Ip 2014 Grade 5 Term 2 Workbook Lesson 1-10

Grade 5 Mathematics Workbook - Term 2 Written by: Liezel Blom Caryn Wilkinson Edited by: Michele van Loggenberg Developed in association with: Gauteng Department of Education Intermediate Phase Mathematics Technical support by: Dreyer Lötter Maryke Hageman Mariska van Tonder Printed by: DL2B Investments cc ISBN: 978-1-920486-80-8 Copyright subsists in this work. No part of this work may be reproduced, transmitted, published or adapted, by any means or in any form, without the prior written permission of the copyright holder.

Index: Lesson 1

Whole numbers

Lesson 2

Rounding off and properties of whole numbers

Lesson 3

Addition

Lesson 4

Subtraction

Lesson 5

Addition and subtraction: Problem solving

Lesson 6

Grouping and sharing

Lesson 7

Comparing and order of fractions

Lesson 8

Addition of fractions

Lesson 9

Collection of objects

Lesson 10

Test

Lesson 11

Measuring instruments

Lesson 12

Recording length

Lesson 13

Converting between lengths

Lesson 14

Round off length

Lesson 15

Add length (fractions)

Lesson 16

Multiples

Lesson 17

Factors

Lesson 18

Properties of number: Distributive property

Lesson 19

Multiplication: 3-digit by 2-digit numbers

Lesson 20

Multiplication: 3-digit by 2-digit numbers

Lesson 21

Flat or curved surfaces

Lesson 22

Flat surfaces

Lesson 23

Making 3-D objects

Lesson 24

3-D objects: making gift boxes

Lesson 25

Test

Lesson 26

Growing shapes

Lesson 27

Patterns with neither a constant difference nor a constant ratio

Lesson 28

Flow diagrams

Lesson 29

Geometric shapes

Lesson 30

Line of symmetry

Lesson 31

Line of symmetry

Lesson 32

Line of symmetry

Lesson 33

Multiples of 10 and 100

Lesson 34

Factors

Lesson 35

Properties of whole numbers

Lesson 36

Grouping and sharing

Lesson 37

Division without remainders

Lesson 38

Division with remainders

Lesson 39

Division: Problem solving

Lesson 40

Ratio

Lesson 41

Revision

Lesson 42

Revision

Lesson 43

Revision

Lesson 44

Revision

Grade 5 Lesson 1 Class work

Whole numbers Introduction:

What do you think a whole number is? In this activity we are going to look at whole numbers:

Whole numbers are simply the numbers 0, 1, 2, 3, 4, 5, … (and so on)

• Counting in whole numbers

A whole number is a number that is not a fraction or a decimal.

• Comparing and ordering whole numbers • Place value • Rounding off DBE workbook: 25a Q 1 – 3 and 25b Q 5 - 8

1. Fill in the missing numbers. a.

b.

c.

22 004

55 015

99 755

d.

e.

f.

