it could be? What makes you think that?’ Invite a student to check by selecting an object. Continue presenting other bird’s-eye views and asking students what object they think it might be and why.
WHOLE-CLASS INTRODUCTION AS THE CROW FLIES You will need: As the Crow Flies: The First Book of Maps by Gail Hartman (Bradbury Press, 1991) Hold up the cover of As the Crow Flies: The First Book of Maps and ask, ‘What can you see?’ Have students describe all the different things they can see and ask, ‘Why do you think the crow can see so much?’ Discuss with students the idea that the crow is so high in the sky that it can see further than if it was on the ground as there is nothing blocking its view. Read the book and discuss the difference between the picture and the map for each animal.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: a digital camera, NTO 2.xx ‘Bird’s-eye View’, Student Book p. 69 ‘Ebony’s Run’
TASK 1: AS THE CHILD SEES Have students look out of the window and name at least three things that they can see. Explain that you want them to draw their map just as there was a map for the eagle, rabbit, crow, horse and gull showing what they saw. Ask, ‘What shape do you think our classroom would be if we were looking down on it from above?’ Have them begin their map by drawing the shape that represents the classroom and then have them draw the other things they identified when looking out of the window.
TASK 2:
INTERACTIVE TASK
Students could use a digital camera to take ‘bird’s-eye view’ pictures of classroom objects. Ask them to share these with other students and to see if the other students can identify the objects. Alternatively students could further explore NTO 2.xx ‘Bird’s-Eye View’.
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TASK 3: STUDENT BOOK p. 69 ‘Ebony’s Run’
TEACHING GROUP
You will need: a fairytale picture book, glue, BLM xx ‘Funtime Park’ FAIRYTALE MAP • For students who require support, read or tell the story of a fairytale, e.g. Goldilocks and the Three Bears, Little Red Riding Hood, Cinderella or The Three Little Pigs. Ask, ‘What are the different places in the story?’ Make a list of the places and have individual students draw a picture of one of the places on a small piece of paper. Then, on a large sheet of paper, have the students place their pictures where they think each place should go. Reread or retell the story and make sure that the drawings have been placed in the correct position. Have students paste the pictures in place. MAP OF A THEME PARK • For students who require a challenge, give them a copy of BLM xx ‘Funtime Park’ whereby they need to read the directions and make a map of the park.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from ‘Fairytale Map’ in the Teaching Group, and ask, ‘How did you know where to draw things on your map? How do you know that you have put them in the correct place?’ • Ask in relation to ‘Map of a Theme Park’ in the Teaching Group, ‘What do you think was the most difficult thing about drawing a map?’ • Discuss with students the things they need to remember when drawing maps and make a poster of their suggestions to display in the classroom for reference during other mapping activities.
LESSON PLAN
TUNING IN
WHERE DO I LIVE? You will need: Where Do I Live? by Neil Chesanow (Barron’s Educational Series) Explain that you are going to read a book about a student who lives in the United States of America and she explains where she lives. Read the story to students, then ask, ‘Where do you live?’ and invite students to explain where they live.
3
WHOLE-CLASS INTRODUCTION OUR SCHOOL You will need: access to SpatialGenie at www.spatialgenie.edu.au (you will need to register for a free login prior to the lesson) Present SpatialGenie to students showing a map of the world. Under ‘My Map’ select the satellite view. Explain to students that this view is just like being in a rocket and coming back to Earth. Double click onto Australia for a closer view. Double click onto your state. Then keep double clicking until you have zoomed in to your school. Point to different buildings of the school and ask students what they think each is. Have students identify places they may know that are close to the school, e.g. shops or parks. You can scroll across from ‘My Map’ to ‘Street View’, and using the icon of an orange figure on the toolbar at the top of the map, you can get a street view of the school building. Once you have explored the school from different angles, scroll back to ‘My Map’ and click on the normal view to see it represented as a map. Have students look at the map and ask, ‘What do you recognise on the map?’ Discuss any specially marked features, e.g. parks, shops and the names of streets.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: SpatialGenie, Student Book p. 70 ‘Our School’
TASK 1:
OUR NEIGHBOURHOOD
Explain to students that you want them to make a map of the neighbourhood where their school is. Ask, ‘What do we have in our neighbourhood that we would record on a map?’ Make a list of students’ responses so they can include them on their own map. Have students draw a map and include their home if they can.
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TASK 2:
INTERACTIVE TASK
Have students explore SpatialGenie to see if they can find their house, and have them look at it as a satellite view and as a map. Have them also use the street view to find their house.
TASK 3: STUDENT BOOK p. 70 ‘Our School’
TEACHING GROUP CLASSROOM MAP • For students who require support, guide them through the process of drawing a map. Begin by asking what is the shape of the classroom if students were looking down on it, and have them draw that. Next, determine the key feature, e.g. tables, and have students count how many and look at the arrangement. Then have students draw the tables on their maps. Continue identifying objects in the classroom and determining which shapes will give a bird’s-eye view of the object and add those to the map. WHICH ROOM? • For students who require a challenge, have them work with a partner whereby one student instructs the other student what to draw for a map of a room of their choice. They can choose a room in the school and their partner should be able to guess which room it is when the map is complete.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their maps from Independent Tasks, Task 1, and have them explain what they drew first and then how they proceeded. Ask, ‘The maps look a bit different. Why?’ • Have students show their maps from ‘Classroom Map’ in the Teaching Group to a partner, and ask, ‘What do you think was good in your partner’s map? What do you think they could improve next time?’
Assessment • Have students complete Student Assessment p. 71. • Review with students Assessment Task Card 2.10. During the three lessons: • Collect created items, e.g. drawings and maps, as work samples for student portfolios. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 71; if the student is experiencing difficulty: Look for opportunities in the school environment for the student to describe how to get from one place Q 1 to the next, e.g. when sending students on messages, ask them to describe the route they would take. Have the student draw classroom objects from different points of view and have others try to determine Q 2 which view the drawing was done from. Increase the difficulty by placing more than one object. Provide street directories, atlases and other simple maps for the student to explore. Q 3 If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 2.10 for specific recommendations. 2. Provide experiences with simple maps of familiar areas, e.g. local parks and shopping centres. 3. Review Nelson Maths: Australian Curriculum Year 1 Unit 7. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Moving forward to Nelson Maths: Australian Curriculum Year 3 Unit xx, pp. xx–xx. 2. Extending the student in any of the listed activities or tasks by including the use of scale.
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Pattern Block Pictures
DATE:
You will need: BLM xx ‘Pattern Blocks’, glue, scissors, sheets of paper 1 Cut out the pattern blocks from BLM xx ‘Pattern Blocks’. Make a picture with the blocks and paste your picture below. Make sure your partner cannot see your picture.
2 Have your partner get another sheet of paper. Tell them where to draw the shapes so that they make a picture that is exactly the same as yours. 3 Now listen to your partner and draw what they tell you on another sheet of paper. 4 Is your partner’s picture the same as yours? How is it different?
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Position (TRB pp. 58–61) Position MA1-16MG represents and describes the positions of objects in everyday situations and on maps
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Ebony’s Run
DATE:
One day, Ebony got up early to go for a run. She walked out of her big house and ran down to the end of her street where there was a big forest. There were two paths into the forest, and she took the path on the right. She ran until she was in the middle of the forest, where she found a small cave. She heard a growl coming from the cave and quickly ran past the cave and further into the forest. Ebony thought she was lost until she came to a road. She turned left into the road and followed it all the way to her street. She ran along her street until she got home. Draw a map of where Ebony ran. Remember to include all of the places mentioned in the story.
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Our School
DATE:
1 List the things that are part of your school buildings. 2 List the things that are outside the buildings but part of the school. 3 Draw a map of your school. Make sure you include all the things on your lists. Remember that a map is a bird’s-eye view.
4 Is there anything else you can add to the map of the school?
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DATE:
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STUDENT ASSESSMENT
1 Write how you would get from your classroom to the office.
2 What could these be? You are looking at them from a bird’s-eye view.
3 Draw a map of your classroom.
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Unit
1
Numbers, Numbers, Numbers
NUMBER AND ALGEBRA Whole Numbers: MA2-4NA applies place value to order, read and represent numbers of up to five digits
ML
even, hundreds, larger, place value, odd, order, smaller, tens, thousands, units
1
LESSON PLAN
TUNING IN WHAT’S IN THE JAR?
You will need: beans, four jars or transparent containers Present students with four jars of beans, with one jar containing 9 beans, the next jar containing 31 beans, the next 53 beans and the final jar 147 beans. Ask, ‘Which jar has about 50 beans?’ Have students discuss their guess and the reasons for their guess. Invite four students to count out the beans in each jar. Record the numbers and tell students that these numbers have something in common that you will ask them about at the end of the lesson.
WHOLE-CLASS INTRODUCTION EXPLORING ODD AND EVEN NUMBERS You will need: sets of number cards made from BLM 1 ‘Number Cards 1’, counters Have students work with a partner. Give each pair some of the number cards made from BLM 1 ‘Number Cards 1’. Have students count out counters according to their number cards. Explain to students that they are going to determine if they have an odd or even number of counters and that this can be done by grouping counters in twos. If all the counters can be made into groups of two, the number is even. If there is a counter that cannot be grouped with another, the number is odd. Have students determine if their number is odd or even and make a list of the even numbers and the odd numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: NTO 3.1 ‘Ten Frames’, BLM 1 ‘Number Cards 1’, Student Book p. 82 ‘Odd or Even?’
TASK 1:
DOT PAIRS
Have students write some 1- and 2-digit numbers, e.g. how old they will be next birthday, the last two digits in their phone numer, their street number, the number of students in their class, etc. Students can then make models of the numbers by sticking dots (or drawing dots) in pairs onto a sheet of paper and writing the number beside their model. Have students share and discuss their numbers with a partner and then label their models either odd or even.
TASK 2:
INTERACTIVE TASK
Provide students with the numbers cards from BLM 1 ‘Number Cards 1’ that were not used in the ‘Exploring Odd and Even Numbers’ activity in the Whole-Class Introduction. Have them use NTO 3.1 ‘Ten Frames’ to determine if the numbers are odd or even.
TASK 3: STUDENT BOOK p. 82 ‘Odd or Even?’
TEACHING GROUP You will need: Unifix blocks, BLM 3 ‘Blank Chart’ FINGERS ON SHOW • For students who require support, give them some Unifix blocks and have them make the numbers to 10 by making them with two groups of blocks joined, e.g. 4 would have two groups of two blocks. Have students write a list of even numbers and odd numbers. Then have students play a game with a partner whereby they put one hand behind their back and decide how many fingers to hold up. On the count of Nelson Maths Australian Curriculum NSW
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three, both students show their hands. One student will score a point if the total number of fingers shown is even and the other will score a point if it is odd. HOW DO YOU KNOW IT IS AN EVEN NUMBER? • For students who require a challenge, give them a copy of BLM 3 ‘Blank Chart’ and have them choose any starting number and fill in the numbers on the chart. Discuss with students the conditions for a number to be even and have them colour all of the even numbers. Have students look at the even numbers and write a rule for how to identify an even number.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from the Whole-Class Introduction or from the Teaching Groups, and ask, ‘How do you know if a number is an even number?’ Then invite students to name even numbers that are more than 20, 50, 100, 200, 500 and 1 000. Ask, ‘Can you think of a rule for deciding if a number is odd or even?’ • Draw students’ attention to the four numbers that you recorded during ‘What’s in the Jar?’ in Tuning In, and ask them what the numbers have in common. Ask, ‘How do you know that they are all odd numbers?’
LESSON PLAN
TUNING IN
TELL ME ABOUT THE NUMBER Write a number on the board, e.g. 46, and ask students to think of as many things as they can about the number, e.g. it is an even number, it is made up of four tens and six ones, it is four less than 50, it is ten more than 36 and so on. Repeat for other numbers.
2
WHOLE-CLASS INTRODUCTION WORDS AND NUMERALS You will need: NTO 3.2 ‘Number Cards’, small whiteboards Present NTO 3.2 ‘Number Cards’, selecting the random number to be shown. Have students read the number and invite a student to show the number with the number cards. Explain that we can see the number written as a numeral, shown with number cards and ask, ‘How can you write the number in words?’ Have students say the number and then ask them to write the number in words on their whiteboards. To support students, write the words ‘thousand’, ‘hundred’, ‘ninety’, ‘eighty’, ‘seventy’, ‘sixty’, ‘fifty’, ‘forty’, ‘thirty’ and ‘twenty’ on the board or on cards. Repeat for other numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 4 ‘Blank Cards’, NTO 3.3 ‘Dice’, Student Book p. 83 ‘Number Sort’
TASK 1:
CARD GAME
Give each student two copies of BLM 4 ‘Blank Cards’. Have them make pairs of cards with numerals on half of the cards and the matching numerals in words on the other half. Students combine with a partner to play ‘Memory’, whereby all of the cards are placed face-down and students take it in turns to turn over two cards to find a pair. Alternatively, students could play ‘Go Fish’ or ‘Snap’.
TASK 2:
INTERACTIVE TASK
Have students work with a partner using NTO 3.3 ‘Dice’. Before rolling the dice, students decide if they will form an odd or even number. They roll four dice and rearrange to form a 4-digit odd or even number, which they record using words. Each time they meet the requirement, they score a point.
TASK 3:
STUDENT BOOK p. 83 ‘Number Sort’
TEACHING GROUP You will need: NTO 3.3 ‘Dice’, five dice for each student in the group STEP BY STEP • For students who require support, begin with 2-digit numbers and build up to 4-digit numbers. Present NTO 3.3 ‘Dice’ and select two dice to randomly generate two digits. Have students write the two possible 2-digit numbers and determine if the numbers are odd or even. Have students write the numbers in words. Have students add 100 to the numeric form of their numbers and ask them to read the numbers and write them in words. Then have students add 1 000 to the numeric form of their numbers and have them read the numbers and write them in words. Repeat the process by rolling the two dice again.
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FOUR CATEGORIES • For students who require a challenge, have them work with higher numbers. Give each student five dice that they use to form four 5-digit numbers: the highest odd number, the highest even number, the lowest odd number and the lowest even number. Have students write their numbers in words and compare with the group. A point is given to the student who is able to form the highest or lowest in each category, and a point deducted if they are unable to form a number for any of the categories. Have students continue to roll the dice and form more numbers.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students discuss any difficulties they encountered when writing numbers in words and ask, ‘How did you know that you had written the number correctly?’ • Create a chart of students’ strategies for writing numbers in words. Display the chart in the classroom.
LESSON PLAN
TUNING IN
3
POPCORN! Explain to students that they are going to play a game in which you will call out numbers, and if the number is odd they crouch down, but if the number is even, they jump up and say: ‘Popcorn’. Have students stand, and begin by calling out 1- and 2-digit numbers. As the game progresses, increase the numbers to 3- or 4-digit numbers.
WHOLE-CLASS INTRODUCTION MOVING NUMBERS You will need: number cards made from BLM 2 ‘Number Cards 2’ Have students sit on chairs in a circle and give each student a number card made from BLM 2 ‘Number Cards 2’. Explain to students that, if their number meets the criteria mentioned, they need to stand up and swap chairs with someone else. Begin by giving criteria like ‘more than 500’, ‘odd number’, ‘7 in the tens place’, ‘4 units’ or ‘4-digit number’. When students have had practice, say ‘even number’ and take away a chair as students are moving around so that one student is left in the centre of the circle. That student must give some criteria and try to find an empty chair to sit on while the others are moving.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: NTO 3.4 ‘Playing Cards’, Student Book p. 84 ‘Correct Statement’
TASK 1:
BEAT THE TEACHER
Model the following game, then have groups of three students play the game using NTO 3.4 ‘Playing Cards’ on individual computers. One student must act as the teacher, while the other two students make the 4-digit number. In pairs, have students draw four boxes joined together and in a horizontal line. Explain to students that the following activity involves them making the largest 4-digit number they can and both students need to agree where to place the numbers. Using NTO 3.4 ‘Playing Cards’, generate a card and students decide in which box to place the number. (You must also choose a 4-digit number, but do not reveal it to the class.) The game continues until four cards have been generated and students have placed the numbers into boxes. Say your 4-digit number to the class. If a pair’s number is lower than your number, they score 1 point, and if it is equal to your number, they score 3 points, but if it is higher than your number, they score 5 points. You score 10 points if you beat all the students. Note: when students are familiar with the game, make it more challenging by deciding that the number must be odd or even.
TASK 2:
INTERACTIVE TASK
Have students work with a partner. Using NTO 3.4 ‘Playing Cards’, the first student draws four cards that they rearrange to make the largest odd or even number they can. Their partner then draws four cards and tries to make a larger odd or even number.
TASK 1: STUDENT BOOK p. 84 ‘Correct Statement’
TEACHING GROUP You will need: dice BONGEL • For students who require support, have them work with smaller numbers. Have students work with two Nelson Maths Australian Curriculum NSW
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or three dice, playing with a partner or in a small group. Each student rolls the dice to form the largest number they can. The student with the largest number in this round writes the letter ‘B’. Students roll the dice again to form the largest number they can, and each time a student wins a round, they write a letter. The first student to form the word ‘BONGEL’ wins. HOW MANY NUMBERS? • For students who require a challenge, have them work with larger numbers. Give students five dice to roll and have them form and record the smallest number they can. Students roll the dice again to form a 5-digit number that is more than the previous number. Students continue to roll the dice, and each time they must form and record a number that is larger than the one before, and if they cannot, they must stop. Have students compare how many numbers they formed.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share the strategies they used to help them win the games they played. • Draw four boxes on the board and tell students that you want them to form the largest number they can. Roll a 10-sided dice, and ask, ‘Which box would you put the number in? Why do you think that is a good choice?’
