Mathematics Class 7

Mathematics Curriculum 2017 - 2018

Mathematics Curriculum 2017 - 2018 Class 7 This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017 - 2018 How to read the document The Mathematics Curriculum is one complete document divided into different sections. The complete curriculum is uploaded on ODP server and is provided to each school in a CD. This document includes: 1. Scheme of Work…………………………………………………………………………………………………… 2. Term wise break up.……………………………………………………………………………………………. 3. Curriculum Planners.………………………………………………………………………………………….. (This is a macro planner for teachers and provides details for which learning objective targeting which content/topic/skill with which resource using what assessment method a teacher will complete in a week/unit.) 4. Technology Integrated Projects………………………………………………………………….……… Important Note It will be pertinent to note that to understand the document and implement it effectively, it is important to refer the complete document on ODP or CD regularly. Especially, the following must be consulted before planning each lesson. Assessment and examination: Information gathered through assessment will help teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations in each grade. This information will serve to guide teachers in adapting instructional approaches to students’ needs and in assessing the overall effectiveness of programmes and classroom practices. For students, it is of significant determinant of what, when and how they are going to be assessed. This section helps teachers to take aid while planning ongoing assessments to prepare their students in the same way in which they are going to be assessed in the examination using the assessment policy to be part of their daily understanding (since policy document is not easily available with every teacher at all times). It specifically talks about AfL (assessment for learning) and AoL (assessment of learning) including coursework assessment details and unified paper structure. Guidelines for teachers: The successful implementation of any curriculum involves thoughtful planning and hard work on many levels. At the classroom level, developing supportive and productive teaching activities that engage the range of learners in understanding is the key. This section provides a bank of teaching strategies, criteria for various subject topics, from where the teachers can pick and choose the activities and contexualise them as per their lesson planner and learners. Digital Resources: digital copies of teachers’ resource books for Mathematics and books are available on ODP and on CD with the school head. This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017 - 2018

Term wise break up The total number of active teaching weeks for AY 2017-18 is 31 (excluding revision and examination weeks):  

first term: 14 weeks second term: 17 weeks

Term I Unit Numbers

Decimals Number Sequence Algebraic Expression Algebraic Formulae & Equations Measurement Perimeter and Area

Topic  Tests of Divisibility  Integers  Rational Numbers  Estimation  Rounding off  Significant figures  General term  Linear algebraic equations  Substitution  Construction  Length, Mass and Capacity  Circle  Parallelogram  Trapezium  Composite shapes  Unknown sides

Total

Time 2 weeks

2 weeks

2 weeks 2 weeks 1.5 week 1.5 week 3 weeks

14 weeks

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Mathematics Curriculum 2017 - 2018

Term II Unit Numbers - Percentages Ratio, Rate and Proportion

Algebra Time Volume and Surface Area Angles

Constructions Symmetry Position and Movement Statistics

Topic  Percentage Change  Ratio  Rate  Proportion  Fractional coefficients  Linear Equations  Calculation of time  Volume  Surface Area  Lines  Triangles  Polygons  Perpendicular bisector  Angle bisector  Rotational Symmetry  Graphs  Frequency Table  Bar Graph  Pie Chart  Averages - Mean - Median - Mode

Time 2 weeks 3 weeks

1.5 weeks 1 week 1.5 weeks 3.5 weeks

1 week 1 week 1 week 1.5 weeks

Total

17 weeks

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Mathematics Curriculum 2017-18

Mathematics Curriculum Planners 2017 - 2018 Class 7 Term I This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/Topic: Numbers – Integers Duration: 2 weeks (1, 2 of 14) Objectives:

Class: 7 Term: 1 Lessons: 16 Suggested Resources:

Content

In this unit you will learn to:  Calculate using rules of four Arithmetical operations on integers  

Calculate using rules of four Arithmetical operations on rational numbers. Apply commutative, associative and distributive laws on integers