77 025

22 006

22 008

55 021

55 024

99 760

88 033

88 053

77 050

77 100

66 324

66 524

22 012

55 027

99 785

99 790

88 063

88 073

77 150

66 724

66 824

2. Fill in <, > or =. a. 70 999 ______ 80 000

b. 40 000 ______ 40 000

c. 40 000 ______ 40 404

d. 50 500 ______ 50 550

e. 10 000 ______ 50 000

f. 10 000 ______ 100 000

g. 60 999 ______ 90 666

h. 90 008 ______ 80 009

i. 70 500 ______ 70 050

1

3. Complete the following. i. Write down all the odd numbers between: a. 10 and 20

______________________________________________________

b. 100 and 120

______________________________________________________

c. 1 000 and 1 008

______________________________________________________

d. 30 450 and 30 460

______________________________________________________

e. 50 090 and 50 100

______________________________________________________

f. 99 990 and 100 000

______________________________________________________

g. 20 670 and 20 690

h. 30 672 and 30 700

i. 60 120 and 60 134

______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________

ii. Write down all the even numbers. a. 10 and 20

______________________________________________________

b. 100 and 120

______________________________________________________

c. 1 000 and 1 008

______________________________________________________

d. 30 450 and 30 460

______________________________________________________

e. 50 090 and 50 100

______________________________________________________

f. 99 099 and 100 000

______________________________________________________

g. 20 670 and 20 690

h. 30 672 and 30 700

i. 60 120 and 60 134

______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ 2

4. What is the place value of the underlined digit? a. 46 756

_____________

b. 79 132

_____________

c. 97 744

_____________

d. 80 419

_____________

e. 28 153

_____________

f. 54 511

_____________

g. 35 417

_____________

h. 63 116

_____________

i. 12 697

_____________

c. 367

≈ ___________

5. Round off the following to the nearest 10. a. 740 d. 494 g. 238

≈ ___________

≈ ___________

b. 589 e. 156

≈ ___________

h. 875

≈ ___________

b. 2 785

≈ ___________

≈ ___________

f. 923

≈ ___________

i. 612

≈ ___________

≈ ___________

c. 3 373

≈ ___________

6. Round off the following to the nearest 100. a. 5 183 d. 7 567 g. 4 893

≈ ___________

e. 4 979

≈ ___________

h. 9 565

≈ ___________

b. 59 780

≈ ___________

f. 4 921

d. 41 147 g. 18 531

≈ ___________

≈ ___________

e. 12 992 h. 28 594

Problem solving

≈ ___________

≈ ___________

i. 8 696

≈ ___________

≈ ___________

c. 85 167

≈ ___________

7. Round off the following to the nearest 1 000. a. 97 424

≈ ___________

≈ ___________

≈ ___________

f. 76 085 i. 50 155

≈ ___________

≈ ___________

Give any 10 odd numbers that are bigger than a four-digit number but smaller than a six-digit number.

Extra activities ANA examples Write each of the following numbers in words a. 42 749 b. 348 706 Which number is represented by: 40 000+ 2 000 + 5 + 60 + 700 Arrange the following numbers from smallest to biggest. 36 589, 35 698, 38 569 and 39 958

3

Grade 5 Lesson 2 Class work

Rounding off and properties of whole numbers Introduction: Revise rounding off 10, 100 and 1 000. Round the following off. Highlight the number that helped you to round off.

We use ≈ as the rounding off symbol.

Rounding off

to the nearest 10

to the nearest 100

to the nearest 1 000

8 765

8 765 ≈ 8 770

8 765 ≈ 8 800

8 765 ≈ 9 000

6 243 26 289 35 924 99 999 DBE workbook: 26 Q 1 – 2 DBE workbook: 27a Q1 - 2 1. Round off the numbers to the nearest 10, 100 and 1 000. Example: 8 765

8 765 ≈ 8 770 to the nearest 10

8 765 ≈ 8 800 to the nearest 100

a. 86 239 b. 65 438 c. 37 595 d. 72 299 e. 92 496 f. 58 368 g. 64 659 h. 49 421 i. 26 074 4

8 765 ≈ 9 000 to the nearest 1 000

2. Round off the numbers to the nearest 5. Example: Round off 2 to the nearest 5.

Round off 1 to the nearest 5.

a. 56 d. 35 g. 11

≈ __________

b. 83

≈ __________

h. 97

≈ __________

e. 29

≈ __________

c. 78

≈ __________

i. 64

≈ __________

f. 42

≈ __________

≈ __________

3. What would make the following number sentences true? Example:

(4 + 5) + 3 = 4 + (5 + 3)

a. 9 + 7 = 7 + g. 3 x 9 =

(2 x 5) x 3 = 2 x (5 x 3)

b. (3 + 6) + 2 = 2 + (

d. (8 + 2) + 1 =

+(

+ 2)

x3

≈ __________

e. 8 x 1 =

+

)

c. 7 x 4 =

x8

h. (6 + 9) + 4 = (

x7

f. (8 + 5) + 6 = 6 + (5 + + 9) +

i. 5 + 7 =

+

)+(

x

)

)+(

x

)

4. What will make the following number sentences true. Example: 4 rows of 5

4 rows of 2 plus 4 rows of 3

4 rows of 3 + 2

4 x (2 + 3) = (4 x 2) + (4 x 3) 4x5 = 8 + 12 20 = 20 a. 5 x (4 + 1) = (5 x ( = =

c. 8 x (9 + 2) = ( ( = =

) + (5 x )

x

)+( )