Home Tasks Select from the possible Home Tasks: • Have students look at the newspaper (hard copy or online) for examples of numbers used in the media. Have them find examples of 4-digit numbers and what they are used for in daily life.
Assessment • Have students complete Student Assessment p. 85. • Review with students Assessment Task Card 3.1. During the three lessons: • Observe which students are able to read and write numbers in word and numeric form during ‘Card Game’ in Lesson Plan 2, Independent Tasks, Task 1 and mark on a class list. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 85; if the student is experiencing difficulty: Have the student use counters to explore which numbers can make groups of two without any left-over Q 1 counters. Have the student mark these even numbers on a 100 chart and identify patterns associated with even numbers. Q 2–3 Include numbers in word form in weekly spelling lists. Q 4 Have the student revisit what makes a number even or odd number and have them model 2-, 3- and 4-digit numbers using MAB blocks. Have them order numbers by comparing models. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 3.1 for specific recommendations. 2. Have the student work with 2- and 3-digit numbers in any of the listed activities or tasks prior to moving to 4-digit numbers. 3. Review Nelson Maths: Australian Curriculum Year 2 Unit xx, pp. xx–xx. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. The student completing Nelson Maths Building Mental Strategies Skills Book Year 4, pp. 10–11, to reinforce mental strategies with 4- and 5-digit numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 4 Unit xx, pp. xx–xx. 3. Extending the student in any of the listed activities or tasks by using larger numbers.
Unit 1
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Numbers, Numbers, Numbers
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BLM
1
Number Cards 1
24
48
27
34
43
36
38
42
19
25
23
20
30
33
31
45
14
37
26
29
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
Teacher’s Note: This BLM can be photocopied, laminated and cut up to make cards for number activities.
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BLM
2
Number Cards 2
348
2 604
215
111
239
1 380
564
92
1 487
935
74
2 460
803
158
1 643
857
2 596
971
726
29
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
Teacher’s Note: This BLM can be photocopied, laminated and cut up to make cards for number activities.
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BLM
3
Blank Chart
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
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BLM
4
Blank Cards
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA2-4NA
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3.1 F.1
Year 3: Assessment Task Card Unit
Numbers, Numbers, Numbers
1
Resources: NTO 3.3 ‘Dice’, blank ten frames, counters, a number line
1
Present NTO 3.3 ‘Dice’ with four digits generated on four dice. Have the student arrange the digits to form an even number. Have the student record the number and read it aloud.
2
Have the student use the four digits to form an odd number, record the number and read it aloud.
3
Have the student form two other numbers using the four digits and record with the two previous numbers.
4
Have the student write all of the numbers in order of smallest to largest.
5
Have the student write the numbers in word form.
Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
3.1 F.1
Year 3: Assessment Task Card Unit
1
Numbers, Numbers, Numbers TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1–2
Have the student use ten frames and counters to explore odd and even numbers to 10. Each time they determine that a number is odd or even, have them add a ten frame, then another. Discuss with the student that, it does not matter how many tens or hundreds are added to the number, it will remain an odd or even number depending on what is in the ones place.
Q3–4
Begin by having the student locate 2-digit numbers on a number line and use it to compare to other numbers. When the student is able to identify larger or smaller 2-digit numbers by their position on a number line, extend to 3-digit numbers.
Q5
Have the student write the words for the numbers 1 to 9 and then the numbers 20, 30 up to 90. Have them practise writing in words the numbers 20 to 99. Next have the student practise the numbers 11 to 19. When the student is proficient, have them learn the words for 100 and 1 000 and write the words for 3- and 4-digit numbers.
Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 3 may be photocopied for educational use within the purchasing institution.
Nelson Maths Australian Curriculum NSW
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Odd or Even?
DATE:
You will need: counters
1 Use counters to work out if the following numbers are odd or even. 1 2 3 4 5 6 7 8 9 10
2 Colour the odd numbers green and the even numbers yellow
in the chart below.
3 Use counters to work out if the following numbers are odd or even. 11 12 13 14 15 16 17 18 19 20
4 Colour the odd numbers green and the even numbers yellow
in the chart below.
5 Is there a pattern?
What is the pattern?
6 Use the pattern to colour all of the odd numbers green and all of the even numbers yellow.
1 11 21 31 41 51 61 71 81 91
2 12 22 32 42 52 62 72 82 92
3 13 23 33 43 53 63 73 83 93
4 14 24 34 44 54 64 74 84 94
5 15 25 35 45 55 65 75 85 95
6 16 26 36 46 56 66 76 86 96
7 17 27 37 47 57 67 77 87 97
8 18 28 38 48 58 68 78 88 98
9 19 29 39 49 59 69 79 89 99
10 20 30 40 50 60 70 80 90 100
7 What do you notice about all of the odd numbers? 8 What do you notice about all of the even numbers?
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Numbers, Numbers, Numbers (TRB pp. 22–25) Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
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Number Sort
DATE:
1 Write the following numbers in word form in the table below.
Make sure you put them in the correct box! 372
621
509
196
765
Even
1 2
54
440
3 007
Odd
Numbers more than 500
Numbers less than 500
2 Write your own 3-digit number here.
Write it in words in the table above.
Unit
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Numbers, Numbers, Numbers (TRB pp. 22–25) Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
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True Statement You will need:
DATE:
a partner, a 10-sided dice
1 Take turns to roll the dice. • E ach time you roll the dice, write the number in an empty box. • R epeat these steps until you have a number in every box. Score 1 point if you make each statement true. is an even number less than 550. is greater than 7 500. is a number less than 2 500 but greater than 2 000. is an odd number less than 5 500. is a number between 6 000 and 7 000. is a number more than 8 000. Total score:
2 Play the game again. See if you can get a better score. is an even number less than 550. is greater than 7 500. is a number less than 2 500 but greater than 2 000. is an odd number less than 5 500. is a number between 6 000 and 7 000. is a number more than 8 000. Total score:
3 Which numbers were the hardest to score a point on? Why?
Which numbers did you try to fill in first? Why?
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Numbers, Numbers, Numbers (TRB pp. 22–25) Whole numbers MA2-4NA applies place value to order, read and represent numbers of up to five digits
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Unit
DATE:
1
STUDENT ASSESSMENT
1 Look at the numbers. Draw a circle around the odd numbers. 16 57 99 123 312 450 671 3 025
7 138 9 734
How do you know the numbers you circled are odd?
2 Write the following numbers in words. a 2 763 b 919 c 5 044 d 3 900 3 Write the following numbers as numerals. a Three thousand, four hundred and fifty-two b Eight thousand and forty-seven c Two hundred and ninety-six d Seven thousand and thirteen 4 Use the four digits below to make the following numbers.
1
8
7
6
a an even number more than 8 500 b an odd number less than 3 500 c a number between 5 000 and 8 000
Unit
1
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Unit
20
Chance
STATISTICS AND PROBABILITY Chance: MA2-19SP describes and compares chance events in social and experimental contexts
ML
certain, even chance, event, fair, impossible, likely, no chance, possible, outcome, unlikely
LESSON PLAN
TUNING IN
1
WHAT DOES IT MEAN? You will need: book titles or newspaper headlines including the word ‘chance’ Present book titles, e.g. Cloudy with a Chance of Meatballs (J Barrett, 1978) and Mostly Sunny with a Chance of Storms (M Roberts, 2010). Ask, ‘What does the word “chance” mean?’ Discuss to find out what students know about chance and its reference to the weather. Ask, ‘What is the chance that it will be cloudy and rain meatballs?’ Discuss the idea that some things have no chance of happening and can be described as impossible. Explain to students that particular terms are used to describe the chance of something happening, and write on the board the words impossible, certain, likely and unlikely. Have students brainstorm events that they think are impossible, certain, likely and unlikely, and record these.
WHOLE-CLASS INTRODUCTION HEADS OR TAILS? You will need: NTO 3.x ‘Coin Toss’ Present NTO 3.x ‘Coin Toss’ to students and ask, ’What can you see? What is on the other side of the coin?’ Explain to students that they are going to play a game whereby they need to predict if the coin toss will result in heads or tails. Have students stand and make their prediction by either placing their hands on their head if they think it will be a head and hands on their backside if they think it will be a tail. Flip the coin and those students who predicted correctly make another prediction and the others sit down. Continue until one student remains. Ask, ‘When a coin is tossed, how many possible outcomes are there? Is one outcome more likely than the other?’ Discuss with students that, when a single coin is tossed, there are two possible outcomes and that the outcome of a head or a tail is 1 out of 2, so both outcomes are equally likely and have an ‘even chance’ of happening.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: LO 115 ‘Slushy Sludger: Questions’, Student Book p. 90 ‘What’s the Chance?’
TASK 1:
WHAT WILL HAPPEN TODAY?
Working in pairs, students write or draw two things that have an ‘impossible’ chance of happening, two things that are ‘certain’ to happen, two things that are ‘likely’ to happen, two things that are ‘unlikely’ to happen and two things that have an ‘even chance’ of happening during a normal school day.
TASK 2:
INTERACTIVE TASK
Have students explore LO 115 ‘Slushy Sludger: Questions’ whereby a vending machine squirts coloured ‘slushies’ into ice-cream cones. Students work out which ‘sludge events’ are possible and then choose a matching probability word.
TASK 3: STUDENT BOOK p. 90 ‘What’s the Chance?’
TEACHING GROUP COULD HAPPEN 1 • For students who require support, ask them to think about things that could happen to them today. As a group, make a list, e.g. read a book, draw a picture, eat lunch, play with their friends, walk home. Encourage students to think of things that are personally relevant to them. Read through the list and ask, ‘Do you think some things are more likely to happen during a day at school than others?’ Discuss and have students draw a picture of something they think is likely to happen and something that is possible but unlikely to happen. Nelson Maths Australian Curriculum NSW
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COULD HAPPEN 2 • For students who require a challenge, have them work in pairs to write ten things that could happen in the classroom today. Discuss with students how some things are more likely to happen than others. Have students order their list from the least likely to the most likely. Have them share their list and reasoning with the group.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from the Independent Tasks and ask, ‘How did you decide which things were more likely to happen?’ • Ask, ‘If I told you it was likely/unlikely that we would do something tomorrow at school, what do you think it could be?’ Have students give their suggestions and discuss their reasoning.
LESSON PLAN
TUNING IN
2
WHEN PIGS HAVE WINGS Explain that there are many sayings that have something to do with chance. Write ‘It will happen when pigs have wings’ on the board, and ask students if they know what it means. Discuss with students that it means there is no chance or it is impossible. Ask, ‘If I roll a dice with the numbers 1 to 6, what is my chance of rolling a 7?’ Discuss possible outcomes and how there is no chance at all of rolling 7. Have students think of other things that there is no chance of happening. Record their ideas.
WHOLE-CLASS INTRODUCTION LUCKY THREE You will need: NTO 3.3 ‘Dice’ Present NTO 3.3 ‘Dice’ and ask, ‘If I roll the dice, what number could I get?’ Have students name the numbers that could be rolled. Tell students that you would like to roll a 3 because that is your favourite number. Ask, ‘Could I roll 3 next? Do you think it is likely that I will roll 3?’ Discuss with students that, while it is possible to roll 3 as it is one of the numbers on the dice, the chance of rolling 3 is 1 out of 6. Have students predict how many times they think the dice will need to be rolled before 3 comes up. Use the NTO and roll until 3 comes up. Ask, ‘If I want to roll 3 again, do you think it will take the same number of rolls? Why?’
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM x ‘Car Race’, card, scissors, yellow and red pencils, glue, BLM x ‘Spinner’, paperclips, sharp pencils, LO 2378 ‘Spinners: Predict and Test’, Student Book p. 91 ‘Spinners’
TASK 1:
RACING CARS
Using BLM x ‘Car Race’, students work in pairs to cut out and paste the race track on to card. They then cut out and colour the two cars, one yellow and one red. Using the first spinner on BLM x ‘Spinner’, students colour one section red and two sections yellow. Explain that they are to use the results of the spinner to move the cars along the track. Have students predict which car they think will win the race. Then conduct the race. When all races are complete, have students share their results. Have students look at the final positions of each car and discuss variations in results. Have students design and colour a spinner so that both cars have an even chance of winning. Students can conduct a race to test their spinner.
TASK 2:
INTERACTIVE TASK
Using LO 2378 ‘Spinners: Predict and Test’, students race two cars along a track determined by the results of a spinner. Students compare actual results with predicted results.
TASK 3: STUDENT BOOK p. 91 ‘Spinners’
TEACHING GROUP
You will need: NTO 3.x ‘Spinner’, BLM x ‘Spinner’, paperclips, sharp pencils, small whiteboards or paper, a dice SPIN THE SPINNER • For students who require support, have them explore spinners so that they can make the connection between the area on the spinner and the likelihood of occurrence. Present students with NTO 3.x ‘Spinner’ and have all segments the same colour. Ask, ‘When I spin the spinner, what colour do you think it will land on? Why?’ Discuss how, as the whole area of the spinner is one colour, it can only land on that colour. Invite all students to spin the spinner. Next click on one segment and ask, ‘When I spin the spinner, what colour could it land on? Which colour do you think it will land on? Why?’ Invite students to spin the spinner. Continue to click on segments, discuss possible outcomes and determine most likely outcomes and test.
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Chance
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SPINNING CHANCE • For students who require a challenge, give pairs of students a copy of BLM x ‘Spinner’ and have them make the fourth spinner. Using a dice, students roll the dice and record the number on the segments of the spinner. Have students write a statement about the likelihood of each number occurring on their spinner. Pairs of students then swap statements with another pair and use the information to make an identical spinner. Have students compare spinners. Have students compare both spinners they have drawn and ask, ‘Are they the same? Why?’
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their work from the Independent Tasks and the Teaching Groups, and discuss the findings from their chance experiments in Independent Tasks. Ask, ‘Did all outcomes have the same chance of happening? Why?’ • Present NTO 3.x ‘Spinner’ and click on five segments to change the colour. Ask, ‘Which colour is the more likely to occur? How do you know?’ Discuss with students how they can calculate the chance by counting the segments of same colour and comparing to the total number of segments in the circle. Change the colours on the spinner and ask, ‘What are the chances of each of the colours occurring now?’
LESSON PLAN
TUNING IN
3
WHICH LETTER? You will need: a 10-sided dice Take students to an area where they can line up side by side. Give each student a letter of the alphabet. Tell them that you are going to roll a 10-sided dice, and if the number rolled has their letter in it, then they can take a step forward. The first student to take five steps is the winner. After a student has won the game, ask, ‘Did everyone have the same chance of winning? Why?’ Discuss with students that some students with the letters a, b, c, d, j, k, l, m, p, q, y and z have no chance of moving forward as no number uses those letters, and that as the letter e is used in seven numbers, the student with the letter ‘e’ would be the most likely to win. Ask, ‘If we played the game again, do you think we would get the same result? Why?’
WHOLE-CLASS INTRODUCTION IN THE BAG You will need: a paper bag, counters Place a red, blue, green and yellow counter into the paper bag and ask, ‘If I take a counter from the bag, what colour might it be?’ Tell students that your favourite colour is red and ask, ‘What is my chance of taking a red counter from the bag?’ Discuss that red is one of four counters in the bag, so the chance is one in four. Shake the bag, select a counter from the bag and place it back in the bag until a red counter has been collected. Repeat. Ask, ‘How can I increase my chance of selecting a red counter from the bag?’ As students make suggestions (e.g. add more red counters, place only two counters in), have them work out the chance and trial. Continue trialling students’ suggestions.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 4 ‘Blank Cards’ with either a W, I or N written on the cards, paper bags, LO 116 ‘The Slushy Sludger: Best Guess’, Student Book p. 92 ‘Chance Machine’
TASK 1:
WIN
Students can play with a partner or in a small group. Each group needs a paper bag and three cards with the letters W, I and N, which are placed in the bag. Each student takes it in turns to shake the bag and select a card. They record the letter and place the card back in the bag. When a student has recorded at least one of each letter, they tally how many times they had to draw a card from the bag to make the word ‘WIN’. Have students share how many times it took. Ask, ‘What was the least and the most number of draws?’ Discuss the variation in results.
TASK 2:
INTERACTIVE TASK
Students can explore LO 116 ‘The Slushy Sludger: Best Guess’ whereby a vending machine squirts ‘slushies’ into ice-cream cones. The machine serves coloured slush randomly from four slots, and students work out which colour is the most common (most likely to be served). However, least common colours are sometimes served. After several guesses, students can check their results from the random sample.
TASK 3: STUDENT BOOK p. 92 ‘Chance Machines’
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TEACHING GROUP
You will need: paper bags, coloured counters, paper bags containing a different combination of eight counters HALF AND HALF • For students who require support, have them work with a partner to put an equal number of two differentcoloured counters into a paper bag. Ask, ‘If you were to draw a counter 20 times from the bag, how many of each colour do you think you would draw?’ Discuss students’ reasoning for their predictions. Have them shake the bag, draw a counter, record its colour and place it back into the bag. Repeat the process 20 times. Have students share their results and discuss in relation to their predictions. WHAT’S IN THE BAG? • For students who require a challenge, have students work with a partner whereby they draw a counter from a paper bag containing a different combination of eight counters. They then place the counter back into the bag and repeat this process 20 times. Have students record their results, and then based on their results, make a prediction about what they think is in the bag. Have students share predictions and discuss their reasoning.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share and disuss the results of their chance activities. Ask, ‘Were your results always the same?’ Why or why not? • In front of students, place a blue, green and yellow counter and four red counters into a paper bag. Ask, ‘What colour counter am I most likely to draw out of the bag? Does that mean I will draw out a red counter?’ Have students explain their reasoning.