Prior Knowledge: You have learnt to:  add, subtract, multiply and divide integers;  convert improper fractions to mixed numbers and vice versa;  use a common denominator to simplify fractions

Words to Remember: Integers, Negative integer, Positive integer, Number line, Directed numbers, Absolute value, Additive inverse, Additive Identity

Syllabus - D Book 1 Chapter 3 Ex. 3d, 3e

Cambridge O Level Mathematics Volume 1 Chapter 1 Ex. 1.6, Questions 5, 6, 7 Reinforcement/ Diagnostic Week: Syllabus – D Book 1 Exercise 2a – 2 d Reinforcement/ Diagnostic Week: Exercise 3a, 3b,3c

Syllabus – D Book 1 Chapter 2 Ex. 2e, Review Questions 2

Lesson Support Teaching Tips/Teaching Strategies: Solve the innermost bracket first. Work from left to right if there are only two operations to perform that is either addition and subtraction together or multiplication and division together. LCM can be taken when multiplying or dividing rational numbers. Basic task: Check the learners competence in the four operations with integers, both mentally and using written methods. Teach methods such as long multiplication and long division if necessary. (W/G) Talk about the meaning of, e.g. 4 + 3 × 2 and establish with learners the correct order of operations and the need to use brackets to do (4 + 3) × 2. Similarly the solution of division problems where there is more than one term in the numerator or denominator. (W) Give the learners practice in using their calculators efficiently to solve such problems, as well as those which they should do without a calculator. (G/I) Include the fact that all terminating and recurring decimals may be expressed as fractions and so are rational, and that non-recurring decimals are irrational. Learners could investigate this by converting fractions to decimals using their calculators, identifying that some give terminating decimals and some give recurring decimals. (G/I)

Misconceptions/Facts to Remember:

Project/Bulletin Board Ideas/ Subject Integration:

Misconceptions LCM can be taken when multiplying or dividing rational numbers. Facts to Remember: All rules of four operations of whole numbers are applicable on integers too. Absolute value of any integer will always be positive. 𝑎 A rational number is a number which can be expressed in the form , where a and 𝑏 b are integers and b ≠ 0. Every integer is a rational number. Zero divided by any other integer equals zero, therefore zero is a rational number.

Online: Practising basic mental calculation skills: The 24 game provides practice in mental calculation. Learners can be encouraged to write their solutions as single calculations using the rules of BODMAS/BIDMAS. Instructions for the game can be found at www.24game.com/t-about-howtoplay.aspx or play online at www.mathplayground.com/make_24.html (please note: this site carries advertising) Understanding the Laws of Arithmetic, a resource from the UK Department for Education’s Standards Unit, has materials that ask learners to interpret calculations in words and as area diagrams in order to develop their understanding of arithmetical rules and laws: www.nationalstemcentre.org.uk/elibrary/resource/1962/understanding-the-laws-of-arithmetic-n5 Don Steward has a collection of mental calculation problems involving the rules of BODMAS/BIDMAS http://donsteward.blogspot.co.uk/search/label/bidmas

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Mathematics Curriculum 2017-18 Denominator of the fraction should not be equal to zero, as division by zero is undefined. 22 𝜋 is an irrational number while its approximate value which is equal to is a 7 rational number. 3 4 Reciprocal is the inverse of the fraction. For example reciprocal of is 4

Questions based on the construct ‘Would you rather?’ can be found at: http://wyrmath.wordpress.com/2014/04/16/would-you-rather-32/ The questions can be used in in the form in which they are offered or adapted to suit local currencies etc. http://nrich.maths.org/9923

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Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student. The Strange Bank Account from NRICH could provide a starting point for an interesting investigation: http://nrich.maths.org/9923 (I/F)

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q2a Jun 12 Paper 12 Q10a Jun 13 Paper 12 Q9c Nov 13 Paper 11 Q1b Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/Topic: Estimation and Approximation ( numbers and decimals) Duration: 2 weeks (3, 4 of 14) Objectives: In this unit you will learn to:  estimate numbers and measures;  understand the difference between rounding off and estimation;  find the number of significant figures in a given number;  express numbers correct to the indicated number of decimal places or significant figures