)

x

)

b. 6 x (5 + 8) = ( ( = =

x

d. 3 x (9 + 2) = ( ( = =

x

5

)

)

)

e. 9 x (2 x 4) = ( ( = =

x

)+( )

x

g. 7 x (5 + 3) = ( ( = =

x

)+( )

x

)

)+( )

x

)

i. 2 x (3 + 7) = ( ( = =

x

)

f. 8 x (6 + 1) = ( ( = =

x

)+( )

x

)

h. 7 x (6 + 4) = ( ( = =

x

)+( )

x

)

5. Fill in the missing numbers. Example: Complete examples with the learners on: • 0 in terms of its additive property, e.g. 50 + 0 = 50, 3 456 + 0 = 3 456, etc. • 1 in terms of its multiplicative property, e.g. 65 x 1 = 65, 87 342 x 1 = 87 342, etc. a. 345 x ________ = 345

b. 895 + ________ = 895

c. 928 x ________ = 928

d. 502 x ________ = 502

e. 815 + ________ = 815

f. 674 + ________ = 674

g. 791 + ________ = 791

h. 430 + ________ = 430

i. 369 x ________ = 369

Problem solving • If you multiply any number by 1, what will your answer be? • If you add zero to any number, what will your answer be?

Extra activities ANA examples 1. 126 rounded off to the nearest 10? 2. 74 rounded off to the nearest 10? 3. 3 097 rounded off to the nearest 1 000? Calculate: a. 23 + 0 = b. 23 - 0 = 6

Grade 5 Lesson 3 Class work

Addition Introduction:

Revise expanded notation. Do the following examples. (You can use place value cards).

Give the answer for: 90 000 + 6 000 + 400 + 30 + 8 =

78 326

50 000 + 7 000 + 200 + 90 + 6 =

70 000 + 8 000 + 300 + 20 + 6 43 578

60 000 + 300 + 8 =

40 000 + 3 000 + 500 + 70 + 8 30 286 30 000 + 200 + 80 + 6

DBE workbook: 29a Q2 and 3 1. Write the following in expanded notation. Example:

78 326

a. 25 912

___________________________

b. 68 634

___________________________

c. 96 768

___________________________

d. 59 456

___________________________

e. 82 523

___________________________

f. 43 277

___________________________

g. 74 345

___________________________

h. 37 819

___________________________

i. 11 986

___________________________

70 000 + 8 000 + 300 + 20 + 6

2. Complete the following. Make use of the horizontal method. Example: 56 423 + 7 581 + 21 479 50 000 + 6 000 + 400 + 20 + 3 + 7 000 + 500 + 80 + 1 + 20 000 + 1 000 + 400 + 70 + 9 = (50 000 + 20 000) + (6 000 + 7 000 + 1 000) + (400 + 500 + 400) + (20 + 80 + 70) + (3 + 1 + 9) = 70 000 + 14 000 + 1 300 + 170 + 14 = (70 000 + 10 000) + (4 000 + 1 000) + (300 + 100) + (70 + 10) + 4 = 80 000 + 5 000 + 400 + 80 + 4 = 85 484 a. 25 218 + 64 651 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 7

b. 32 526 + 46 272 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. 63 963 + 24 016 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ d. 51 552 + 5 213 + 12 234 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ e. 84 965 + 2 021 + 13 013 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ f. 87 482 + 1 315 + 11 102 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ g. 79 747 + 2 695 + 56 768 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 8

h. 46 458 + 9 517 + 82 843 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ i. 18 331 + 7 406 + 63 952 _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 3. Complete the following. Make use of the expanded vertical method. Example: 56 423 + 7 581 + 21 479 56 423 = 50 000 + 6 000 + 400 + 20 + 3 + 7 581 = 7 000 + 500 + 80 + 1 + 21 479 = 20 000 + 1 000 + 400 + 70 + 9 Total 70 000 + 14 000 + 1 300 + 170 + 14 = 70 000 + (10 000 + 5 000) + 400 + 80 + 4 = 85 484 a. 56 984 + 32 013

b. 74 987 + 15 012

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

c. 87 642 + 12 156

d. 65 464 + 4 321 + 20 3213

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

9

e. 31 331 + 6 436 + 51 232

f. 16 497 + 1 501 + 72 001

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

g. 13 216 + 6 674 + 54 246

h. 23 647 + 5 131 + 61 221

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

i. 74 641 + 5 256 + 20 102 ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ 4. Complete the following. Example: 56 423 + 7 581 56 423 + 7 000  63 423 + 500  63 923 + 80  64 003 + 1  64 004 a. 34 689 + 45 301 _______________________________________________________________________________ b. 74 684 + 25 213 _______________________________________________________________________________ c. 32 164 + 37 625 _______________________________________________________________________________