Home Tasks Select from the possible Home Tasks: • Have students think about events that could happen at home in the next week. Have them think of an event that is certain to happen, one that is unlikely to happen, one that has an even chance of happening and one that is unlikely to happen. • Have students teach someone at home how to play WIN, a game played in Lesson Plan 3.
Assessment • Have students complete Student Assessment p. 93. • Review with students Assessment Task Card 3.20. During the three lessons: • Collect created items from Lesson Plan 1, Independent Tasks, Task 1, as work samples for student portfolios. • Make note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 93; if the student is experiencing difficulty: Q 1 Encourage the student to use the language of chance by having them predict the likelihood of a particular event happening each day, e.g. the principal coming into the room, the school being flooded, a student from another class entering the classroom. Check the student’s predictions before they leave at the end of the day. Q 2 Have the student use spinners to play games and utilise NTO 3.x ‘Spinner’ to explore the results of shading the spinner in different ways. Q 3 Look for opportunities to conduct chance experiments, e.g. drawing counters from a bag to group students randomly or holding reward raffles where students can earn tickets. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 3.20 for specific recommendations. 2. Review Nelson Maths: Australian Curriculum Year 2 Unit 13. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student make their own chance boardgame using a coloured spinner to move players around the board. Have them explore the concept of fairness in relation to how the game has been designed. 2. Moving forward to Nelson Maths: Australian Curriculum Year 4 Unit xx, pp. xx–xx.
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Chance
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What’s the Chance?
DATE:
1 Read the statements below. Write a word from the box beside each statement to describe the chance of it happening.
likely
unlikely
even chance
impossible
certain
a You will roll an even number on a dice. b You will have fire drill practice today. c You will walk home from school today. d You will eat an ice-cream at lunchtime. e You will toss heads on a coin. f Tomorrow will be Friday. g Your teacher will turn into a fish. h The next lesson will be music. 2 Write down the statement you think is the most likely to happen.
Why do you think this?
3 Write down the statement you think is the least likely to happen.
Why do you think this?
4 Write down two other things that you think are unlikely to happen today. 5 Your teacher said that after lunch on Wednesday your class would be likely to do something. What might it be?
Why do you think that?
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Chance (TRB pp. 86–87) Chance MA2-19SP describes and compares chance events in social and experimental contexts
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Spinners
DATE:
You will need: a partner, a paperclip, a sharp pencil
1 Colour half of the circle green
and the other half yellow.
2 If you were to spin a paperclip 20 times, how many times do you think it will land on yellow?
3 Spin the paperclip 20 times and record the results in the table below.
Green
Yellow
4 Was your prediction correct?
Explain why.
5 Write your partner’s
Green
Yellow
results in the table.
6 Were the results the same?
Why do you think that happened?
7 What results do you think you might get if you used your spinner
1 000 times?
Unit
20
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Chance (TRB pp. 87–88) Chance MA2-19SP describes and compares chance events in social and experimental contexts
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Chance Machines
DATE:
1 Colour in the balls so it is certain
that you will get a red ball.
2 Colour in the balls so it would be
likely that you would get a green ball.
3 Colour in the balls so it would be
impossible that you will get a yellow ball.
4 Colour in the balls so it is certain that
you have an even chance of getting
a red or blue ball.
5 Mike puts his money into the toy machine.
Do you think he will be happy with
the toy he gets?
Explain why.
6 Jo wants a yo-yo. What advice would you give her about spending her money in the machine?
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20
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DATE:
Unit
20
STUDENT ASSESSMENT
1 Write likely, certain, impossible or unlikely to describe
the chance of drawing out a black counter from each bag.
2 Colour the spinners to show the following. It is impossible
It is unlikely to
There is a 3 out
equal chance of to get black but
get red and
of 4 chance of
likely to get red.
likely to get
getting green.
There is an blue and yellow.
yellow.
3 There were 2 blue, 1 green and 2 yellow counters in a bag.
What do you predict will happen after 2 draws from
the bag?
4 After 20 draws, these were the results.
Blue
Green
Yellow
12
3
5
Are the results the same as you predicted? Explain why.
Unit
20
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Unit
18
Decimals to 2 Decimal Places
NUMBER AND ALGEBRA Fractions and decimals: MA2-7NA represents, models and compares commonly used fractions and decimals
ML
decimal, decimal point, hundredths, larger, number line order, place value, smaller, tenths, units, whole number, zero
LESSON PLAN
TUNING IN
1
ORDERING NUMBERS 1–1 000 You will need: A4 paper, scissors Give each student a sheet of A4 paper. Have students fold and cut the paper into quarters. On each quarter, have students write: their favourite number between 1 and 1 000, a number less than 500, a number greater than 800 and a number between 600 and 700. Have students work in pairs to order the eight pieces of paper from smallest to largest. To extend the activity, students could work in groups of four. Note: this can be used as a pre-assessment activity.
WHOLE-CLASS INTRODUCTION EXPLORING PLACE VALUE WITH DECIMAL NUMBERS You will need: an IWB, NTO 4.5 ‘Place-Value Chart’ Generate numbers with either one or two decimal places, and have students place the digits into the relevant place-value columns using NTO 4.5 ‘Place-Value Chart’. Ask, ‘What are each of the columns called? What happens after the decimal point? What happens if there is a zero in the number?’ The activity could be completed on the IWB, by drawing a place-value chart with columns from thousands to hundredths and giving students numbers to write into the chart.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: dice (four for each pair – a different colour for each student in the pair), Excel, Word, Student Book p. 102 ‘Place-Value Chart’
TASK 1:
PLACE-VALUE CHART
Have pairs of students draw a place-value chart with columns from tens to hundredths. Give each pair four dice – allocate two of one colour to one student and two of a different colour to the other student. Have each student roll their dice and create the largest 2-digit number possible. Now have the two students combine their numbers to make a decimal number – one student’s dice represent the whole number, the other’s represent the decimal. Finally, have each student record the number on their place-value chart. Students collect 10 numbers, then swap the roles of whole number and decimal. Extend this activity by using more dice to create larger whole numbers.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets to create a place-value chart in Excel or Word. Give students a set of numbers with up to two decimal places, and have them insert these into the correct columns on the place-value chart.
TASK 3: STUDENT BOOK p. 102 ‘Place-Value chart’
TEACHING GROUP
You will need: three dice for each student who requires support 2-DIGIT NUMBERS • For students who require support, give them two dice and have them roll to create a 2-digit number. Have students repeat this 10 times to make 10 different numbers. Ask students to create a place-value chart, with columns for ones and tens, and record their numbers on their charts. When students are confident,
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give them a third dice, and have them create 2-digit numbers with one decimal place and record their numbers on another place-value chart featuring tens, ones and tenths. ORDER THE NUMBER • For students who require a challenge, give them a set of 10 numbers with two decimal places to order from smallest to largest. Include numbers such as 3.20, 408.63, 408.4. Have students discuss why different numbers are larger or smaller. Students create their own sets of 10 decimal numbers to order, and swap with a partner.
REFLECTION Select from the following to suit your class and their learning outcomes: • Ask, ‘Why are zeros important in decimal numbers?’ Create a class chart about the importance of the zero in place value. Have students record their different ideas and display. • Using an IWB, have students display the charts they created in Independent Tasks, Task 2, to share with the class. • Revisit NTO 4.5 ‘Place-Value Chart’, and provide students with ‘tricky’ numbers to add to the chart, e.g. 0.42, 1.06, 3.20, 180.40, 293.04. Discuss.
LESSON PLAN
TUNING IN
2
TRAFFIC LIGHTS You will need: sticky notes Draw a place-value chart on the board with columns from hundreds to hundredths. On a sticky note, write a number that would fit into the place-value chart, containing different values for each digit, e.g. 327.14. Invite students to guess the whole number recorded on the sticky note. On the chart, record the number and under each numeral mark with symbols: for correct digit, for incorrect digit, and o for a digit in the number but in the incorrect position. Students keep guessing, and try to beat you in a set number of rounds, e.g. eight. The student who guesses correctly selects the next number to be recorded on the sticky note.
WHOLE-CLASS INTRODUCTION READING AND WRITING DECIMAL NUMBERS You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’ Enlarge and cut up BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’. Give each student a card and have them silently move around the room to find their pair. Then have the class order themselves from smallest to largest. Do this in individual sets, i.e. all the numbers, then all the word forms. Ask, ‘Are the orders the same?’
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’, BLM 42 ‘Symbols’, PowerPoint, Student Book p. 103 ‘Matching Decimal Numbers and Words’
TASK 1: NUMBER CARDS Give groups of students cards from BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’ and the symbols <, > and = from BLM 42 ‘Symbols’. Have students create statements with the cards, e.g. 1.3 > One and three hundredths. When the group agrees, have the students record their statement on a sheet of paper. Each statement needs to include one numeric card and one word card. Note: review the symbols < and > if necessary.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets to create a PowerPoint presentation that has a number of matching decimal numbers and words on each slide. Students should be encouraged to make the slides interactive, e.g. a) the user has to draw a line matching words and numbers or b) select a match from two or three options.
TASK 3: STUDENT BOOK p. 103 ‘Matching Decimal Numbers and Words’
TEACHING GROUP
You will need: 20 blank cards for each student who requires a challenge NUMERIC ORDER • For students who require support, play a comprehension game. Read out decimal numbers (these could be from BLM 33 ‘Decimal Numbers and Words 1’ or BLM 34 ‘Decimal Numbers and Words 2’ ) and have
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students record them in their books in numeric form. Once students are confident, have them record the numbers read out in word form. Provide an incentive, e.g. once a student has 10 correct answers, they become the reader. DECIMAL MEMORY GAME • For students who require a challenge, give them 20 cards and have them develop their own decimal memory game, e.g. where they write the decimal number and matching word on individual cards. Once complete, pairs of students combine two sets and play the game. Earlier finishers from other activities could be invited to play.
REFLECTION Select from the following to suit your class and their learning outcomes: • Cut out cards from BLM 33 ‘Decimal Numbers and Words 1’. Invite three students to sit in front of the whiteboard, with their backs towards it. Attach one card above each student’s head so they can’t see it, and have them take turns to guess the number, using Yes/No questions. For example: ‘Does my number have two decimal places? Is my number greater than 10?’ Play a number of rounds, with different students taking turns to guess. • Invite students to share what they have learned in the Teaching Groups. Students describe the activity and their discoveries. Ask, ‘What was easy? What was challenging?’ • Create a chart of students’ strategies for writing decimal numbers in words. Ask, ‘What little tricks did you use?’ Display the chart in the classroom.
LESSON PLAN
TUNING IN
3
LET’S RUN You will need: a space to run, tape measure/trundle wheel, stopwatches Have students measure a distance of 100 m. Revise with them how to use a stopwatch. Have students time each other running the 100 m length, and to make note of their individual times. Ask, ‘How do we write down/record the time?’
WHOLE-CLASS INTRODUCTION ORDERING DECIMAL NUMBERS You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’ Show students pairs of numbers and have them identify which is the largest decimal number. (You could use BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’ for this.) Play this as a game: show students 10 pairs of numbers, have them silently record the largest in each pair on a piece of paper, and then find who has the most correct.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’, long rolls of paper, glue, LO 2005 ‘Scale Matters: Hundredths’, Student Book p. 104 ‘Ordering Decimal Numbers’
TASK 1:
DECIMAL NUMBERS AND WORDS
Give pairs of students the cards from BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’ and a long roll of paper. Have students create a giant number line to scale, attaching the decimal numbers in the correct order. Leave the task fairly open-ended. Note: this could be used as informal assessment.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using a hundredths scale on LO 2005 ‘Scale Matters: Hundredths’ to locate or place a number on a number line.
TASK 3: STUDENT BOOK p. 104 ‘Ordering Decimal Numbers’
TEACHING GROUP
You will need: BLM 33 ‘Decimal Numbers and Words 1’, BLM 34 ‘Decimal Numbers and Words 2’, a long sheet of paper, times from a sporting event, poster paper SMALLEST TO LARGEST • For students who require support, use level-appropriate numbers from BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’. Have students work as a group to order the decimal numbers from smallest to largest, and then to create a number line. Give support and guidance through questioning as required. Nelson Maths Australian Curriculum NSW
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FASTEST TO SLOWEST • For students who require a challenge, give them a set of times (out of order) from a sporting event, e.g. running, cycling, swimming, car racing. Have students place them in order from fastest to slowest. Have students present this task as a poster. Students could include pictures related to the sport.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students present the number lines they made in Independent Tasks, Task 1. Ask, ‘Why did you place this number first? How did you decide your order? What was tricky about this task?’ • Have students write their running times from ‘Let’s Run’ in Tuning In on a piece of card. Attach these to the whiteboard. Then, as a group, have students order the times from fastest to slowest.
Home Tasks Select from the possible Home Tasks: • Have students look for things around the home that show numbers with two decimal places, e.g. items from the pantry, books, newspapers, measuring equipment. Have them list the item and the decimal. • Have students look at a newspaper (hard copy or online) for examples of decimal numbers, e.g. results of sporting events, news reports or advertisements. Have students cut out/print/save and bring to class to share. These items could be used in some of the activities in Lesson 3.
Assessment • Have students complete Student Assessment p. 105. • Review with students Assessment Task Card 4.18. During the three lessons: • Collect created items e.g. the Excel spreadsheets from Lesson Plan 1, Independent Tasks, Task 2, and number lines from Lesson Plan 3, Independent Tasks, Task 1, as work samples for student portfolios. • Make note of students who completed the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 105; if the student is experiencing difficulty: Q 1 Work with whole numbers, then numbers with only one decimal place. Q 2–3 Use BLM 33 ‘Decimal Numbers and Words 1’ and BLM 34 ‘Decimal Numbers and Words 2’ to revisit matching the numeric form of a number to its word form. Q 4–8 Practise drawing number lines with whole numbers, before moving to numbers with one decimal place. Give the student numbers like 3.1, 5.6 and 7.2. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 4.18 for specific recommendations. 2. Have the student work with whole numbers in any of the listed activities (at their level) before moving to decimal numbers. Scaffold them with the use of a place-value chart to reinforce the values and positioning of the decimal parts. 3. Review Nelson Maths: Australian Curriculum Year 3 Unit 13. If the student has achieved the recommended skills and these skills are firmly established, consider: 4. Moving forward to Nelson Maths: Australian Curriculum Year 5 Unit 18. 5. Having the student complete Nelson Maths Mental Strategies Big Book 4, pp. 8–9, to reinforce mental strategies with decimal numbers. 6. Extending the student in any of the listed activities or tasks by using decimal numbers to three decimal places.
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BLM
33
Decimal Numbers and Words 1
4.3 Four and three tenths
43.3 43.33 43.03 Forty-three and three tenths
Forty-three and thirty three hundredths
Forty-three and three hundredths
40.30 40.33 40.03
6.9
Forty and thirty-three hundredths
Six and nine tenths
Forty and three tenths
69.9 Sixty-nine and nine tenths
Forty and three hundredths
69.99 69.09 60.90 Sixty-nine and ninety-nine hundredths
Sixty-nine and nine hundredths
Sixty and nine tenths
60.99 60.09 17.05 17.50 Sixty and ninety-nine hundredths
Sixty and nine hundredths
Seventeen and five hundredths
Seventeen and five tenths
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution. Unit
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18 27
Fractions and decimals MA2-7NA
Teacher’s Note: This BLM can be enlarged, photocopied, laminated and cut up to make cards.
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BLM
34
Decimal Numbers and Words 2
17.55 17.75 Seventeen and fifty-five hundredths
Seventeen and seventy-five hundredths
17.77 17.57 Seventeen and seventy-seven hundredths
Seventeen and fifty-seven hundredths
17.07 15.07 15.77 15.70 Seventeen and seven hundredths
Fifteen and seven hundredths
Fifteen and seventy-seven hundredths
Fifteen and seven tenths
3.1
3.11
3.01
1.03
Three and one tenth
Three and eleven hundredths
Three and one hundredth
One and three hundredths
1.3
1.33
1.31
3.31
One and three tenths
One and thirty-three hundredths
One and thirty-one hundredths
Three and thirty-one hundredths
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution. Unit
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18 27
Fractions and decimals MA2-7NA
Teacher’s Note: This BLM can be enlarged, photocopied, laminated and cut up to make cards.
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BLM
42
Symbols
<
>
=
+
–
÷
×
≠
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution. Unit
Unit
18 27
Fractions and decimals MA2-7NA
Teacher’s Note: This BLM can be enlarged, photocopied, laminated and cut up to make cards.
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4.18
Year 4: Assessment Task Card Unit
18
Decimals to 2 Decimal Places
1
Give the student a set of decimal numbers, e.g. 2.45, 3.07, 4.6, 3.90, 2.42. Ask them to record the numbers in order from smallest to largest.
2
Have the student select one of the numbers with two decimal places and write it in words.
3
Ask the student to draw a number line and place on all of the listed numbers. Point to the number line and ask questions, e.g. ‘Why did you place 4.6 here? Would 3.4 be smaller or larger than 4.6?’
4
For the student who requires extension, give them a decimal number, e.g. 4.126. Ask them to round the number to the nearest hundredth and add the number to their number line (marked in a different colour).
Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
4.18
Year 4: Assessment Task Card Unit
18
Decimals to 2 Decimal Places
TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Review with the student the ordering of numbers with no decimal places.
Q2
Use the cards from BLM 33 ‘Decimal Numbers and Words 1’. Give the student a number card and have them find the matching word card.
Q3
Using LO 2005 ‘Scale Matters: Hundredths’, have the student review the use of number lines.