Content Syllabus - D Book 1 Chapter 4 Ex. 4a, 4b 4c

Class: 7 Term: 1 Lessons: 16 Suggested Resources: Cambridge Checkpoint Maths 2 Chapter 1 Ex. 1.2C, 1.2D Cambridge Checkpoint Maths 3 Chapter 8 Ex. 8.2A, 8.2B, 8.3 Cambridge O Level Mathematics Volume 1 Chapter 4Ex. 4.4, 4.5

Lesson Support Prior Knowledge:

Teaching Tips/Teaching Strategies:

You have learnt to estimate and round off small numbers

Estimate totals mentally, from grocery bills etc. Have a quick recap of rounding off to the nearest whole number and to the nearest 10, 100, 1000…… Collect real numbers from documents and round off and discuss the necessity and usage of rounding off. Clearly explain the difference between writing numbers correct to the indicated number of decimal places and significant figures. Basic task: Teach learners how to round, using a number line to position the unrounded numbers, to the nearest 100, nearest 10, to 1 decimal place etc., 3 significant figures etc. Show the learners which are the vital digits to look at in each case. Use the convention of rounding halfway positions up, e.g. 8.5 rounding to 9 to the nearest unit. Discuss that rounding to the nearest number is not always appropriate, e.g. if calculating the number of cans of paint required, an answer of 3.2 would need to round up to 4. (W). Apply rounding skills to making estimates. Consider appropriate rounding, for example if estimating a square root, rounding to the nearest square number is usually appropriate. Model efficient use of an electronic calculator, emphasising that intermediate values should not be rounded in a multi-step calculation. The use of memory or answer functions avoids the need for premature rounding. Loss of accuracy marks as a result of premature rounding is a common error in examinations, so it is worth taking some time to address this. (W)

Words to Remember: Estimate, Approximate, Accurate, Round off, Significant figures, Degree of accuracy

Misconceptions/Facts to Remember:

Project/Bulletin Board Ideas/ Subject Integration:

When finding an estimate answer round up or round down depending on the question Memorize rules for rounding a number to a given number of significant figures. Memorize rules for determining the number of significant figures.

Challenging task: Investigate the effect on the final answer in a multi-step calculation if intermediate values are rounded. (G/I) Nrich has some challenging problems involving estimating. (G/I) Online: ‘Rounding Numbers’ a resource from the UK Department for Education’s Standards Unit, suggests an approach to teaching rounding: www.nationalstemcentre.org.uk/elibrary/resource/1960/rounding-numbers-n3 BBC Bitesize has a section on rounding and estimating: www.bbc.co.uk/schools/gcsebitesize/maths/number/ A game from the BBC to practise simple rounding: www.bbc.co.uk/schools/mathsfile/shockwave/games/saloonsnap.html The Nrich task 'Approximately Certain' asks learners to order a series of quantities: http://nrich.maths.org/6505 The Nrich task 'Does This Sound about Right?' asks learners to check a series of calculations: http://nrich.maths.org/7418

Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q6 , Jun 12 Paper 12 Q10b, Nov 12 Paper 11 Q7a Nov 12 Paper 12 Q17a and Q17c, Jun 13 Paper 12 Q9a, Nov 13 Paper 11 Q7 Nov 13 Paper 12 Q9 Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/Topic: Number Sequence Duration: 2 weeks (5, 6 of 14) Objectives: In this unit you will learn to:  recognize simple patterns from various number sequences,  continue a given number sequence and find its general terms

Class: 7 Term: 1 Lessons: 16 Suggested Resources:

Content

Cambridge Checkpoint Maths 2 Chapter 16 Ex. 16.2A Cambridge Checkpoint Maths 3 Chapter 16 Ex. 16.1A, 16.1B Cambridge O Level Mathematics Volume 1 Chapter 5 Ex. 5.7, Questions 1 to 6; only a and b parts Reinforcement: Syllabus – D (Book-1) Exercise 6a