10

d. 45 896 + 2 101 + 52 002 _______________________________________________________________________________ e. 13 325 + 2 142 + 54 532 _______________________________________________________________________________ f. 87 469 + 1 310 + 11 220 _______________________________________________________________________________ g. 56 173 + 2 823 + 41 003 _______________________________________________________________________________ h. 28 173 + 1 400 + 60 426 _______________________________________________________________________________ i. 73 418 + 5 461 + 21 120 _______________________________________________________________________________ Problem solving Which three numbers will give you 100 000? The last three digits of each number should not be zeros.

Extra activities ANA examples Calculate: a. 1 470 + 2 312 =  b. 3 122 + 20 332 + 24 253 =  What number is missing from this calculation? 13 252 + 12 632 = 13 000 + 12 000 + ________ + 84

11

Grade 5 Lesson 4 Class work

Subtraction Introduction: Revise the following. 740 – 680

7 0 0

4 0

–

= 6 0 0

1 0 0

= 1 0 0

4 0

–

6 0 0 4 0

–

8 0 6 0 0

8 0

8 0

= 6 0 DBE workbook: 30a Q 2 and 3

1. Complete the following. Example:

740 - 680 = 700 + 40 - 600 + 80 = 600 + 100 + 40 - 600 + 80 = 100 + 40 - 80 = 60

a. 554 - 474 =

b. 763 - 669 =

c. 673 - 593. =

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

d. 487 - 397 =

e. 925 - 828 =

f. 392 - 296 =

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

g. 891 - 793 =

h. 369 - 279 =

i. 261 - 165 =

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

_________________________

12

2. Complete the following by using the expanded notation method. Example: 8 743 - 5 684 8 743 - 5 684 = (8 000 + 700 + 40 + 3) - 5 000 - 600 - 80 - 4 = (8 000 + 600 + 130 + 13) - 5 000 - 600 - 80 - 4 (compensate by breaking up 743 into 600 + 130 + 13) = 8 000 - 5 000 + 600 - 600 + 130 - 80 + 13 - 4 = 3 000 + 0 + 50 + 9 = 3 059 a. 9 594 - 5 362 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. 3 998 - 1 726 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. 6 278 - 3 134 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ d. 4 874 - 2 895 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

13

e. 8 658 - 5 779 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ f. 2 768 - 1 689 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ g. 5 434 - 2 675 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ h. 2 357 - 1 489 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ i. 7 124 - 3 456 = _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 14

3. Complete the following by using the column expanded notation method. Example: 98 743 = 90 000 + 8 000 + 700 + 40 + 3 - 45 684 = 40 000 + 5 000 + 600 + 80 + 4 50 000 + 3 000 + 0 + 50 + 9 = 53 059 a. 97 678 - 36 234 =

b. 48 168 - 15 036 =

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

c. 35 947 - 13 526 =

d. 54 564 - 15 395 =

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

e. 87 471 - 38 566 =

f. 27 454 - 13 579 =

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

g. 66 274 - 27 495 =

h. 72 358 - 36 598 =

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________

i. 34 546 - 15 595 = ______________________________________ ______________________________________ ______________________________________ ______________________________________ 4. Complete the following. Example: 74 687 - 52 143 74 687 - 50 000  24 687 - 2 000  22 687 - 100  22 587 - 40  22 547 - 3 = 22 544 15

a. 95 674 - 61 253 = _______________________________________________________________________________ b. 48 787 - 12 364 = _______________________________________________________________________________ c. 32 454 - 11 312 = _______________________________________________________________________________ d. 66 527 - 28 659 = _______________________________________________________________________________ e. 21 736 - 19 378 = _______________________________________________________________________________ f. 75 815 - 56 739 = _______________________________________________________________________________ g. 67 844 - 32 865 = _______________________________________________________________________________ h. 74 945 - 43 986 = _______________________________________________________________________________ i. 45 467 - 26 498 = _______________________________________________________________________________ Problem solving My brother saved R52 876 and then bought a motorcycle for R35 950. How much money does he have left?