If the student has demonstrated an understanding beyond the skills, consider: Having the student order a set of decimal numbers to three decimal places and place them on a number line.
Q4
Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 4 may be photocopied for educational use within the purchasing institution.
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Place-Value Chart
DATE:
Expand each decimal number by using the correct columns in the place-value chart. a 42.39
b 21.78
c 130.45
d 17.09
e 12.6
f 710.56
g 11.08
h 403.6
Extension: i
five and six tenths
j
seventeen and forty-two hundredths
k
ninety and nine tenths
l
twenty-seven hundredths
m
nine hundred and twenty-five and three tenths
Hundreds
Tens
Ones
Tenths
a
•
b
•
c
•
d
•
e
•
f
•
g
•
h
•
i
•
j
•
k
•
l
•
m
•
102
Unit
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Hundredths
Decimals to 2 Decimal Places (TRB pp. 94–95) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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Matching Decimal Numbers and Words
DATE:
Match the words and the decimal numbers. Write the letter that corresponds to the matching words on the line above each decimal number to complete the puzzle. The first one has been done for you. A
ninety-three and five hundredths
S
three and seven tenths
D
one hundred and six and thirty-nine hundredths
P
eighteen and twenty-five hundredths
O
eighty-one and seventy-six hundredths
E
eight and fifty-five hundredths
W
ninety-nine and ninety-nine hundredths
I
two hundred and sixteen and ninety-three hundredths
N
twenty-one and five hundredths
C
eighteen and five hundredths
T
three hundred and forty-two and thirty-nine hundredths
I
sixteen and thirty-nine hundredths
X
two hundred and fifteen
L
eight hundred and twenty-seven and twenty-five hundredths
M
four hundred and twenty-one and five hundredths
F
fifty-one and seven tenths
A
seventy-six and thirty-five hundredths
*
What is small and round? A
93.05
Unit
18
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106.39
8.55
18.05
216.93
421.05
18.25
81.76
16.39
21.05
342.39
76.35
827.25
Decimals to 2 Decimal Paces (TRB pp. 95–96) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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DATE:
Ordering Decimal Numbers 1
2
3
Order each set of decimal numbers from smallest to largest. a
42.39
12.85
15.72 29.46
30.08
b
20.36
25.49
21.39 19.86
23.76
c
8.46
8.59 8.62
d
150.26
150.73
8.73
150.07
8.21
150.54
150.37
Create a number line for each set of decimals. a
16.3
16.5 16.9
b
100.5
100.9
101.3 101.6
101.9
c
3.6
4.7
3.8
4.1
d
126.7
128.9
124.6 123.5
125.8
17.3
17.5
3.3
These times in minutes are from a car race. Place them in order from shortest to longest to find who came 1st, 2nd and 3rd. 9.45
4
9.00 8.45
9.30
9.15
9.27
9.06
8.54
These are the weights in kilograms of 5 elephants. Place them in order from largest to smallest to find the heaviest and the lightest elephant. 3 200.49
5 505.69
4 370.56
5 505.05
4 465.98
104
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Decimals to 2 Decimal Places (TRB pp. 94–95) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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DATE:
Unit
18
STUDENT ASSESSMENT
Look at these numbers:
2.45 3.07 4.6 3.90 3 2.42 4.05 1
Order the numbers from smallest to largest.
2
Select one of the numbers that has 2 decimal places. Write it here:
3
This is your special number.
Write your special number in words.
4
Draw a number line and include all of the numbers in the box.
5
Explain where you placed your special number on the number line and why.
6
Is the number 5.01 smaller or larger than your special number?
How do you know? 7
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Draw a picture of your special number.
Decimals to 2 Decimal Places (TRB pp. 94–95) Fractions and decimals MA2-7NA represents, models and compares commonly used fractions and decimals
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Unit
8
Shape
MEASUREMENT AND GEOMETRY Two-dimensional space: MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
ML
area, centimetres, formal, informal, irregular, regular, shape, units
LESSON PLAN
TUNING IN
1
BLOCKS You will need: shape blocks Give groups of students a pile of blocks to sort by criteria that they determine. Have groups share their sorting criteria and the different groupings they have created.
WHOLE-CLASS INTRODUCTION REGULAR SHAPES You will need: poster paper Write the term ‘shapes’ on the board and have students brainstorm what it means. Then write the term ‘regular shapes’. Ask, ‘What makes a regular shape?’ (A regular shape is a polygon where all sides and all angles are equal.) Have students come up with criteria. Record the criteria on poster paper and display.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: an assortment of regular shapes, blank cards, LO 10736 ‘Shape Sorter: Wand Tool’, Student Book p. 110 ‘Regular Shapes’
TASK 1:
WHAT AM I?
Give students an assortment of regular shapes and blank cards. Have students write ‘Who am I?’ cards for individual shapes. Ask students to focus on features, e.g. whether all angles are equal, the number of equal sides, and so on. Have students include the answer on the back of the card. Have them make a number of these cards and then test them on a friend. An example of text on a card could be: Who am I? I have 4 equal sides and 4 equal angles.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 10736 ‘Shape Sorter: Wand Tool’ to examine examples of single shapes. They use the wand tool to compare the sides, right angles and lines of symmetry for each shape, and to work out its features. Note: there are more Learning Objects in this series, which will cater for different learning abilities.
TASK 3:
STUDENT BOOK p. 110 ‘Regular Shapes’
TEACHING GROUP
You will need: computers/tablets, LO 3547 ‘Tessellations’, rulers, protractors LO 3547 ‘TESSELLATIONS’ • For students who require support, have them work independently on computers/tablets using LO 3547 ‘Tessellations’ to create tessellations with coloured shapes. CREATING SHAPES • For students who require a challenge, have them practise drawing exact regular shapes, building on the features they identify as important. Give students rulers and protractors to help with accuracy.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their cards from Independent Tasks, Task 1, reading out the description to the class and having the group identify the shapes. • Have students share their electronic tessellations from the Teaching Group. Ask, ‘Why did you select that shape? How did you know to place that shape there?’ • Have students share their accurate drawings from ‘Creating Shapes’ in the Teaching Group. Ask them to reflect on the difficulty of the task, and how they used the tools, e.g. the ruler, to help. Display their work.
LESSON PLAN
TUNING IN
DRAWING SHAPES Ask students to draw a regular six-sided shape and an irregular six-sided shape. Have students share their drawings. Ask, ‘Why is this shape regular? How do we know this shape is irregular?’
2
WHOLE-CLASS INTRODUCTION Go over some of the features of regular shapes, i.e. a polygon where all sides and all angles are equal. Extend to examine what makes a shape irregular. Have students draw a number of different irregular shapes on the board.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 15 ‘1 cm Grid Paper’, an assortment of regular shapes (e.g. blocks), Word, Student Book p. 111 ‘Regular or Irregular?’
TASK 1:
FINDING THE AREA
Give students copies of BLM 15 ‘1 cm Grid Paper’ and an assortment of regular shapes. Ask, ‘How could we find the area of the shapes?’ Guide students towards placing the shape on the grid paper and tracing around it, then counting squares to find the area. Have students write the area (in cm2) in the centre of the shape. Have them measure the area of three different regular shapes. Then ask students to find three irregular shapes in the classroom and repeat the process.
TASK 2:
INTERACTIVE TASK
Have pairs of students work on computers/tablets to use the ‘Shape’ function in Word to create irregular shapes. Under each shape they create, have them write why the shape is irregular. Have students create at least five different shapes.
TASK 3:
STUDENT BOOK p. 111 ‘Regular or Irregular?’
TEACHING GROUP
You will need: BLM 16 ‘Regular and Irregular Shapes’, sheet of paper, scissors, glue, BLM 15 ‘1 cm Grid Paper’ SORTING REGULAR AND IRREGULAR • For students who require support, give them copies of BLM 16 ‘Regular and Irregular Shapes’ to cut up into cards. Have students sort the shapes into two piles – regular and irregular. Students then identify the features of each different set. The cards could be pasted onto a sheet of paper under the headings ‘Regular’ and ‘Irregular’, with students writing the features of each group in the relevant section. This activity could be extended by having students find the areas of the shapes, placing them on BLM 15 ‘1 cm Grid Paper’ and tracing around them to find the area. Note: students would need another copy of BLM 16. DESIGN WITH SHAPES • For students who require a challenge, have them play with a design tool, e.g. Google SketchUp (a free Google application). Allow students to explore what they can design and create.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students write a written reflection on the differences in finding the area of regular and irregular shapes in Independent Tasks, Task 1. Ask, ‘Which was easier to measure – this shape or this shape? Why?’ • Invite students to share their electronic creations of irregular shapes from Independent Tasks, Task 2. Have students explain how they created certain aspects of the shapes.
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• Invite students to share their SketchUp designs from ‘Design with Shapes’ in the Teaching Group. Ask, ‘What did you discover about the program?’
LESSON PLAN
TUNING IN
3
COMPARING AREAS OF REGULAR AND IRREGULAR SHAPES You will need: a regular shape and an irregular shape (these could be sourced from BLM 16 ‘Regular and Irregular Shapes’) Show students a regular and an irregular shape. Ask, ‘How could we compare the areas of these two shapes?’ Have students make suggestions and try out ideas. Guide students towards measuring the respective areas on grid paper, and then comparing.
WHOLE-CLASS INTRODUCTION COMPARING AREAS OF REGULAR AND IRREGULAR SHAPES You will need: IWB, a grid to project onto the board Project a large grid onto the whiteboard or IWB. Note: all IWB software comes with a grid option or these can also be found on the internet. Ask a student to draw a regular shape on the projection. Have another student work out the area of the shape. Revisit the most effective methods of doing this. Repeat with an irregular shape. Ask, ‘What are the units of the area? Which shape has the greatest area? How do we know?’ Repeat the activity with different shapes.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 15 ‘1 cm Grid Paper’, Word, Student Book p. 112 ‘Comparing Regular and Irregular’
TASK 1:
COMPARING AREA OF SHAPES
Give each student a copy of BLM 15 ‘1 cm Grid Paper’. Challenge pairs of students to find in the classroom at least two shapes – one regular and one irregular – that have the same area. Students may select anything in the classroom. Have them find as many different pairs as they can and record their findings. As an extension, once an irregular shape has been outlined on the grip paper in pencil, have students change it in some way to make it a regular shape with the same area.
TASK 2:
INTERACTIVE TASK
Have students work individually on computers/tablets to use the ‘Shape’ function in Word to create regular and irregular shapes that have the same area. Students could overlay their work on electronic grid paper, such as that found on IWB software, to aid the construction.
TASK 3:
STUDENT BOOK p. 112 ‘Comparing Regular and Irregular Shapes’
TEACHING GROUP
You will need: BLM 15 ‘1 cm Grid Paper’, flat blocks, computers/tablets, LO 3547 ‘Tessellations’ COMPARING AREAS OF BLOCKS • For students who require support, give them a copy of BLM 15 ‘1 cm Grid Paper’ and some flat blocks. Have the students look at the blocks and estimate two that may be of equal area. Have them record their estimate. Then have students place the blocks on the grid paper, trace around them and then find the areas. Ensure that students count the squares correctly and talk to them about how to accommodate for the partial squares. Have them check their prediction. Repeat the activity. LO 3547 ‘TESSELLATIONS’ • For students who require a challenge, have them work independently on computers/tablets, using LO 3547 ‘Tessellations’ to create tessellations with coloured shapes. Have students complete a tessellation, then identify which tiles are regular and which are irregular. Have students make a comment about whether or not the regularity (or otherwise) of the tiles had an impact on creating tessellating patterns.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their equal area shapes from Independent Tasks, Task 1. Ask, ‘How did you find the two shapes? Did you have a strategy? How did you check that the areas were the same?’
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• Have students share the equal area shapes from Independent Tasks, Task 2. Ask, ‘How did you know the areas were the same? How did you check? Which shape is regular and why?’ Students could show their work electronically. • Invite students from the Teaching Group to share their tessellation patterns. Ask them to comment on whether or not the regularity (or otherwise) of the tiles had an impact on creating tessellating patterns.
Home Tasks Select from the possible Home Tasks: • Have students conduct a shape hunt at home, looking for regular and irregular shapes. Have them list five things from the kitchen that are a regular shape and five that have an irregular shape. Have students bring the items (if possible) or their list to school to share. • Give each student a copy of BLM 15 ‘1 cm Grid Paper’. Have them find three items at home (regular or irregular) that have an area of 10 cm2. Have students trace around the items and label.
Assessment • Have students complete Student Assessment p. 113. • Review with students Assessment Task Card 4.8. During the three lessons: • Collect a copy of students’ designs, e.g. the irregular shapes from Lesson Plan 2, Independent Tasks, Task 2, or the equal area shapes from Lesson Plan 2, Independent Tasks, Tasks 1 and 2, to add to students’ digital portfolios. • Collect students’ written reflections, e.g. the reflection on finding the area of regular and irregular shapes from Lesson Plan 2, Independent Tasks, Task 1. • Make a note of the students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 113; if the student is experiencing difficulty: Q 1–2 Review the difference between shapes. Have the student sort shapes into groups and then identify properties of the particular groups. Repeat, separating regular and irregular shapes. Q 3 Have the student practise tracing shapes and counting squares. Show them strategies for recording the number of squares, e.g. numbering each individual square or colouring in and keeping a tally. Examine how to count partial squares. Talk about the importance of units. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 4.8 for specific recommendations. 2. Work with simple shapes, e.g. squares, rectangles and triangles. Consolidate ideas with these shapes before moving forward. 3. Practise counting squares to determine areas. 4. When making area comparisons, have the student cut out the shapes and try to overlay them to determine which one is larger. 5. Review Nelson Maths: Australian Curriculum Year 3 Unit 13. If the student has achieved the recommended skills and these skills are firmly established, consider: 6. Having the student investigate circles and how they fit into the classification. They may wish to use references. 7. Moving forward to Nelson Maths: Australian Curriculum Year 5 Unit 8. 8. Having the student complete problems that require multiple steps to solve, i.e. nominate an area of x amount, then create both an irregular and a regular shape of this area.
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Regular Shapes
DATE:
Write a description for each regular shape.
1
a
b
c
d
e
f
2
Circle the shape in each set that is the odd one out (not a regular shape).
a
c
c
d
Extension: On another sheet of paper, draw and name each shape from
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Question 2.
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Regular Shapes (TRB pp. 106–107) Two-dimensional space MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
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Regular or Irregular?
DATE:
1
Colour all of the regular shapes.
2
Circle each shape in each set that is the odd one out (not regular). a
3
b
Using the grid paper as a guide, draw 2 different irregular shapes and 2 regular shapes. Label each shape regular or irregular.
4
Find the area of each shape by counting squares. Write the area on your shape in cm2.
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Regular Shapes (TRB pp. 106–107) Two-dimensional space MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
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Comparing Regular and Irregular Shapes 1
DATE:
For each shape, find the area and write it inside the shape.
a
c
b
d
e
f g
2
Shade each regular shape red and each irregular shape green.
3
Find the shapes that have the same areas and list them below.
4
Create an irregular shape that has an area the same as shape g.
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Regular Shapes (TRB pp. 106–107) Two-dimensional space MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
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DATE:
Unit
8 1
STUDENT ASSESSMENT Label each shape regular or irregular.
a
b
2
c
d
e
f
Describe what features make a regular shape, e.g. a pentagon.
3
Find and record the area of each shape.
1
2 3 4
a Which two shapes have the same area?
b Which shape has the largest area? c What is the area of the smallest shape? Extension: Draw an irregular shape that is 4 cm2.
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Unit
1
Place Value
NUMBER AND ALGEBRA Whole numbers: MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
ML
abacus, digits, expanding numbers, hundreds, hundreds of thousands, integers, millions, number expanders, place value, tens, tens of thousands, thousands, units
LESSON PLAN
TUNING IN
1
ORDERING NUMBERS You will need: sticky notes, poster paper Provide each student with a sticky note. Have each student write a 5- to 6-digit number on their sticky note, and then collect the sticky notes. Redistribute the sticky notes, and have students in small groups order their notes from smallest to largest. Then have the whole group arrange the sticky notes on poster paper from smallest to largest. This activity could be varied by setting a range for the numbers according to students’ abilities. Have students share and discuss the different strategies they used to order the numbers.
WHOLE-CLASS INTRODUCTION NUMBER KNOWLEDGE You will need: sticky notes, NTO 5.1 ‘Spike Abacus’, NTO 5.2 ‘Place-Value Chart’ Invite a number of students to write a 3- or 4-digit number on a sticky note. Have students attach their sticky notes to the board. Ask, ‘How could we represent these numbers?’ NTO 5.1 ‘Spike Abacus’ and NTO 5.2 ‘PlaceValue Chart’ could be used. Discuss place value and what it means if there is a zero acting as a place holder. Have students order the numbers from smallest to largest on the sticky notes using either NTO.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: newspapers or magazines, scissors, glue, poster paper, BLM 1 ‘Place-Value Chart’, LO 1999 ‘Scale Matters: Tens of Thousands’, Student Book p. 112 ‘Identifying Place’
TASK 1:
REAL PLACE-VALUE CHARTS
Individually, have students look in newspapers or magazines for different numbers, cut them out and paste them on poster paper. Then have students write the number into a place-value chart, either one they have drawn or a copy of BLM 1 ‘Place-Value Chart’. Set minimum numbers for students to collect or a time limit.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 1999 ‘Scale Matters: Tens of Thousands’ whereby students explore the use of scale on a number line.