Syllabus - D Book 1 Chapter 6 Ex. 6 b

Lesson Support Prior Knowledge: You have learnt to complete simple number sequence Words to Remember: Next term, Consecutive, Sequence, Series, Continue, Predict, Pattern, General term, nth term

Teaching Tips/Teaching Strategies: Ask open-ended questions. A number sequence is a set of numbers arranged in such a way that each successive term follows the preceding term according to a specific rule; and the difference between these terms is constant. Find out the pattern of a sequence, giving reasons or explain the method how the number sequence is generated. Basic task: Start with some simple linear sequences, expressed in numbers or in patterns using matchsticks etc. Ask learners to explain the patterns and how to find the next term, the 10th term etc., leading on to finding the nth term. Make comparisons with gradient and the equation for a straight line. (W) Lead on to other basic number patterns such as squares, cubes, powers of 2 and triangle numbers before other quadratic sequences. (W/G/I) For an activity using sequences, learners could explore the number of games, rounds etc. needed for any number of competitors for a knockout tournament such as the Wimbledon tennis tournament. (G/I)

Misconceptions/Facts to Remember:

Project/Bulletin Board Ideas/ Subject Integration:

Numbers are written in a sequence through a rule. An increasing sequence is generated by addition or multiplication, whereas a decreasing sequence is generated by division and subtraction Some sequence follow dual or triangular pattern so complete sequence should be consider to predict the unknown terms.

Online: A fascinating site about the Fibonacci sequence and the Golden section: www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html The NRich site has many puzzles about sequences, such as this one about triangle numbers: http://nrich.maths.org/2274/

Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q19a, b Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/Topic: Fundamentals of Algebra Duration: 2 weeks (7,8 of 14) Objectives: In this unit you will learn to:  simplify linear algebraic expressions with fractional coefficients;  solve linear algebraic equations

Class: 7 Term: 1 Lessons: 16 Suggested Resources: Cambridge Checkpoint Maths 1 Chapter 9 Ex. 9.1A, 9.1B Cambridge Checkpoint Maths 3 Chapter 9 Ex. 9.1, 9.2A, 9.2B Cambridge O Level Mathematics Volume 1 Chapter 3 Ex. 3.2

Content Syllabus – D Book 1 Chapter 5 Ex. 5f Chapter 7 Ex. 7a, Ex. 7b Lesson Support

Prior Knowledge: You have learnt to add and subtract simple algebraic expressions. Words to Remember: Letters, Alphabets, Variables, Constant, Coefficient, Statement, Expression, Equation, Linear equation, Identity

Teaching Tips/Teaching Strategies: Through explanation and discussion show the difference between algebraic expression and algebraic equations. Take the LCM of the fractional coefficient and work with variables the same way as with whole numbers. Ask students to form simple linear algebraic expressions and equations from sentences. Basic task: Puzzles such as ‘I think of a number, I multiply it by 2, then add 1; the answer is 7. What number did I think of?’ can be used to introduce the ideas of inverse operations. Then represent the same situation by an equation, showing how to set out the algebraic solution. (W) Formulae can be used again here, substituting a number this time for the subject of the formula and solving an equation to find the unknown variable.(G/I) Challenging task: Learners can use contextual information to form and solve equations. (G/I) For example, ‘Angles and Algebra’ provides a diagrammatic context, but will require prior knowledge or research about angles in order to complete the task. Alternatively, Don Steward has a collection of puzzles that can be solved using algebra. (G/I)

Misconceptions/Facts to Remember:

Project/Bulletin Board Ideas/ Subject Integration:

While solving algebraic expressions follow the same order as in Arithmetic operations. Expressions can only be simplified; while equations can be solved to give a solution. Algebraic operations follow the same conventions and order as Arithmetic operations