Extra activities AMESA examples Here is a subtraction problem, but the problem is missing: ?? -?? 63 How many different 2-digit subtraction problems could have the answer 63? 16

Grade 5 Lesson 5 Class work

Addition and subtraction: Problem solving Introduction: Look at the pictures and say how you feel when you get a problem to solve. After doing this activity, how should you feel if you want to do well in mathematics.

DBE workbook: 29a Q4 and 5 DBE workbook: 30b Q4 and 5 1. Solve the following problems. a. My dad bought two motorcycles. The one cost R35 660 and the other one R29 550. How much did he pay altogether?

b. My dad saved R90 000. How much money does he have left after paying for the two motorcycles?

17

c. My mother wants to buy furniture of R12 650, R21 970 and R19 900. How much money does she need in total?

d. My mother saved R40 000. How much more does she need to save to buy the furniture?

Problem solving Write your own story sum and ask a friend to calculate the answer.

Extra activities ANA examples 23 458 live in Lwandle and 25 249 people live in Sun City. How many more people live in Sun city than in Lwandle? Ann is a flower seller. Today she sold 1 403 flowers and yesterday she sold 2 364 flowers. How many more flowers did she sell yesterday than today? Find the sum of 3 624 and 2 304 The sum of four numbers is 20 500. Three of the numbers are 2 341, 578 and 10 690. What is the fourth number?

18

Grade 5 Lesson 6 Class work

Grouping and sharing Introduction: Revise the following. Share the 28 sweets amongst 4 children.

Answer the following questions: • How many sweets are there in total? • Amongst how many children were the sweets shared? • How many sweets did each child get? • What fraction did each child get?

1. Solve each. You can use a drawing to help you.

DBE workbook: 36 Q1

a. Share 40 sweets amongst 10 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________ b.

Share 49 sweets amongst 7 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________ 19

c. Share 36 sweets amongst 4 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________ d. Share 33 sweets amongst 11 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________ e. Share 48 sweets amongst 8 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________

20

f.

Share 45 sweets amongst 5 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________

g. Share 24 sweets amongst 12 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________ h.

Share 36 sweets amongst 3 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________

21

i.

Share 42 sweets amongst 6 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________

j.

Share 36 sweets amongst 9 children. • How many sweets are there in total? ____________________________________ • Amongst how many children were the sweets shared? ____________________________________ • How many sweets did each child get? _______________________________ • What fraction did each child get? ____________________________________

Problem solving Share 487 marbles equally amongst 6 boys.

Extra activities ANA examples Divide 200 objects into 5 equal groups. Share 300 apples equally amongst 20 people.

22

Grade 5 Lesson 7 Class work

Comparing and order of fractions Introduction: Revision: Name all the fractions equivalent to half.

1 whole 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12

DBE workbook: 35 Q1 , 4 and 5 1. You need: •A 30 𝒄𝒄 ruler

Answer the following questions. Give your answers in 𝒄𝒄. What is:

One half of the ruler? __________

One quarter of the ruler? __________

One third of the ruler? __________

One tenth of the ruler? __________

2. You need: •1 litre container Answer the following questions. Give your answers in 𝒎𝒎. Fill:

One half of the container. _________

One quarter of the container. _________

One fifth of the container. _________

One tenth of the container. ________ 23

3. You need: •30 𝒄𝒄 ruler

•A metre stick

Answer the following questions. What is more? One half of the ruler or one half of a metre stick? _______________ One half of a metre stick or one quarter of a ruler? _______________ One fifth of a metre stick or four fifths of a ruler? _______________ 4. You need: •1 litre container •2 litre container Answer the following questions. What is more? One quarter of the 1𝑙 container or one quarter of the 2𝑙 container? ______________ One half of the 2𝑙 container or three quarters of a 1𝑙 container? _______________ One eighth of a 2𝑙 container or six eighths of a 1𝑙 container? _______________ Problem solving My friend and I walked the following distances. I walked seven eights of a 3

kilometre. She walked 4 of a kilometre. Who walked the furthest? Encourage learners to solve it by drawing diagrams.