TASK 3: STUDENT BOOK p.122 ‘Identifying Place’
TEACHING GROUP
You will need: NTO 5.1 ‘Spike Abacus’, NTO 5.2 ‘Place-Value Chart’, blank cards, a long sheet of paper (optional) ABACUS • For students who require support, display NTO 5.1 ‘Spike Abacus’ and have students take it in turns to display or read a selection of numbers. Review with students what each of the spikes represents. Repeat the activity using NTO 5.2 ‘Place-Value Chart’ with the MAB materials and the same numbers. Ask students to identify what is similar and what is different between the two representations. 7-DIGIT NUMBERS • For students who require a challenge, have each student write a 7-digit number on a piece of card. Have them represent the number three different ways, e.g. in words, as a diagram, on a place-value chart. Then, as a group, have students order the numbers from smallest to largest. This activity could then be extended with students creating a number line of their 7-digit numbers on a long sheet of paper. Nelson Maths Australian Curriculum NSW
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their collected numbers from Independent Tasks, Task 1. Ask, ‘How did you know how to record the number in the place-value chart? Why did you write a zero there?’ • Invite students to share their 7-digit number representations from the Teaching Group. Have them share the number line (if created) and display in the room. • Have students list three strategies that they use when ordering numbers from largest to smallest.
LESSON PLAN
TUNING IN
2
NUMBER EXPANDERS You will need: BLM 2 ‘5-digit Number Expander’, scissors, contact (optional), | NTO 5.3 ‘Number Expander’ Have students create a 5-digit number expander from BLM 2 ‘5-digit Number Expander’. You may wish to use contact with the number expanders so students can write the numbers on the number expander with whiteboard markers and erase. Note: it is difficult to fold the number expanders if they have been laminated. Once complete, have students work in pairs providing each other with 5-digit numbers to explore on the number expander. Use NTO 5.3 ‘Number Expander’ to support and extend the activity.
WHOLE-CLASS INTRODUCTION WRITING IN EXPANDED FORM You will need: NTO 5.4 ‘Expanded Form’ Explore writing numbers in expanded form, e.g. 421 = 400 + 20 + 1, by providing examples on the board. Have students come to the board, show the expanded form and explain how they work it out. This could be supported with NTO 5.4 ‘Expanded Form’. Then provide a number of expanded numbers, and have students write as a set of digits, again having them explain their ideas.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: five different-coloured dice per pair of students, sheets of paper, LO 871 ‘Wishball: Whole Numbers’, Student Book p. 123 ‘Comparing Expanded Form’
TASK 1:
EXPANDING WITH DICE
Provide students in pairs with at least five different-coloured dice. On a sheet of paper, students identify what colour represents each place value, e.g. blue is hundreds. Have students take it in turns rolling the dice to generate 5-digit numbers. Have students record the number and then express it in expanded form. This activity could be altered by the number of dice used.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 871 ‘Wishball: Whole Numbers’. This is where students receive a starting number, such as 3 786, and work towards turning it into a target number, 7 664, based on addition and subtraction with place value. The aim is to reach the target number in the smallest number of goes. Note: this activity could be used as a whole-class activity and is one of a series of Learning Objects.
TASK 3: STUDENT BOOK p. 123 ‘Comparing Expanded Form’
TEACHING GROUP
You will need: sticky notes, sheets of paper, dice (optional), NTO 5 ‘Flipbook’ EXPANDED FORM IN PARTS • For students who require support, provide them with a number, e.g. 421. Have students expand the number with each part of the expansion on a different sticky note, e.g. 400 + 20 + 1. Have students mix up the equation using the sticky notes and record, e.g. 20 + 400 + 1. Then have them swap with a partner. The other student needs to write the number in digits, e.g. 421. Repeat a number of times. Begin with smaller numbers, e.g. 3-digit numbers, and work to 5-digit numbers if possible. EXPANDED NUMBER QUIZ • For students who require a challenge, have them write a number in expanded form but not in order, e.g. 1 + 300 + 50 + 6 000 + 90 000 = . Have them complete 10 different examples on one sheet of paper with the answers on another. Then have students swap and complete each other’s questions. Students can check the answers. Numbers could be randomly produced using dice. To extend this activity, students could write their numbers in expanded form in words.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Using NTO 5.5 ‘Flipbook’, have a discussion with students about internal zeros in numbers and how these are represented using place-value charts and expanded notation. • Have students share their results from ‘Expanding with Dice’, Independent Tasks, Task 1. Ask, ‘What numbers did you have difficulty with? Did the same number come up twice?’ • Provide five digits on the board, e.g. 4 2 5 0 0. Have students form these digits into three diferent 5-digit numbers and represent them on their number expanders made from BLM 2 ‘5-digit Number Expander’. Write all of the different variations on a place-value chart on the board. Note that NTO 5.3 ‘Number Expander’ could be used to support this activity.
LESSON PLAN
TUNING IN
3
IN WORDS You will need: poster paper Read out a set of numbers, and have students write them in words, starting with the smaller numbers, e.g. 45, and moving to the larger numbers, e.g. 45 689. Correct as a group, with students coming to the board to share their work. Collect on poster paper any of the numbers that are tricky to spell, e.g. forty, eighty etc, creating a word chart.
WHOLE-CLASS INTRODUCTION STRATEGIES FOR WORDS You will need: NTO 5.2 ‘Place-Value Chart’ Explore strategies that would help students to write numbers in words. Revisit NTO 5.2 ‘Place-Value Chart’ to look at how knowing the place-value language helps write numbers into words. Expanded notation ideas like the number expander could also aid students’ understanding.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: Student Book p. 124 ‘Which Animal?’
TASK 1:
WHO AM I?
Read out a ‘Who am I?’ problem about a number, e.g. ‘I am a 5-digit number less than 40 000. My tens place is occupied by the digit 2 and the digit in the ones place is 2 more than in the tens place. My hundreds and thousands digits are the same and total 8. All of my digits add up to 17. Who am I?’ (34 424) Have students solve and discuss the different strategies they used to solve the problem. Have students write their own ‘Who am I?’ problems about a number.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using level-appropriate software for the following task. Provide each student with a number according to their ability. Then, have students key in everything they can think of about that number, e.g. in words, expanded form, what it is larger than, less than, if it represents something, if it is odd or even. Allow students to be creative in their presentation.
TASK 3: STUDENT BOOK p. 124 ‘Which Animal?’
TEACHING GROUP
You will need: packs of playing cards MULTIPLYING WITH PLAYING CARDS • For students who require support, use packs of playing cards with the aces, tens and picture cards removed. Provide students with a set of cards. Have them create a 3-digit number by turning over the cards. Have students record the number, and then write the number in words below. Discuss strategies to help students, e.g. identifying the value of each place, being aware of the place such as tens. Have students say the word out loud. If students are still struggling, provide a word list of the first 20 numbers and all of the tens numbers to 100 to support students with their writing. WHO AM I? IN WORDS • For students who require a challenge, have them write ‘Who am I?’ problems for numbers into the millions only using words. Students could type their problems on the computer.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students present their ‘Who am I?’ problems from Independent Tasks, Task 1, and the Teaching Group. Have the student read them out and the rest of the class can solve. • Have students share their number investigation from Independent Tasks, Task 1. Look for interesting and unusual representations. Collect into a class book, either digital or hard copy. • Put students in teams of three or four. Read out a number, e.g. 54 291. Have students write the number out in words in large text on a sheet of paper or on a tablet and hold it up. The first group that does this correctly collects a point. The aim of the activity is accuracy. Play a number of rounds. This activity could be varied by writing numbers in words as well.
Home Tasks Select from the possible Home Tasks: • Have students take home their number expanders and explain to their parents or carers how the expanders work with a number of examples. These examples could be provided on a sticky note according to students’ abilities. • Have students look around at home for five numbers with at least four digits. Have students record the numbers, where they found them and then expand them. Have students bring the numbers into class to share.
Assessment • Have students complete Student Assessment p. 125. • Review with students Assessment Task Card 5.1. During the three lessons: • Collect a copy of students’ ‘Who am I?’ problems from Lesson 3, Independent Tasks, Task 1, as evidence of their understanding of place value. Add the extension activity (Lesson Plan 3, Teaching Group) if completed. • Collect students’ ideas about their number from Lesson 3, Independent Tasks, Task 2, as evidence of their knowledge of place value, how to express the number in different forms and so on. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 125; if the student is experiencing difficulty: Review the use of the place-value chart and what each of the columns represents. NTO 5.2 ‘Place-Value Q 1 Chart’ could be used to aid discussion. Have the student practise inserting numbers into the chart. Review how to expand numbers by breaking them into each of the place values. Practise with the Q 2 student-made number expanders and NTO 5.3 ‘Number Expander’. Q 3–4 Review the writing of numbers in words and vice versa. The student could complete matching activities of words and numbers. The student could also create their own word/number chart to remind them of spelling. Q 5–6 To help the student with comparison of numbers, discuss strategies, e.g. working with the tens of thousands, then thousands etc., essentially the place-value chart backwards. The student could also circle the part of the number that they find to be the largest when comparing. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 5.1 for specific recommendations. 2. Have the student work with 2- and 3-digit numbers before moving to larger numbers. 3. Consolidate ideas by creating a ‘tool box’ for the student including a place-value chart, their number expander, their word/number chart as reference points. 4. Review Nelson Maths: Australian Curriculum Year 4 Units 2–3. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student apply the ideas and concepts to larger numbers in the millions. 2. Moving forward to Nelson Maths: Australian Curriculum Year 6 Unit 1. 3. Have the student complete Nelson Maths Building Mentals Strategies Book 5 Unit 4 ‘Ordering 6-digit Numbers’, Unit 5 ‘Expanding Numbers’ and Unit 6 ‘Less Than and Greater Than’, pp. 10–15. 4. Extending the student in any of the listed activities or task by using decimal numbers.
Unit 1
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BLM
1
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Place-Value Chart M
HTh
TTh
Th
H
T
O
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Whole numbers MA3-4NA
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BLM
2
Ones Tens Thousands Tens of thousands
Hundreds
Ones Tens Thousands Tens of thousands
Hundreds
Thousands Tens of thousands
Hundreds
Tens
Ones
5-digit Number Expander
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 5 may be photocopied for educational use within the purchasing institution. Unit
1
Whole numbers MA3-4NA
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5.1
Year 5: Assessment Task Card Unit
1
PLACE VALUE
Resources: a sheet of paper per student, NTO 5.2 ‘Place-Value Chart’, NTO 5.3 ‘Number Expander’, NTO 5.4 ‘Expanded Form’
1
On a sheet of paper, have the student write the number 2 542 368.
2
Have the student write the number in words.
3
Have the student expand 45 807.
4
Have the student write three numbers larger than 9 999 999.
5
For students who require extension, have them write a 7-digit number that has two internal zeros, and then write this number in words.
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
5.1
Year 5: Assessment Task Card Unit
1
PLACE VALUE TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Review writing numbers based on place-value charts. Work with NTO 5.2 ‘Place-Value Chart’ and how this can help with writing numbers. Work with numbers with only three digits.
Q2
Practise writing numbers in words, beginning with numbers less than 100. Have the student develop a word chart to assist with the spelling of the numbers.
Q3
Use NTO 5.3 ‘Number Expander’ and NTO 5.4 ‘Expanded Form’ to revisit number structure and expanding numbers.
Q4
Have the student practise ordering numbers from smallest to largest noting the strategies. When writing numbers that are larger, have the student consider strategies, e.g. counting on.
If the student has demonstrated an understanding beyond the skills, consider: Q5
Having the student work with larger numbers in all forms up to billions and also with decimal numbers.
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 5 may be photocopied for educational use within the purchasing institution.
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Identifying Place
DATE:
1 Write the numeral shown on each abacus. a b
Hth Tth Th H T
Hth Tth Th H T
O
c
O
Hth Tth Th H T
O
2 State the value of the 6 in the following numbers. a 61 432
b 11 056
c 46 161
d 16 528
e 43 601
f 50 116
3 Circle the largest number in each pair. a 29 006
2 998
b 42 119
41 911
c 16 832
17 852
d 60 479
60 794
e 185 609
185 690
f
4 600 142
4 006 142
4 Describe how you worked out which number was largest in Question 3c.
5 Order the following sets of numbers from smallest to largest. a 16 487, 15 058, 17 598, 16 993 b 42 3147, 406 102, 450 328, 44 199, 424 199 c 84 294, 84 105, 84 336, 84 156 d 307 421, 4 714 809, 3 074 456, 37 201, 471 809 6 To turn 9 million into 10 000 000 I would: (Shade the correct bubble.) Add 100 000
Subtract 1 000 000
Add 1 000 000
Subtract 100 000
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Place Value (TRB pp. 20–23) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Comparing Expanded Form
DATE:
1 Write the numeral for the following numbers. a 70 000 + 2 000 + 500 + 20 + 1
b 30 000 + 5 000 + 800 + 90 + 5
c 20 000 + 400 + 50 + 6
d 10 000 + 1 000 + 400 + 30 + 3
2 Express each of the following in expanded form. a 60 419
c 81 403
3 Circle the largest number in each pair. a 21 432
20 000 + 1 000 + 400 + 40 + 1
b 42 119
40 000 + 2 000 + 400 + 20 + 6
c 16 832
10 000 + 5 000 + 700 + 90 + 5
d 60 000 + 4 000 + 300 + 5
64 350
e 10 000 + 8 000 + 900 + 20 + 1
14 922
f 4 000 + 200 + 5
40 205
4 Describe how you worked out which number was largest in 3e.
5 Order the following numbers from smallest to largest. 70 000 + 5 000 + 200 + 80 + 1 70 000 + 5 000 + 400 + 90 + 5 70 000 + 5 000 + 300 + 40 + 6
Extension: Using the digits 4, 8, 7, 6, 5, 1 a Write the smallest number using all of the digits.
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b Write the largest number using all of the digits.
Place Value (TRB pp. 114–115) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Which Animal?
DATE:
Complete the gaps to find the unused number on the animal that will complete the joke. 1 10 658 = ten thousand hundred and fifty-eight 2 25 306 = twenty-five thousand three hundred six 3 61 259 = sixty-
thousand two hundred and fifty-nine
4 89 220 = eighty-nine thousand, two hundred and 5
44 244 =
-four thousand, two hundred and forty-four
6
16 225 =
thousand, two hundred and twenty-five
7 98 178 = ninety-
thousand, one hundred and seventy eight
8 54 115 = fifty-four thousand, one hundred and 9 54 10 11
24 = fifty-four thousand, nine hundred and twenty-four 10 = eleven thousand, one hundred and ten
84 56
11
= eighty-four thousand, five hundred and sixty
12 9 325 = ninety-five thousand, three hundred and twenty-five 13
4 235 = fourteen thousand, two hundred and thirty-five
fift e
eight
en
sixteen
one
forty tw en
and
en
six
e et
9
ty
n
ni
1
1 5
What goes 29-clonk, 29-clonk,
0
29-clonk? A
with
a wooden leg!
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Unit
DATE:
1
STUDENT ASSESSMENT
1 Write the following numbers in the place-value chart. a
54 236
d 4 782 368
TM
b 11 054
c 724 000
e 921
f 31 270 356
M
Hth
TTH
Th
H
T
O
a b c d e f 2 Expand each of the following numbers. a 58 920 b 32 560 3 Write each number in words. a 32 561 b 14 560 4 Write the numeral for each number. a twenty-five thousand, three hundred and eleven b eighty-two thousand, one hundred and three 5 Order the following numbers from smallest to largest. a 56 123, 56 892, 56 741, 56 334
b 2 114 021, 12 114 201, 12 114 210, 2 114 201
6 Circle the largest number of this pair. How did you work it out? 42 631 and 42 813
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Place Value (TRB pp. 20–23) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Unit
14
Perimeter
MEASUREMENT AND GEOMETRY Length: MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
ML
centimetre, length, metre, millimetre, perimeter, rectangle, ruler, square, units, width
1
LESSON PLAN
TUNING IN
MEASURING LENGTH You will need: rectangular objects, rulers Provide each student with a rectangular object, e.g. a tissue box. Have students measure the length of each of the sides with a ruler, and record on a diagram. Check students are measuring correctly using the ruler, and are recording an appropriate diagram with the correct units of measurement. Repeat if necessary and have students share results.
WHOLE-CLASS INTRODUCTION WHAT IS PERIMETER? You will need: recorded measurements and objects from Tuning In, calculators Ask, ‘What is perimeter?’. Brainstorm students’ ideas on the board. Then have students find the perimeter of their object from Tuning In. Ensure they add the perimeter of their object correctly. Have them compare their results with a partner. They may need to use calculators to aid the calculations. If time permits, have students swap objects and find the measurement.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: rulers, sheets of paper, LO 3528 ‘Geoboard’, Student Book p. 130 ‘Perimeter of Rectangles’
TASK 1: MEASURING PERIMETER Provide students with a ruler and a sheet of paper and have them select five rectangular objects (from around the classroom) to measure the perimeter of. Have them record the measurements of each side length on a diagram. Students could be encouraged to collect their information in the form of a table with the following headings.
TASK 2:
Name of object/ where found
Diagram with labels
Perimeter
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 3528 ‘Geoboard’, whereby students can use the virtual geoboard to stretch bands to create shapes and then find the perimeter. Have students record their results.
TASK 3: STUDENT BOOK p. 130 ‘Perimeter of Rectangles’
TEACHING GROUP You will need: rulers
MEASURING RECTANGLES ON THE BOARD • For students who require support, draw some rectangles on the board. Have students use a ruler to take it in turns to measure and label each of the side lengths. Then discuss with students the idea of perimeter being ‘the total distance around the shape’. Repeat with a number of examples. FINDING THE PERIMETER • For students who require a challenge, provide them with the task of finding objects with a set value perimeter, e.g. 10 cm or 50 cm or even 100 cm or 1 m. Have students work in pairs to see how many objects they can find to meet the criteria.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their collected perimeters from Independent Tasks, Task 1. Look for different objects that have the same perimeter. Perhaps they could be listed together. Ask students why they selected particular objects. • Invite students to share the objects they found that met the perimeter requirements in ‘Finding the Perimeter’ from the Teaching Group. Ask students to explain how they solved the task. • As a class, create a perimeter poster with facts, ideas and reminders to be displayed in the classroom.