Online: Don Steward has an ‘unjumbling’ activity in which learners need to sort the steps in solving various equations into order http://donsteward.blogspot.co.uk/2014/05/unjumbling.html Forming and solving equations: ‘Angles and Algebra’ provides a diagrammatic context: www.tes.co.uk/ResourceDetail.aspx?storyCode=6296832 Don Steward has a collection of puzzles that can be solved using algebra: http://donsteward.blogspot.co.uk/2013/06/puzzles-that-you-could-use-algebra-to.html

Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q18a Nov 13 Paper 22 Q3d Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18

Subject: Mathematics Unit/Skill/Topic: Algebraic Equations Duration: 1.5 weeks (9, 10.5 of 14) Objectives:

Content

In this unit you will learn to:  substitute numbers for letters in formulae to find the unknown;  construct simple formulae using variables

Syllabus - D Book 1 Chapter 7 Ex. 7d , Q1 - Q 12 Ex. 7e , Q1a - i

Prior Knowledge:

Class: 7 Term: 1 Lessons: 12 Suggested Resources: Cambridge Checkpoint Maths 1 Chapter 2 Ex. 2.1B, 2.2 Cambridge Checkpoint Maths 3 Chapter 2 Ex. 2.2B Cambridge O Level Mathematics Volume 1 Chapter 3 Ex. 3.2

Lesson Support Teaching Tips/Teaching Strategies:

Words to Remember: Basic task: Variable, Substitute, Formula, Construct a formula Use word formulae representing practical situations, such as costs – substitute numbers

into these, then show that the same situation can be represented generally using letters to represent the variables. Move on to substituting numbers into formulae. Challenging task: Ask learners to try more using complex algebra, for example substituting negative values into expressions involving powers, e.g. 3x2 – x3 when x=-4. (G/I)

Project/Bulletin Board Ideas/ Subject Integration: Online: Work on formulae: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bka2.pdf

www.tes.co.uk//Resource Detail.aspx?story code=6027 Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q22a Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Measurements (Length, weight and Capacity) Durations: 1.5 weeks (10.5, 11 of 14) Objective (s)  Conversion of units of length: cm to mm, m to cm, km to m and vice versa.  Conversion of units of weight: Kilogram to gram and vice versa.  Conversion of units of capacity: Litre to mililitre and vice versa.  Convert cm3 to litres and vice versa

Content Cambridge Checkpoint Maths book1, Chapter 4,Ex 4.1A.4.1B

Class: 7 Term: 1 Lessons: 12 Suggested Resources Cambridge Checkpoint workbook 1,Ex 4.1 Cambridge O Level Mathematics Volume 1 Chapter 4 Pg. 73

Prior Knowledge

Teaching Tips/ Teaching Strategies

Compare and order measurements in different units. Convert larger units of measurements into smaller units of measurements and vice versa. Use decimal points to convert lengths of compound units to bigger unit and vice versa.

1 km is 1000m, so To change from km to m, multiply by 1000. To change from m to km, divide by 1000. 1 tonne is 1000 kg, so To change from tonnes to kg, multiply by 1000. To change from kg to tonnes, divide by 1000. 1 litre is 1000 ml, so To change from litres to ml, multiply by 1000. To change from ml to litres, divide by 1000. Basic task: Check that learners can convert competently between length units. Progress to finding the area of a rectangle in different units, and give learners practice in converting from one area unit to another, e.g. cm² to m². Similarly, apply this process to volume and capacity. Find the mass of an object in different units.