Extra activities ANA examples Fill in >, < or = to make the correct statements 1 4 4 8

3

 4; 2

 4;

1

Write down 2 fractions that are smaller than 2; 3

Write down a fraction that is bigger than 4 2

Which fraction is equal to 4?

24

Grade 5 Lesson 8 Class work

Addition of fractions Introduction: • First count in fractions. • Then make hoops on the number line to give the answer of the fraction number sentence. 1 2

0

0

1 2

1

1

3 2

2 3

1

1

1

1 3

1

1

2 3

5

2

+ 3 + 3 + 3 + 3 = 3 or 13 1 4

0 0

1

1

1 4

2 4

1

6

2 4

2

+ 4 + 4 + 4 = 4 or 1 4 1 5

0 0

4 5

4

1 3

0

3 4

1

2

2

1 5

2 5

8

1 2

2 2

+ 2 + 2 + 2 = 2 or 2

0

1 3

1 2

1

1

2 5

3

+ 5 + 5 = 5 or 1 5

2

4 2

1

1 3

3 3

4 3

3 4

1

2

1 2

5 2

1

2 3

5 3

1

1 4

3 4

4 4

5 4

3 5

4 5

1

3 5

4 5

5 5

3

6 2

2 6 3

2

1 5

1

6 5

1 3

7 3

1

6 4

1 2

7 2

2 4

1

1

3

3 4

7 4

2 5

7 5

4

8 2

2

2 3

8 3

2 8 4

1

3 5

8 5

1 2

4

9 2

3 9 3

1 4

2

9 4

1

4 5

9 5

DBE workbook: 39 Q1 and 4 1. Complete the number lines and then solve the number sentence. Show it on the number line. a. 0 0

1 12

3

3

+ 12 + 12 = 1 12

2 12

25

5

10 2

3

1 3

10 3

2

2 4

10 4

2 10 5

3

1

2

b. 7 + 7 + 7 = 0 0

1

1 7

1

3

2 7

2

c. 9 + 9 + 9 + 9 = 0 0

d. 0

2 6

1 9

1

2 9

1

+6+6=

0

3

3

1 6

1

1

2 6

e. 11 + 11 + 11 + 11 = 0 0

1 11

2 11

2. Complete the number chains. Example: Count in tenths:

4

4

+ 10

4

1 10

+ 10

4

2 10

+ 10

4

3 10

+ 10

4

4 10

9 10

+ 10

1

4

8 10

+ 10

1

4

7 10

+ 10

1

4

6 10

+ 10

1

4

5 10

Add a.

1

1 10

6

1

and then to count in tenths. 1

1

1

1

+9

+9

+9

1

+9

1

+9

+9

1

1

26

1

+9

1

+ 10

b.

c.

d.

e.

f.

5

8

7

9

4

1

1

1

+3

+3

+3

+3

1

+3

1

+3

+5

1

+5

1

+5

+5

1

+5

1

+5

+2

1

+2

1

+2

+2

1

+2

1

+2

+8

1

+8

1

+8

+8

1

+8

1

+8

+4

1

+4

1

+4

1

+4

1

+4

+4

1

1

+3

1

1

1

+5

1

1

1

+2

1

1

1

+8

1

1

27

1

+4

g.

h.

3

7

1

1

1

+6

+6

+6

+6

1

+6

1

+6

+7

1

+7

1

+7

1

+7

1

+7

+7

1

1

+6

1

1

1

+7

Problem solving 1

1

I ate 8 of a cake. My other ten friends also ate 8 each. How many cakes did we eat?. Solve by using a diagram.

Extra activities Maths challenge: Write a poem about fractions - use some rules that you have learnt to make fractions easier.