LESSON PLAN
TUNING IN
2
WORKING WITH GRIDS You will need: NTO 5.6 ‘Grid Paper’ Using NTO 5.6 ‘Grid Paper’, create a rectangle on the board and have students find the length of each side and then the perimeter. Repeat with a number of different examples.
WHOLE-CLASS INTRODUCTION IS THERE A QUICKER WAY? You will need: NTO 5.6 ‘Grid Paper’ Using NTO 5.6 ‘Grid Paper’, have a student create a rectangle on the board. Discuss with students the strategies for finding the perimeter. Ask, ‘Is there a quicker way to find the perimeter?’ Draw out ideas, e.g. ‘length + width × 2 = perimeter’ or ‘2 × Length + 2 × width = perimeter’. Add these to the perimeter poster from the Reflection in Lesson Plan 1. Try the processes (ideas) with a number of examples at the board.
INDEPENDENT TASKS
Note: Choose from Tasks1, 2 or 3. You will need: metre rulers, tape measures, trundle wheels, NTO 5.6 ‘Grid Paper’, Student Book p. 131 ‘Rectangles on Grids’
TASK 1:
PERIMETER OF A LARGE OBJECT
As a class, have students measure the perimeter of a large object, e.g. the basketball court or a school building or playground. Before moving outside, have students brainstorm how, as a group, they will complete the measurement task, e.g. they could divide into smaller groups and each group measures a particular section. Have students consider how they will record this information.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets to explore NTO 5.6 ‘Grid Paper’, whereby they will add a rectangle and find the side lengths and perimeter of the shape. Students could record their work by taking a screen shot or photo of the page. Have students complete a number of measurements. This activity could be extended by providing the perimeter and the students determine the side lengths of the rectangle.
TASK 3: STUDENT BOOK p. 131 ‘Rectangles on Grids’
TEACHING GROUP
You will need: BLM 3 ‘1cm Grid Paper’, rulers, calculators PRACTISING WITH GRIDS • For students who require support, provide them with a copy of BLM 3 ‘1 cm Grid Paper’. Have students draw rectangles to specifications, e.g. length 5 cm, width 3 cm, using rulers. Then have students find the perimeter. Encourage students to consider ‘length + width × 2 = perimeter’ or ‘2 × length + 2 × width = perimeter’, perhaps working through examples of each. Note: students may need to use calculators. SOLVING THE GRID PROBLEM • For students who require a challenge, provide them with a copy of BLM 3 ‘1 cm Grid Paper’. Have them examine the problem: to find the number of rectangles with a perimeter of 24 cm that will fit on their page. Allow students to use any strategies they wish. They must be able to justify the number they arrive at.
REFLECTION Select from the following to suit your class and their learning outcomes: • Draw the ideas and calculations of students finding the perimeter of a large object from Independent Tasks, Task 1. Ask, ‘What was challenging about this task? How do you know the answer is correct? How would grids have aided you to find the answer?’
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• Have students share their discoveries and results from ‘Solving the Grid Problem’ in the Teaching Group. Display NTO 5.6 ‘Grid Paper’ on the board and invite students to share some of their ideas. • Draw a rectangle on the board. Ask students how they could they find the perimeter. Draw out students’ different strategies and calculate the perimeter of the rectangle with each of the strategies. Ask students which strategies they prefer and why.
LESSON PLAN
TUNING IN
3
SQUARES AND RECTANGLES Provide students with a number of squares and rectangles for them to find the perimeter of, including rectangles and squares that have been rotated. Provide these on shapes with the side lengths labelled. Have students find the perimeters of the shapes in pairs.
WHOLE-CLASS INTRODUCTION PERIMETER OF A SQUARE Review the definition of perimeter with students. Then discuss the perimeter of a square. Ask, ‘Do you know a short cut when finding the perimeter of a square?’ i.e. 4 × length = perimeter of a square. Ask, ‘Why is a square a special case?’
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: Student Book p. 132 ‘Perimeter’
TASK 1:
INVESTIGATING PERIMETER
Provide students with a total perimeter, e.g. 24 cm or 48 cm, and have students in pairs investigate all of the different rectangles and squares that could have that total perimeter. Encourage students to be systematic in solving the task. Have them write up their results on poster paper. To extend the activity, provide students with a perimeter measurement featuring decimals.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets. Provide students with the task of designing a garden bed that has a perimeter of 100 m. The garden bed could be rectangular, or it may be an irregular shape, the only stipulation being that the sections of the garden bed are straight.
TASK 3: STUDENT BOOK p. 132 ‘Perimeter’
TEACHING GROUP
You will need: rulers, square-based objects, calculators, rulers, NTO 5.7 ‘Length Convertor’ PERIMETER OF A SQUARE • For students who require support, provide a range of square-based objects and have students measure the side lengths with rulers. Have them record the lengths on a diagram and label it. Ask them to find the perimeter, reminding students about the measuring units to use. Repeat a number of times, then ask students what they notice, and if there are any ‘short cuts’ they may be able to use. Note: students may need to be supported with the use of calculators. CONVERTING UNITS • For students who require a challenge, provide them with a number of different-sized squares with sides labelled in metres, e.g. side length 2 m or 2.5 m, etc. Ask them to find the perimeter and then have them convert their answers into cm and even mm. Students will need access to calculators for this activity. Note: NTO 5.7 ‘Length Convertor’ could be used to assist with this activity.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their findings from Independent Tasks, Task 1. Ask, ‘How did you solve the problem? Did you have a process?’ • Have students share their garden bed designs from Independent Tasks, Task 2, either in hard copy or electronically. Ask, ‘Why did you create your garden bed like that?’ Check students have side lengths recorded and that they total 100 m. • Draw a number of squares and rectangles on the board and have students find the perimeter of each. Ask, ‘What is a quicker method than adding all 4 side lengths with the square? How do we know the value of each side length, if it is not labelled?’ Nelson Maths Australian Curriculum NSW
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Home Tasks Select from the possible Home Tasks: • Have students find the perimeter of two squares and three rectangles from around their home. Have students record the item, its side lengths and perimeter. This could be represented in a table. • Provide students with a value, e.g. 16 m, and have them determine the different perimeters of rectangles and squares that could give that perimeter. Have students record their ideas and share with the rest of the class.
Assessment • Have students complete Student Assessment p. 133. • Review with students Assessment Task Card 5.14. During the three lessons:
• Collect a copy of students’ results from Lesson Plan 3, Independent Tasks, Task 1, for their student portfolio. • Collect a copy of the gardens designed by students from Lesson Plan 3, Independent Tasks, Task 2, for their student portfolio. • Make a note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 133; if the student is experiencing difficulty:
Q 1
Review the concept that opposite sides in a rectangle are equal in length. Review that all four side lengths in a square are equal. Q 2–3 Review how to find perimeter by adding each of the side lengths. When this concept is strong, the student could be encouraged to use strategies such as 4 × side length = perimeter of a square. Q4 Review the finding of perimeter by adding each of the side lengths. Then have the student work out what numbers could add to give 10 cm, e.g. 2 + 2 + 3 + 3 = 10. Then have them add this to a diagram. Remind the student that two pairs of the side lengths need to be the same/equal. If the student has not achieved the recommended skills for this unit:
1. See Assessment Task Card 5.14 for specific recommendations. 2. Have the student continue to work with the physical materials, tracing and then measuring the side lengths with rulers. 3. Review the use of rulers. 4. Have the student work with small numbers and not worry about the measurements units initially. 5. Create a reminder chart about perimeter to display. 6. Review Nelson Maths: Australian Curriculum Year 4 Unit 14. If the student has achieved the recommended skills and these skills are firmly established, consider:
1. Having the student work with larger numbers. 2. Moving forward to Nelson Maths: Australian Curriculum Year 6 Unit 13. 3. Having the student complete questions with conversions involved. 4. Extending the student to include more word-based problems.
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Perimeter of Rectangles
DATE:
You will need: a ruler 1 Find the length of each of the sides of the rectangles and label the diagrams. 2 By adding the side lengths, find the total perimeter for each of the rectangles
and write this in the centre of the rectangles.
a
b
c
d e
f
Extension: On another sheet of paper, draw two different rectangles that each have a total perimeter of 10 cm.
130
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Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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Rectangles on Grids
DATE:
You will need: a ruler 1 Find the length of each of the sides of the rectangles and label the diagrams. 2 Find the total perimeter for each of the rectangles and write this in the centre of
the rectangles. Use one of these strategies:
• length + width × 2 = perimeter
• 2 × length + 2 × width = perimeter
b
c
a
d
e
3 Which method did you use to find the perimeter of rectangle c?
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Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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Perimeter
DATE:
You will need: a ruler 1 Find the perimeter of each shape and label the diagram. a
c
b
d
2 Find the perimeter of each square and label the diagram. a
c
b
3 Which method did you use to find the perimeter of square c?
4 Complete the table.
Rectangle
Length
Width
a
7 cm
4 cm
b
12 cm
10 cm
c
5m
1m
d
10 m
20 m
Perimeter
Extension: On another sheet of paper, draw an irregular shape with a perimeter of 20 cm.
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Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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DATE:
Unit
14
STUDENT ASSESSMENT
You will need: a ruler 1 Find the missing side lengths on each rectangle and square
and add to the labels. c
a
b
d
2 cm 4 cm
3 cm
1 cm
e 8 cm
2 Find the perimeter of each rectangle and square. Write the perimeter
in each shape.
a
c
d
3 cm
3 cm 6 cm 5 cm
5 cm e
b 2 cm 2 cm
2 cm
4 cm
4 cm 3 Explain how you found the perimeter of the shape c in Question 2.
4 On another sheet of paper, draw a shape that has a total perimeter
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of 10 cm, and label each of the side lengths.
Perimeter (TRB pp. 126–127) Length MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length
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Unit
3
Integers
NUMBER AND ALGEBRA Whole numbers: MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
ML
integers, negative numbers, number line, positive numbers, zero
LESSON PLAN
TUNING IN
1
SORTING INTEGERS You will need: sets of cards made from BLM 1 ‘Integer Cards 1’ Ensure there are enough cards from BLM 1 ‘Integer Cards 1’ for one set between two students. Have students sort the cards into positive and negative numbers. Ask, ‘What is similar about each group? What is different about each groups? What about zero?’
WHOLE-CLASS INTRODUCTION INTEGERS Discuss what makes up the set of integers (whole numbers). Talk about the symbol representing negative numbers, and look at the importance of zero. Introduce the term ‘integers’. Ask students where we see negative numbers in real life, e.g. thermometers, on graphs, etc. Collect ideas and comments on the board.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: newspapers or magazines, scissors, glue, poster paper, calculators, sheets of paper, NTO 6.1 ‘Calculator’, Student Book p. 144 ‘Knights in Maths’
TASK 1:
NEWSPAPER HUNT
Individually, have students look in newspapers or magazines for integers (positive and negative). Have students cut out and collect these on poster paper, explaining the context in which the integers were found. Challenge students with a minimum number of negative numbers and zeros for them to collect or set a time limit.
TASK 2:
INTERACTIVE TASK
Provide each student with a calculator. Have students create different numbers (up to millions) from a starting point. Ask, ‘If I begin with a 5, how can I create 5 million? How do I create negative 5?’ Have students record what they do on a sheet of paper. Repeat with a number of different numbers. Note: NTO 6.1 ‘Calculator’ could be used to support this activity.
TASK 3: STUDENT BOOK p. 144 ‘Knights in Maths’
TEACHING GROUP
You will need: sets of number cards made from BLM 1 ‘Integer Cards 1’ and BLM 2 ‘Number Line’, sheets of paper SORTING INTEGERS • For students who require support, provide them with a set of number cards made from BLM 1 ‘Integer Cards 1’ and a copy of BLM 2 ‘Number Line’ with the numbers from –10 to 10 filled in. Have students match the cards to the numbers on the number line, and then have them sort into piles of positive and negative numbers. Observe how students sort the numbers. LARGER RANGE • For students who require a challenge, ask them to order the number cards made from BLM 1 ‘Integer Cards 1’ from smallest to largest and record these on paper. Ask students to write a comment below their work, articulating the process they used for the sorting. Students could then be encouraged to place these on a number line to scale.
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REFLECTION Select from the following to suit your class and their learning outcomes: • Have students share their integers posters from Independent Tasks, Task 1, and explain where they found negative numbers. On the back of their posters, have students write about what they learnt looking for the numbers. • Ask, ‘What is the difference between a negative number and a decimal?’ Explore ideas and comments on the board. • Give each student a number card from BLM 1 ‘Integer Cards 1’ and have students sort themselves into groups of positive and negative numbers. Give the zero card to one of the stronger students. Ask students from the different groups, ‘How do you know you are in the right group?’
LESSON PLAN
TUNING IN
2
ORDERING INTEGERS You will need: BLM 1 ‘Integer Cards 1’, BLM 3 ‘Integer Cards 2’ Provide each student with an integer card made from BLM 1 ‘Integer Cards 1’ or BLM 3 ‘Integer Cards 2’. Have students order themselves from smallest to largest. Note that these numbers may be sequential the first time the activity is completed, but it could be repeated with non-sequential numbers.
WHOLE-CLASS INTRODUCTION CONVERTING TO A NUMBER LINE You will need: number cards made from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’, Blu Tack, NTO 6.2 ‘Number Line’ Using the cards made from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’, have students add Blu Tack to their card and place it on a number line on the board. Note that NTO 6.2 ‘Number Line’ could be used for this activity. Discuss with students the importance of zero. Look at the way the 1 and –1 sit on either side of the zero. This activity could be expanded by having students complete counting patterns on the number line, including negative numbers.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: sets of number cards made from BLM 1 ‘Integer Cards 1’ and BLM 3’ Integer Cards 2’, long sheets of paper, LO 2001 ‘Scale Matters Negatives’, Student Book p. 145 ‘Ordering Integers’
TASK 1:
NUMBER LINES
Provide pairs of students with a range of number cards made from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’, e.g. from –20 to 20, and have them represent these numbers on a number line on a long sheet of paper. Have students explore a number sequence, e.g. counting backwards by 2s starting at 20. Adjust the activity based on students’ abilities. Repeat this activity, if required, either using the same number line with a different number sequence to explore or a new set of numbers represented on a number line.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using LO 2001 ‘Scale Matters Negatives’, whereby students explore the use of scale on a number line including negative numbers.
TASK 3: STUDENT BOOK p. 145 ‘Ordering Integers’
TEACHING GROUP
You will need: BLM 1 ‘Integer Cards 1’, BLM 3 ‘Integer Cards 2’, paper, glue, long sheets of paper ORDERING GROUPS OF INTEGERS • For students who require support, provide them with the positive numbers and zero from BLM 1 ‘Integer Cards 1’ and BLM 3 ‘Integer Cards 2’. Have students order these numbers from smallest to largest and discuss how they worked this out. Repeat the activity with the set of negative numbers and zero. If students are ready, move them to combining the two sets. Students could then paste these to a long sheet of paper in order. LARGER NUMBER LINES • For students who require a challenge, have them create a number line between –30 and 30 on long sheets of paper. Have them write in all of the numbers and then include some decimal numbers and fractions. Determine which extra numbers students include according to their ability.
REFLECTION Select from the following to suit your class and their learning outcomes:
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• Using NTO 6.2 ‘Number Line’, place numbers –10 to 10 on the number line. Ask, ‘Where would a decimal such as 1.5 or 0.5 go on the number line? What about ½ and ¼?’ Have students locate these numbers on the number line. Explore the difference between these numbers and negative numbers. Have students who completed ‘Larger Range’ in the Teaching Group share their number lines. • Go through students’ responses to Student Book p. 141. Note any students who seem to be struggling with the numbers. • Create on a large piece of card a < or > sign. Have one student hold the card. Then provide two other students with a number card made from BLM 1 ‘Integer Cards 1’ or BLM 3 ‘Integer Cards 2’. Have students arrange themselves in order to create a correct number sentence. Note that it may be necessary to revise what < and > mean.
LESSON PLAN
TUNING IN
3
LOOK AT TEMPERATURE You will need: NTO 6.3 ‘Thermometer’ Show students NTO 6.3 ‘Thermometer’, and have them identify the positive numbers, the negative numbers and integers. Ask students to come to the board and represent different temperatures on the thermometer, including negative temperatures, and perhaps relate to locations where the temperature is –5ºC, e.g. snowfields.
WHOLE-CLASS INTRODUCTION ADDITION You will need: NTO 6.3 ‘Thermometer’, NTO 6.2 ‘Number Line’ Continuing with NTO 6.3 ‘Thermometer’, create scenarios for students to find the final temperature, e.g. ‘It was –1ºC when I woke up, but the temperature increased by 3 degrees. What is the temperature now?’ Have students use the thermometer to determine the answer, then have students write an equation. Repeat a number of times. Then move to a horizontal number line, completing similar equations. Note that NTO 6.2 ‘Number Line’ could be used with this activity.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: BLM 4 ‘Plotting Points’, NTO 6.4 ‘Grid Paper’, BLM 5 ‘1 cm Grid Paper’, Excel, Student Book p. 146 ‘Addition with Negative Numbers’
TASK 1:
PLOTTING POINTS
Have students complete BLM 4 ‘Plotting Points’. It may be necessary to review the process of plotting points, and NTO 6.4 ‘Grid Paper’ could be used to assist with this. To extend the activity, provide students with a copy of BLM 5 ‘1 cm Grid Paper’ and have them create their own tracing to solve.