Words to Remember kilometer(km), metre(m), centimeter (cm)and millimeter (mm) tone (t), Kilogram(kg), grams (g) and milligrams (mg) litre and milliliter (ml)

Misconceptions / Facts to Remember

Project / Bulletin Board Ideas / Subject Integration

The metric unit for length are kilometer(km), meter(m), centimeter (cm)and millimeter (mm) The metric units for mass are tone (t), Kilogram(kg), grams (g) and milligrams (mg) The metric unit for capacity are liter and milliliter (ml)

Work on units: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb7.pdf An image that could be used to generate a variety of interesting questions about volume: Viva las Colas! www.101qs.com/112-viva-las-colas

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers: Jun 12 Paper 11 Q13a, Jun 12 Paper 12 Q17a, Nov 12 Paper 11 Q13a, Jun 13 Paper 11 Q3 Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Perimeter and Area of Simple Geometrical figures Durations: 3 weeks (12, 13, 14 of 14) Objective (s) Content Syllabus - D  Find circumference and area of a circle, semicircle and quadrants Book 1 Chapter 8,  Find area and perimeter involving composite Ex 8 a Q no 2. shapes (shaded and un- shaded region).

Class: 7 Term: 1 Lessons: 24 Suggested Resources Mathematics Workbook 1 Chapter 8, Q no 43-54 Cambridge Checkpoint Maths book 2 page 174-179 Ex 18.5A. 18.5B .18.5C Cambridge O Level Mathematics Volume 1 Chapter 8 Ex. 8.3, 8.4

 

Cambridge Checkpoint workbook 2 Ex 18.3 Cambridge O Level Mathematics Volume 1 Chapter 8 Ex. 8.4



Find area of a parallelogram and a trapezium; Find unknown measurements when area/perimeter is given; Find area and perimeter involving composite shapes (shaded and un- shaded region).

Prior Knowledge     

draw circles with different radii Find perimeter and area of rectangles and squares by using formula; Find the unknown side when the area of rectangle or square is given; Find perimeter of regular and irregular polygons; Find the perimeter of composite shapes

Real World Connection

Syllabus - D Book 1 Chapter 8, Ex 8 b, Ex. 8 c

Words to Remember Perimeter, Area, Circumference, Radius, Diameter, pi, Revolution, rotation, Base, Parallel sides, Adjacent sides, Parallelogram, Trapezium, Perpendicular distance i.e. height, Square unit

Misconceptions / Facts to Remember

Lesson Support Teaching Tips/ Teaching Strategies Teaching Tips Make the units same before finding the perimeter or area if two different units are given. Composite shapes can be divided into small sections to find their perimeter and area Make the units same before finding the perimeter or area, if two different units are given. Composite shapes can be divided into small sections to find their perimeter and area It may be helpful to show learners how the area formulae for a parallelogram and a trapezium may be obtained by splitting them into two triangles. After this, encourage them to work with the area formulae. (W) Give them practice in finding areas and perimeters, making sure that they give the appropriate units in their answers. (G/I) Learners need to be able to solve problems involving area, for example finding out how many square paving slabs would cover a given area. (G/I) Learners also need to be able to find area and perimeters of compound shapes, for example splitting an L-shape into two rectangles. (G/I) Project / Bulletin Board Ideas / Subject Integration

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 The distance travelled on a bicycle is calculated by multiplying the number of rotations by a point on the wheel circumference. Finding the areas of different shape is essential in architecture, from houses and flats to the most spectacular buildings in the world.

Facts to remember Unit of area is a square unit, read as square centimeter or square metre. Perimeter of any quadrilateral is the sum of the measurements of its sides. Unit of area is a square unit, read as square centimeter or square metre.

Work on circles in section 7.7 of: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb7.pdf BBC Bitesize has work on circles: www.bbc.co.uk/schools/gcsebitesize/maths/geometry/ Articles giving more background about the formulae for area and circumference, and π, may be found for example at www-gap.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html Learners can make a project in which they calculate the cost of redecorating a room, deciding what measurements they require; finding areas and using them to calculate paint or wallpaper quantities, costs of flooring etc. (G/I) Work on the area and perimeter of squares, rectangles and triangles at section 7.6: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb7.pdf BBC Bitesize has work on area and perimeter: www.bbc.co.uk/schools/gcsebitesize/maths/geometry/ Evaluating Statements about Length and Area, a resource from the UK Department for Education’s Standards Unit, asks learners to consider a variety of statements and respond using their own examples or counter-examples: www.nationalstemcentre.org.uk/elibrary/resource/2031/evaluating-statementsabout-length-and-area-ss4