Example: The Rules of Fractions Adrian The rules of fractions are as simple as pie, Learn them at your own risk otherwise good-bye. When adding some fractions as one, Make denominators the same, you’re soon done. The last step has no stress, Just add numerators and the answer’s success! Subtracting is pretty much the same, Just take one numerator from the other and you’re in the game. http://mathematicsgradesix.wikispaces.com/Poetry

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Grade 5 Lesson 9 Class work

Collection of objects Introduction: Revise. Divide 12 sweets amongst three learners.

Divide 12 sweets amongst four learners.

1

1

• What fraction did each one get? 3 • How much sweets did each learner get?

• What fraction did each one get? 4 • How much sweets did each learner get? Homework: Complete the activity

1. Write a fraction number sentence for each. Examples: • If we divide 12 sweets amongst 3 learners, each one gets 4 sweets. 1 • This means that each learner gets 3.

• If we divide 12 sweets amongst 4 learners, each one gets 3 sweets. 1 • This means that each learner gets 4. 1

1

• 4 of 12 sweets equals 3. • We write it as a number sentence: 1 of 12 = 3 4

• 3 of 12 sweets equals 4. • We write it as a number sentence: 1 of 12 = 4 3

a. If we divide 18 marbles amongst 3 children, each one will get 6 marbles.

b. If we divide 35 cards amongst 5 children, each one will get 7 cards.

• This means that each learner gets: __

• This means that each learner gets: __

• _____ of _____ sweets equals _____.

• _____ of _____ sweets equals _____.

• We write it as a number sentence:

• We write it as a number sentence:

____________________________________

____________________________________

c. If we divide 35 counters amongst 7 children, each one will get 5 counters.

d. If we divide 32 sweets amongst 4 children, each one will get 8 sweets.

• This means that each learner gets: __

• This means that each learner gets: __

• _____ of _____ sweets equals _____.

• _____ of _____ sweets equals _____.

• We write it as a number sentence:

• We write it as a number sentence:

____________________________________

____________________________________

29

e. If we divide 72 blocks amongst 8 children, each one will get 9 blocks.

f. If we divide 84 coins amongst 6 children, each one will get 14 coins.

• This means that each learner gets: __

• This means that each learner gets: __

• _____ of _____ sweets equals _____.

• _____ of _____ sweets equals _____.

• We write it as a number sentence:

• We write it as a number sentence:

____________________________________

____________________________________

2. Solve the following. Show a drawing for each. Example: 1 5

a.

of 15 = 3

1 6

1 8

b. 11 of 55 =

of 12 = 2

1

of 24 =

1

d.

1

f. 12 of 48 =

c. 9 of 63 =

1 5

1

e. 7 of 77 =

30

of 40 =

1

1

g. 10 of 100 =

i.

1 6

h. 4 of 24 =

of 54 =

Problem solving My father has collect 564 stamps over 45 years. If he plans to sell a sixth of the stamps, how many stamps will he sell?

Extra activities AMESA example For his party, Justin bought a Super-Duper Pizza and cut it into 24 equal slices. At 1 1 1 the party, Mary ate 6 of the pizza, Veronica ate 4 of it, and Ron ate 3 of it. Justin ate the rest. How many slices if pizza did Justin eat? a. b. c. d. e.

4 6 8 2 None of these

31

Grade 5 Lesson 10 Class work

Test Introduction: These test tips should be given to the learners in preparation for their test. Tips! Before looking at what to prepare for the test, let’s see what we did during the last two terms. You should ask yourself the following questions: Before the test Have you attended all your mathematics classes up to now? Remember, in mathematics one concept builds on another concept. If you missed any classes, make sure that you have caught up all the work in order to prepare for your test. Have you been doing all your homework? Remember, if you really want to do well, you always have to do your homework assignments. Check if you did all of them. Preparing for your test. Do you practice mathematics every day? Remember that you should practice and understand in order to do well in your tests. Do you ever ask for help? Remember, it is important to ask for help if you don’t understand. You should always feel free to discuss any problem with your teacher. Do you fully understand all the examples? Going through all the examples will prepare you better for the tests. GOOD LUCK with your Mathematics test! Source: How to Better Prepare for your Math test | eHow.com http://www.ehow.com/how_4397684_better-prepare-math-test.html#ixzz1HGK62ozf

Your test will include the following: • Adding and subtracting with up to 5 digit numbers. • Fractions

32