TASK 2:
INTERACTIVE TASK
Have students work independently on computers/tablets using level-appropriate spreadsheet software, e.g. Excel. Have students create lists or grids of equations to explore the addition of negative numbers, e.g. 1 + –1 = 0, 1 + –2 = –1 and then –1 + 1 = 0, –1 + 2 = 1 and so on. As they are exploring, have students record comments about their findings.
TASK 3: STUDENT BOOK p. 146 ‘Addition with Negative Numbers’
TEACHING GROUP
You will need: NTO 6.2 ‘Number Line’, counters ON NUMBER LINES • For students who require support, use either NTO 6.2 ‘Number Line’ or counters and a drawn number line. Have students place their token at a starting place and then move it so many units forwards or backwards. Have students record this as an equation, e.g. 5 – 7 = –2. Repeat. Then provide students with a selection of equations (according to their ability) and have them work out the answers using the number line. EXTENDING EQUATIONS • For students who require a challenge, provide them with more challenging equations either containing 2-digit positive and negative numbers or equations that would require multiple steps, e.g. 3 – 8 + 2 – 10 = ?. Spend time discussing with students the appropriate layout and organisation of their work.
REFLECTION Select from the following to suit your class and their learning outcomes:
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• Revisit NTO 6.3 ‘Thermometer’ and provide students with different temperatures. Ask, ‘What would the temperature be if it dropped 5ºC?’ Have students show this using the thermometer. • Have students share their work from Independent Tasks, Task 1. Ask, ‘What is important about negative numbers on the grid? Where does this mean points will be plotted?’ Have students share tracings they may have created. Point out the use of negative numbers. • As a group, have a discussion about the general observations students may have made with what happens when two signs are next to each other in an equation, e.g. 3 + –4 = ?. Ask, ‘What does it mean? Is 3 – 4 = the same thing?’ If possible, extend the discussion to include equations like 3 + + 4 = ? and 3 – –4 = ?. Check to see whether or not students can make generalisations.
Home Tasks Select from the possible Home Tasks: • Have students explore at home to find positive and negative integers. Have students note where these integers are located. Have them bring samples to school and share with the group. • Have students create a number line from –10 to + 10. Have them write five equations that could be solved using the number line. Criteria could be set, e.g. two of the equations must include negative numbers.
Assessment • Have students complete Student Assessment p. 147. • Review with students Assessment Task Card 6.3. During the three lessons: • Note students who are experiencing difficulties with positive and negative numbers through reflection activities, e.g. using NTO 6.3 ‘Thermometer’ in Lesson Plan 3. • Keep a copy of students’ home task of creating a number line and writing five related equations as evidence of their understanding of integers. • Keep copies of students’ work examining the addition of negative numbers from Lesson Plan 3, Independent Tasks, Task 2. • Make a note of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of areas of difficulty.
Recommendations for Future Learning Specific to Student Assessment p. 147; if the student is experiencing difficulty: Review the difference between positive and negative numbers. Also review the writing of such numbers. Q 1 Q 2–3 Review how to order positive and negative numbers on a number line. This could be completed with the student drawing a number line and adding in values, or by using NTO 6.2 ‘Number Line’. Review the structure of the number line before and after the zero and the importance of zero in its construction. Q 4–5 Review the addition of numbers. First have the student work with positive numbers and then use either NTO 6.2 ‘Number Line’ or NTO 6.3 ‘Thermometer’ to explore the addition of positive and negative numbers. When the student is more confident, they could move away from the number line to complete equations. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 6.3 for specific recommendations. 2. Have the student work with only positive numbers for both order-type activities and addition-based activities, using a number line as support. Move to ordering activities and the addition of positive and negative numbers supported by a number line. 3. Review Nelson Maths: Australian Curriculum Year 5 Unit 1. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student apply the ideas and concepts to larger numbers. 2. Moving forwards to Nelson Maths: Australian Curriculum Year 6 Plus Unit 2. 3. Having the student complete Nelson Maths Building Mentals Strategies Big Book 6 Unit 7, pp. 16–17. 4. Extending the student in any of the listed activities or tasks by creating equations with multiple steps, e.g. 15 – 16 + 17 – 3 = ?. 5. Extending the student to consider the effect of negative numbers on multiplication and division equations. This could be explored through the use of calculators and spreadsheets.
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BLM
1
Integer Cards 1
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
Teacher’s Note: This BLM can be enlarged, photocopied and cut up to use as number cards.
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BLM
2
Number Line
Paste here
Paste here
Paste here
Paste here
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
Teacher’s Note: This BLM can be cut out and individual sections used or a number of sections pasted together.
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BLM
3
Integer Cards 2
14
15
16
17
18
19
20
21
22
23
24
–23
–11
–12
–13
–14
–15
–16
–17
–18
–19
–20
–21
–22
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
Teacher’s Note: This BLM can be enlarged, photocopied and cut up to use as number cards.
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BLM
4
Plotting Points
Plot the following points on the grid. The first one has been done for you. (0, 4), (0, 0), (2, –3), (3, –4), (4, –3), (5, 0), (6, 4), (7, 5), (9, 4), (10, 0), (10, –3), (9, –5) When you have finished, turn the page on its side to find the letter. Remember in the reference (3, 2), the first number (3) is the one read on the x (horizontal) axis. The second number (2) is the one read on the y (vertical) axis. Where these meet is where the dot is drawn. When all the dots are on the grid, draw the line.
y 5 4 3 2 1 0 -1
x 1
2
3
4
5
6
7
8
9
10 11 12
-2 -3 -4 -5
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
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BLM
5
1 cm Grid Paper
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution. Unit
3
Whole numbers MA3-4NA
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Year 6: Assessment Task Card
6.3
INTEGERS
Unit
3
Resources: a piece of paper per student
1
On a sheet of paper, have the student write three positive numbers and three negative numbers.
2
Have the student order the numbers from smallest to largest on a number line.
3
Have the student write and solve three addition equations related to their numbers, which contain the use of negative numbers.
4
Have the student draw a thermometer showing the temperature 5ºC.
5
Have the student use the thermometer to show what the temperature would be if it decreased by 7oC.
6
For the student who requires extension, have them find the answer to 10 + 16 – 23 = ?.
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
Year 6: Assessment Task Card
6.3
Unit
3
INTEGERS TARGETED ASSESSMENT
If the student is experiencing difficulty: Q1
Review the difference between positive and negative numbers. This could be supported with the use of a number line using NTO 6.2 ‘Number Line’.
Q2
Use the number line in NTO 6.2 ‘Number Line’ to help the student organise the numbers. Examine the numbers that are the closest to zero and how they increase in size as they move away.
Q3
Use a tool like a number line to aid the student in developing equations. ‘On Number Lines’ in the Teaching Group in Lesson Plan 3 could be revisited.
Q4–5
Use NTO 6.3 ‘Thermometer’ to revisit thermometers and where to locate numbers, as well as how to move up and down the scale to find the answer.
If the student has demonstrated an understanding beyond the skills, consider: The student could be encouraged to work with larger numbers, including 2- and 3-digit numbers, and both processes of addition and subtraction of positive and negative numbers.
Q6
Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
© Cengage 2014. This page from Nelson Maths: Australian Curriculum Teacher’s Resource Year 6 may be photocopied for educational use within the purchasing institution.
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Knights in Maths
DATE:
Why did the knight run about shouting for a tin opener? Match the numbers and words, and then write the letters below to find the answer. The first one has been done for you.
1
negative eight
H
4
four
I
–3
two
E
3
negative nine
F
5
ten
B
7
negative six
T
–8
negative three
N
–6
seven
S
–10
zero
U
–9
three
R
2
negative ten
D
–1
eight
Y
0
five
A
8
negative one
M
10
one
O
–2
negative two
W
–8
2
–8
5
–10
5
10
2
2
4
–3
–8
4
7
7
0
4
–6
–1
1
0
3
O
1
–9
5
3
Extension: On another sheet of paper, create your own puzzle.
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Integers (TRB pp. 134–135) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Ordering Integers
DATE:
1 Order each set of numbers from smallest to largest. a 2, 3, 5, 0, –1, –2
b 2, 4, 0, –2, 6, –4
c –1, –3, 5, 0, 3, –5, 1
d 19, 14, 0, –10, 15, –9, –13
2 Show the following numbers on a number line. a 2, –3, 0, 5, –4, 3
b –8, 7, –6, 5, 0, 1, 4
c 3, –10, 5, –8, –6, 0, 2
d –9, 5, 7, 8, –6, –4, –2
3 Circle the largest number in each pair. a –2 6
d 5 2
g –3 –1
b –7 –8
e 2 –5
h
c –2 3
f 0 –4
2 –5
4 Describe how you worked out which number was largest in Question 3e.
Extension: Using all of the digits 5, 6, 2, 1 a Write the smallest number. b Write the largest number. c What might the smallest negative number be?
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Integers (TRB pp. 134–135) Whole numbers MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
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Addition with Negative Numbers
DATE:
1 During winter, the temperature was 5ºC. What would the temperature be if it was: a 4 degrees warmer?
b 5 degrees cooler?
c 7 degrees warmer?
d 10 degrees cooler?
2 Use the number line to solve each equation. a 10 + –6 =
b 2 + –5 =
c 3 + –8 =
d –2 + –3 =
3 Complete each equation. a 6 + –4 =
b –7 + –8 =
c –2 + 3 =
d 2 + –5 =
e 0 + –4 =
f 0 + –4 =
g 5 + 2 =
h 2 + –5 =
4 Describe any patterns you notice when adding negative numbers.
Extension: Use the graph to describe what is happening to the temperature
during the day.
temp oC
9 8 7 6 5 4 3 2 1 0 5am 6am 7am 8am 9am 10am 11am Noon 1pm 2pm 3pm -1 time -2 -3
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3
DATE:
Unit
STUDENT ASSESSMENT
1 Draw lines to match the numbers and words. –3
negative six
15
negative eighteen
0
twenty–one
–18
negative three
21
zero
–6
fifteen
2 Draw each set of numbers on a number line. a –5, 2, 0, 4, 8, –3
b –7, –1, 0, 5, –2, 8, 4
3 Circle the largest number in each pair. a 3 –5
b 1
c –7
0
–5
d 9
11
4 Use a number line to solve each equation. a –7 + –3 = b 4 + –5 = c 0 – 4 = d –1 – 3 = 5 Complete the equations. a 3 + –4 =
b –5 + 3 =
6 Circle the largest number:
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c –1+ –3 =
42 631
d 6 + –7 =
42 813
Describe how you worked this out.
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11
Cartesian System
NUMBER AND ALGEBRA Patterns and Algebra: MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
ML
Cartesian plane, coordinates, location, mapping, quadrant
LESSON PLAN
TUNING IN
PLOTTING POINTS You will need: BLM 5 ‘1 cm Grid Paper’, rulers Provide each student with a copy of BLM 5 ‘1 cm Grid Paper’. Have them rule an xy axis on the paper, labelling 0 to 10 on each axis. Then provide students with a series of points to plot. Use only use positive whole numbers. Review with students which number is plotted first (x, y).
y
1 x
WHOLE-CLASS INTRODUCTION CHECKING THE ANSWERS You will need: plotted points from the Tuning In activity, NTO 6.5 ‘Coordinates Grid’ Using NTO 6.5 ‘Coordinates Grid’, invite students to the board to plot the different points from the Tuning In activity. As students are plotting the points, ask, ‘How did you know to place the point there? Why is the zero important? If there is a zero in the coordinate pair, what does that mean?’ Have students check their answers. You can extend this activity by having students plot additional points.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: coloured chalk, A4 paper, a digital camera, Student Book p. 152 ‘Plot to Create’
TASK LARGEAXIS AXIS TASK 1: 1: LARGE Using a large space, e.g. a basketball court and chalk, create a large xy axis. Discuss with students the importance of putting arrows on the end of the axis as well labelling. Once created, provide different students with a coordinate and have them plot themselves onto the graph. The plotted points may create a line or a shape. Provide each student with at least one opportunity to be plotted. This activity could be varied by having students write their coordinates in large print on a sheet of A4 paper, and then they could hold it up once plotted and a digital photo taken.
TASK INTERACTIVE TASK TASK 2: 2: INTERACTIVE TASK GRID ACTIVITY Have students work independently on computers/tablets, using an online grid plotting activity, e.g. http://www. oswego.org/ocsd-web/games/BillyBug/bugcoord.html, to practise plotting coordinate points.
TASK 3: 3: SB p.XXX ‘Plot to Cr TASK STUDENT BOOK p. 152 ‘Plot to Create’
TEACHING GROUP
You will need: BLM 5 ‘1 cm Grid Paper’, sheets of poster paper, sticky-tape POSTER PAPER • For students who require support, draw an xy axis on large sheets of poster paper taped together and work in the number range from 0 to 10. Provide students with a grid reference and have them stand or place an object in the correct location. Talk about which number is first, e.g. (x, y). An easy way for students to recall x is plotted first followed by y is to say to them, ‘Go across the floor and up the stairs’. Provide students with a number of examples so they can practise plotting. WORKING BACKWARDS • For students who require a challenge, provide them with a copy of BLM 5 ‘1 cm Grid Paper’ and have them rule up an xy axis. Students create a drawing for which they will list the coordinates and swap with
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another student to draw (as with Student Book p. 148). Have students record the list of coordinates on a different sheet of paper.
REFLECTION Select from the following to suit your class and their learning outcomes: • If taken, provide students with a copy of the digital photo from Independent Tasks, Task 1. Have students write a reflection about what they learnt through completing the activity. • Give students some points that are already plotted. You could use NTO 6.5 ‘Coordinates Grid’. Have students identify the coordinates of each of the points. • Using the instructions created by one of the students from ‘Working Backwards’ in the Teaching Group, read out the coordinates and have students plot onto their own copy of BLM 5 ‘1 cm Grid Paper’. Ask, ‘Did you all get the same answer?’
LESSON PLAN
TUNING IN
2
POSITIVE AND NEGATIVE NUMBERS You will need: sheets of paper, rulers Have students rule and draw a number line with zero in the middle on a sheet of paper. Call out numbers and have students locate them on the number line, e.g. 4, –6, 1, –10. Check to see that students have the numbers in y the correct position. Spend some time reviewing the construction with negative and positive numbers and their order in relation to the zero.
WHOLE-CLASS INTRODUCTION
x
x
EXTENDING THE AXIS You will need: BLM 5 ‘1 cm Grid Paper’, rulers y Provide students with a copy of BLM 5 ‘1 cm Grid Paper’. Have them draw an axis that has all four quadrants in the middle of the page. Have them label each of the axis from –10 to 10. Discuss with students where the negative numbers lie, building on the Tuning In activity, and have students think about a thermometer when considering the y axis. Label each of the axis, x and y, and discuss the term ‘Cartesian System’.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3. You will need: created grid from Whole-Class Introduction activity, LO 352 ‘Rainforest: Make a Walking Track’, Student Book p. 153 ‘Plotting on the Cartesian Axis’
TASK TASK 1: 1: PLOTTING ON THE CARTESIAN SYSTEM Have students use their axis created from the Whole-Class Introduction activity. Read out a series of coordinates and have students plot them onto the axis. These may or may not form a shape, but should include points from all four quadrants, e.g. (1, 5), (–2, 6), (–6, –4), (3, –1). Discuss with students which number is plotted first (x) and discuss the importance of the sign (+/–) in locating the point.
TASK 2: 2: INTERACTIVE TASK: TASK TASK LO 352 ‘RAINFOREST: MAKE A WALKING TRACK’ Have students work independently on computers/tablets using LO 352 ‘Rainforest: Make a Walking Track’. Students mark the route for a walking track on a map of a rainforest. Choose a section of track based on instructions about distances, compass directions and grid references.
TASK3: 3: SB STUDENT BOOK p.on 153 ‘Plotting on the Cartesian Axis’ TASK p.XXX ‘Plotting e Cartesian Axis’
TEACHING GROUP
y
You will need: BLM 5 ‘1 cm Grid Paper’, rulers PRACTISING WITH GRIDS • For students who require support, provide them with a copy of BLM 5 ‘1 cm Grid Paper’. Have them draw an axis just looking at positive numbers of the x axis and both positive and negative numbers of the y axis. Provide students with a number of coordinates and have them y plot them onto the axis. Check that students are locating the positions correctly. Then have students draw a number of points onto their grids and write the coordinates under each point.
x
MORE DETAIL • For students who require a challenge, provide them with a copy of BLM 5 ‘1 cm Grid Paper’. Either have them create their own picture and list the coordinates, or provide them with a set of coordinates. Ensure the coordinate sets include halves, e.g. (3½, 4).
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REFLECTION Select from the following to suit your class and their learning outcomes: • Using NTO 6.6 ‘Coordinates Grid’, review student answers from Independent Tasks, Task 1. Invite students to the board to plot the points, and ask, ‘Why did you place that point there?’ • Have students share their result from Student Book p. 149 ‘Plotting on the Cartesian Axis’. Ask, ‘What shape did you find? What other features did you add?’ • Show students a local map with an axis from a street directory and have them locate points using the coordinates, e.g. the coordinate for the school. Extend the activity by asking students to locate a feature and give the related coordinates. Discuss with students what happens if the feature goes across a number of grids.
LESSON PLAN
TUNING IN
3
BATTLESHIPS You will need: BLM 5 ‘1 cm Grid Paper’, NTO 6.5 ‘Coordinates Grid’ Have students draw up a –10 to 10 xy axis. On your grid, draw several ‘ships’ that are of varying line lengths. Write a list of these on the board, e.g. 3 cm ships × 4, 5 cm ship × 1 and so on. The aim of the game is for students to find and sink all of your ships in a set number of goes by calling out the coordinates, e.g. this may be 48 goes, so two guesses per student. You could use NTO 6.5 ‘Coordinates Grid’ to keep a record of the guesses.
WHOLE-CLASS INTRODUCTION GIVING THE COORDINATES You will need: NTO 6.5 ‘Coordinates Grid’, sheets of paper Using NTO 6.5 ‘Coordinates Grid’, construct a shape. Have students record on a sheet of paper the coordinates of each corner or main feature of the shape. Delete the shape, and using a student’s coordinates, recreate the shape using the NTO. Repeat a number of times, checking that students are recording the coordinates correctly.
INDEPENDENT TASKS
Note: Choose from Tasks 1, 2 or 3 You will need: a copy of a local map with a grid reference system or one overlaid, sheets of paper, Turtle Geometry, Student Book p. 154 ‘Listing the Coordinates’
TASK ONMAPS MAPS TASK 1: 1: ON Provide students with a copy of a local map with a grid reference system, e.g. from a street directory, or alternatively Google Maps can be used and a grid overlaid onto it. Have students create a pathway around the map between several locations, e.g. the school, local shops, the sportsground and home. Have students list the coordinates of the pathway on another sheet of paper. You can vary this activity by providing students with a number of coordinates and having them identify the feature at that location.
TASK 2: 2: INTERACTIVE TASK: TURTLE GEOMETRY TASK INTERACTIVE TASK Have students work independently on computers/tablets using Turtle Geometry to program a turtle around the page or through a maze. The program can be found at http://nlvm.usu.edu/en/nav/frames_asid_178_g_3_t_1. html?open=activities
TASK 3: 3: SB p.XXX ‘List the p. Coo4inates’ TASK STUDENT BOOK 154 ‘List the Coordinates’
TEACHING GROUP
You will need: BLM 5 ‘1 cm Grid Paper’ SQUARES AND RECTANGLES • For students who require support, provide them with a copy of BLM 5 ‘1 cm Grid Paper’ and have them draw an axis of –5 to 5. Have students draw a number of squares on the axis, and then list the coordinates of each square. Ask, ‘What do you notice?’ Students should notice common values between coordinate sets. Repeat with rectangles, again drawing out commonalities. LARGE-SCALE TURTLES • For students who require a challenge, say: ‘Imagine you have a large turtle to program, and the screen is the classroom floor. 1 move = 1 m. Program your turtle to move around the room without crashing into the furniture’. Set a number of destinations, e.g. from the student’s seat to the door, etc.
REFLECTION Select from the following to suit your class and their learning outcomes: • Have students do the Battleships activity from Tuning In in pairs, trying to guess the location of each Nelson Maths Australian Curriculum NSW
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other’s ships. It may be best to allocate the size and number of ships for the class for consistency. • Have students share the pathway they created on the local map from Independent Tasks, Task 1. Students could read out the coordinates and have other students follow on their own maps. • Have students share what they discovered from ‘Squares and Rectangles’ in the Teaching Group. • Have students share their large-scale turtle programing from ‘Large-Scale Turtles’ in the Teaching Group.
Home Tasks Select from the possible Home Tasks: • Provide students with a copy of BLM 5 ‘1 cm Grid Paper’ and have them create a basic map of their house or backyard on the grid. Have them create an axis over this, and then list coordinates of the important features of their room, house or yard. • Provide students with a copy of BLM 5 ‘1 cm Grid Paper’ with a –10 to 10 axis drawn on. Have students use this to create a set of instructions of coordinates to create a shape or picture of a rocket. Have students bring to class to share.
Assessment • Have students complete Student Assessment p. 155. • Review with students Assessment Task Card 6.11. During the three lessons: • Collect student work from ‘Working Backwards’ in the Teaching Group from Lesson Plan 1, as evidence of students’ understanding of using coordinates to create a picture. • Collect a copy of student work from Lesson Plan 3, Independent Tasks, Task 1, to provide evidence of students’ understanding of coordinates on a map system and how they relate to locating features. • Collect a copy of the rocket instructions created by students in Home Tasks as evidence of their understanding of coordinates. • Make notes of students completing the scaffolding tasks or the more challenging activities of the Teaching Groups. • Review Student Book pages and make notes of difficult areas.
Recommendations for Future Learning Specific to Student Assessment p. 155; if the student is experiencing difficulty: Q 1 Review the process of finding coordinates on an axis. Ask, ‘What value is read and written first?’ Review how to write a coordinate pair (2, 4). Review plotting of coordinates on a grid, e.g. the x is plotted, then the y. Review the process of reading the scale. Q 2 Q3 Practise looking at maps, having the student locate and identify features and then giving coordinates for the features. The student can practise reading coordinates to find a feature. If the student has not achieved the recommended skills for this unit: 1. See Assessment Task Card 6.11 for specific recommendations. 2. Have the student work with an axis, where they need to plot themselves at coordinate locations. 3. Provide laminated grids with an axis and have the student practise plotting coordinates with whiteboard markers. 4. Provided laminated grids with a drawn shape, and have the student identify the coordinates of the corners of the shape. 5. Have the student practise creating their own axis on grid paper using rulers and developing the scale. 6. Review Nelson Maths: Australian Curriculum Year 5 Unit 12. If the student has achieved the recommended skills and these skills are firmly established, consider: 1. Having the student work with larger scales. 2. Having the student work with scales that are not 1:1, e.g. scales of 5 or 10. 3. Moving forward to Nelson Maths: Australian Curriculum Year 6 Plus Unit 10. 4. Having the student complete more complex plotting. 5. Having the student develop pathways on maps, using the coordinate system.
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Plot to Create
DATE:
1 Plot the following coordinates. Complete each set as a separate part of the
drawing, joining the points together.
a
Part A: (1, 5), (4, 1), (12, 1), (15, 5), (1, 5)
b
Part B: (12, 5), (12, 14), (5, 6), (12, 8)
c
Part C: (3, 5), (3, 15), (1, 13), (3, 13)
2 When completed, colour your picture. 3 Then add some of your own features and give the coordinates.
y 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
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2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 x
Cartesian System (TRB pp. 148–149) Patterns and algebra MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
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Plotting on the Cartesian Axis
DATE:
1 Plot the following coordinates. Join the points together in order.
a
(3, 0)
b
(6, 4)
c
(2, 4)
d
(0, 7)
e
(–2, 4)
f
(–6, 4)
g
(–3, 0)
h
(–6, –5)
i
(–3, –4)
j
(0, –3)
k
(3, –4)
l
(6, –5)
m
(3, 0)
2 What shape have you made? 3 Add features to your picture and list the relevant coordinates.
y 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 –8 –7 –6 –5 –4 –3 –2 –1
x
-1 -2 -3 -4 -5 -6 -7 -8
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List the Coordinates
DATE:
1 List the coordinates of each of the points indicated on the image.
y 8 B
C
F
G
7J
K
N
O
D
E
H
6 I
L
M
P
Q
5 4 b
c
a
z
x
y
3 2 1
e d 0 U –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 V –2
x
T
–3 –4 –5 A
W –6
S
R
–7 –8
154
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DATE:
Unit
11
STUDENT ASSESSMENT 3
1 List the coordinates for
B
each of the corners of
y A
2
the shape.
1 –4 –3 –2 –1 1 2 3 4 0 –1
C
x
D
–2 –3 2 Plot the following points. What shape
a (0, 2)
b (1, 1)
c (2, 0)
f (–4, –2) g (–3, –1) h (–2, 0)
do they make?
d (3, –1)
e (4, –2)
i (–1, 1)
3 y 2 1 0 –4 –3 –2 –1 1 2 3 4
x
–1 –2 –3 3 Give the central coordinates for the following features: a the school
b the oval
c the shop
d the playground 4 y 3 2 1
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6 0
x
–1 –2 –3 –4 Unit
11
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Scope and Sequence
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Kindergarten
Addition and subtraction
Unit 17 Beginning Addition Unit 19 More About Addition Unit 27 Subtraction Unit 28 More About Subtraction Unit 30 Addition, Subtraction and Money
Number and Algebra Unit 1 Numbers to 5 Whole numbers Unit 2 Counting to 5 Unit 3 Groups of Things Unit 5 More Counting Unit 6 Dot Patterns Unit 8 Numbers to 10 Unit 9 Counting with Numbers to 10 Unit 10 Ten Frames Unit 11 Counting and Comparing Groups Unit 13 Ordinal Number Unit 16 Understanding More About Numbers to 10 Unit 22 Numbers Beyond 10 Unit 24 More About Numbers to 20
NSW Mathematics K–10 Syllabus strand and substrand
Unit 12 Developing Mental Strategies for Addition Unit 25 Subtraction Unit 26 More About Subtraction Unit 30 Addition and Subtraction
Unit 1 Recognising Numbers to 20 Unit 2 Counting to 20 Unit 5 Modelling Numbers Unit 6 Number Lines Unit 8 Numbers Beyond 20 Unit 15 2-digit Numbers Unit 16 More About 2-digit Numbers Unit 20 Money Unit 21 More About Money Unit 28 Place Value
Year 1
Unit 4 Numbers Up Unit 5 Strategies for Addition Unit 6 More Strategies for Addition Unit 9 Solving Problems with Addition Unit 11 Strategies for Subtraction Unit 12 Subtraction Unit 15 More About Subtraction Unit 16 Addition and Subtraction
Unit 1 Counting Unit 2 Modelling Numbers Unit 4 Numbers up to 1000 Unit 17 Money
Year 2
Unit 1 Odd and Even Numbers Unit 2 Numbers to Tens of Thousands Unit 3 Place Value Unit 31 Money
Year 4
Unit 5 Mental Unit 13 Addition and Strategies for Subtraction Addition Unit 31 Money Unit 6 Addition Unit 8 Place Value Unit 12 Mental Strategies for Subtraction Unit 13 Subtraction Unit 14 Connections Between Addition and Subtraction Unit 15 Solving Addition and Subtraction Problems
Unit 1 Numbers! Numbers! Numbers! Unit 2 Numbers to 10 000 Unit 3 More About Numbers to 10 000 Unit 8 Place Value Unit 9 More About Place Value Unit 32 Money
Year 3
Unit 1 Place Value and BODMAS Unit 3 Integers Unit 6 Prime Numbers Unit 7 Composite Numbers Unit 18 Problems with Positive and Negative Numbers
Year 6
Unit 2 Addition and Unit 2 All Four Subtraction Operations Unit 6 Estimation Unit 31 Financial Plans
Unit 1 Place Value and BODMAS Unit 3 Factors and Multiples Unit 6 Estimation
Year 5
Note: the Working Mathematically outcomes of Communicating, Problem Solving and Reasoning are integrated throughout the activities and tasks in the program.
Nelson Maths: Australian Curriculum NSW Scope and Sequence across the Year Levels
Nelson Maths Australian Curriculum NSW
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Year 2
157
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Kindergarten
Patterns and algebra
Unit 14 Patterns
Fractions and decimals Unit 23 Halves
Number and Algebra Unit 20 Grouping and Multiplication and Sharing division
NSW Mathematics K–10 Syllabus strand and substrand
Unit 18 Patterns Unit 19 Number Patterns
Unit 13 Halves and Quarters
Unit 3 Skip Counting Unit 9 Grouping and Sharing
Year 1
Unit 26 Fractions Unit 27 More About Fractions Unit 28 Decimals
Unit 18 Mental Strategies for Multiplication Unit 19 More About Mental Strategies for Multiplication Unit 22 Multiplication Unit 24 Division Unit 25 More About Division
Year 3
Unit 18 Number Unit 21 Patterns Patterns Unit 19 More Number Patterns
Unit 7 Fractions Unit 30 More About Fractions
Unit 23 Multiplication Unit 24 More About Multiplication Unit 27 Division Unit 28 More About Division
Year 2
Unit 21 Number Patterns Unit 28 Number Sentences Unit 32 Word Problems
Unit 18 Decimals to 2 Decimal Places Unit 23 Equivalent Fractions Unit 24 Counting with Fractions Unit 27 Fractions and Decimals
Unit 6 Number Sequences: 3s, 6s and 9s Unit 7 Number Sequences 4s, 8s and 7s Unit 10 Multiplication Facts (Times Tables) Unit 11 Multiplication Facts and Related Division Facts Unit 15 Multiplication and Division Strategies Unit 16 More Multiplication and Division Strategies
Year 4
Year 6
Unit 21 Number Patterns Unit 28 Number Sentences
Unit 13 Addition and Subtraction of Decimals Unit 17 Fractions Unit 18 Decimals to Three Places Unit 23 Addition of Fractions Unit 24 Subtraction of Fractions Unit 27 Fractions and Decimals
Unit 11 Cartesian System Unit 21 Number Sequences
Unit 12 Decimal Representations of the Metric System Unit 14 Addition and Subtraction of Decimals Unit 15 Multiplication of Decimals Unit 17 Fractions Unit 23 Addition of Fractions Unit 24 Subtraction of Fractions Unit 27 Fractions of a Quantity Unit 28 Fractions, Decimals and Percentages Unit 31 Percentage Discounts
Unit 2 All Four Unit 3 Factors and Operations Multiples Unit 7 Multiplication of Large Numbers A Unit 10 Multiplication of Large Numbers B Unit 11 Division with Remainders Unit 15 Mental Strategies
Year 5
158
Scope and Sequence
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Unit 22 Data
Unit 11 Our Community – Data
Unit 27 Data
Data
Unit 25 Our Class
Unit 20 Chance
Unit 29 Chance
Unit 7 Position
Unit 24 Chance
Unit 10 Position
Unit 29 Symmetry
Unit 31 3D Objects
Unit 16 Time
Unit 30 Capacity Unit 10 Mass
Unit 4 Length Unit 23 Area
Year 3
Statistics and Probability Chance
Unit 7 Position
Unit 8 Transformation with 2D Shapes
Unit 26 3D Objects
Unit 14 Telling the Time Unit 21 More About Time
Unit 20 Capacity Unit 13 Mass
Unit 3 Length Unit 25 Area
Year 2
Unit 17 Angles
Unit 4 Position
Position
Unit 4 2D Shapes
Unit 17 3D Objects
Unit 14 Time Unit 22 More AboutTime
Unit 29 Capacity Unit 23 Mass
Unit 10 Length and Area
Year 1
Angles
Unit 12 2D Shapes
Unit 18 More About Shapes and Objects
3D Space
2D Space
Unit 15 Time Unit 29 More About Time
Unit 26 How Much Does It Hold? Unit 21 Mass
Unit 7 Length and Area
Kindergarten
Time
Volume and capacity Mass
Measurement and Geometry Length Area
NSW Mathematics K–10 Syllabus strand and substrand
Unit 16 Volume and Capacity Unit 5 Mass and Capacity
Unit 9 3D Objects
Unit 19 Chance
Unit 22 Angles Unit 33 Angle Applications
Unit 12 Grid References
Unit 20 Collecting Data Unit 20 Collecting Data Unit 29 Displaying Data Unit 29 Data Displays Unit 30 Interpreting Unit 30 Interpreting Data Data
Unit 19 Chance
Unit 22 Angles
Unit 12 Mapping
Unit 8 Regular Shapes Unit 8 Shapes Unit 33 Patterns Unit 32 Transformations
Unit 9 Drawings of 3D Objects
Unit 20 Collecting Data Unit 29 Data Displays Unit 30 Interpreting Data
Unit 19 Chance
Unit 22 Angles
Unit 10 Mapping/Grid References
Unit 8 2D Shapes and 3D Objects Unit 9 Prisms and Pyramids Unit 8 2 Shapes and 3D Objects Unit 32 Transformations Unit 33 Use of Transformations
Unit 25 Time Unit 25 Time Unit 25 Time Unit 26 Time Problems Unit 26 Time Problems Unit 26 Timetables and Timelines
Unit 5 Mass and Capacity
Unit 17 Volume Unit 5 Mass and Capacity
Year 6
Unit 4 Area and Perimeter Unit 13 Length and Area Problems
Year 5
Unit 4 Length, Area Unit 4 Length and and Volume Temperature Unit 14 Perimeter and Unit 14 Perimeter Area Unit 16 Area
Year 4
Notes
159 Marketing Sampler.indb 159
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Notes
160 Marketing Sampler.indb 160
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K– 6
NSW 1
2
3
4
5
6
9780170352864
9780170352871
9780170352888
9780170352895
9780170352901
9780170352918
9780170352925
9780170352949
9780170352956
9780170352963
9780170352970
9780170352987
9780170352994
9780170353007
9780170251518
9780170251525
9780170251532
9780170131858
9780170131841
9780170131865
9780170131872
STUDENT BOOKS
TEACHER’S RESOURCE BOOK WITH NELSON TEACHING OBJECTS CD & REPRODUCIBLE RESOURCES CD
BUILDING MENTAL STRATEGIES BIG BOOKS
BUILDING MENTAL STRATEGIES SKILL BOOKS NSW
NELSON MATHS FACTS STUDENT HANDBOOK 9780170127684
CUSTOMER SERVICE PHONE: 1300 790 853 FAX: 1300 790 852 EMAIL: [email protected] Level 7, 80 Dorcas Street, South Melbourne 3205 Printed 04/14 PRI 8368 ABN 14 058 280 149
PRI 8368 NMAC NSW Sampler Cover.indd 1
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STUDENT BOOK AND TEACHER’S RESOURCE SAMPLER
K
LEVEL
NELSON MATHS Australian Curriculum NSW
AUSTRALIAN CURRICULUM
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