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check:

Cambridge Checkpoint Maths workbook 2 Ex 18.5 Mathematics Book 1Revision Exercise II No1 Q no 7a,Revision Exercise II No 3 Q no 9 a, Revision Exercise III No 3 Q no 4 Quick Check: 4024 past examination papers:

Jun 12 Paper 12 Q4,Jun 12 Paper 21 Q4b and 5a,Nov 12 Paper 11 Q22a,Nov 12 Paper 21 Q5a and Q5b,Jun 13 Paper 11 Q5, Q14a and Q14b, Nov 13 Paper 21 Q8a,Nov 13 Paper 22 Q4a, Jun 12 Paper 21 Q4a,Nov 12 Paper 11 Q15,Nov 12 Paper 12 Q3,Jun 13 Paper 11 Q1,Jun 13 Paper 21 Q6aii,Jun 13 Paper 22 Q4a and Q4bi Nov 13 Paper 22 Q1a Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18

Mathematics Curriculum Planners 2017 - 2018 Class 7 Term 2 This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Class: 7 Unit/Skill/Topic: Numbers/ percentages/ percentage change Term: 2 Duration: 2 weeks (1, 2 of 17) Lessons: 16 Objectives: Content Suggested Resources: In this unit you will learn to: Syllabus – D Book 1 Cambridge Checkpoint Maths 2 Chapter 15 Chapter 11 Ex.11 c Q 1 – Q 11 Ex. 15.3D, 15.3 E  Increase or decrease a quantity by a given percentage. Lesson Support Prior Knowledge: Words to Remember: Teaching Tips/Teaching Strategies: You have learnt to: Increase, Decrease, Make sure that students know the relationship between the following: 1/4 = 25 % = 0.25  convert fractions to percentages and Quantity, Percentage 1/2 = 50 % = 0.50 vice versa; 3/4 = 75 % = 0.75  convert decimals to percentages and Basic task: vice versa; Begin by asking orally for 50% of 200g, 10% of $50 etc. and progress to formal  express one quantity as percentage methods of finding a percentage of a quantity. Similarly use questions such as of another. ‘What fraction of 40 cm is 8 cm?’ to progress to expressing one quantity as a percentage of another. (W) Calculate percentage increase and decrease, using contexts such as length, time or mass as well as money (G/I)

Real World Connection:

Misconceptions/Facts to Remember:

Project/Bulletin Board Ideas/ Subject Integration:

Cooking, Banking, Finance and budgeting, Marketing, Evaluation, Prediction, Shopping, Weather reports, Currency exchange rates

Percentage increase: Increased value × 100 Original value Percentage decrease: Decreased value × 100 Original value

Online: BBC Bitesize has a variety of activities linked to percentages: www.bbc.co.uk/schools/gcsebitesize/maths/number/ Work on percentages: www.cimt.plymouth.ac.uk/projects/mepres/allgcse

Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q2a Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/Topic: Ratio, Rate and Proportion Duration: 3 weeks (3, 4, 5 of 17) Objectives:

Content

In this unit you will learn to:  use ratio to compare similar quantities  express ratios in its simplest form  express one quantity as a ratio of another in the form a:b  find the ratio of two or more quantities (a:b:c)  Increase and decrease given quantities in the given ratio  solve problems involving rates

Syllabus - D Book 1 Chapter 10 Ex.10 a Q 6 – Q 10,

In this unit you will learn to:  solve problems based on direct proportion;  solve problems based on inverse proportion

Book 2 Chapter 2 Ex. 2 a , Ex. 2 d

Ex.10 b Ex. 10 d Q 6 – Q 10

Class: 7 Term: 2 Lessons: 24 Suggested Resources: Cambridge Checkpoint Maths 1 Chapter 22 Ex. 22.1B, 22.1C Cambridge Checkpoint Maths 2 Chapter 22 Ex. 22.1A, 22.1B, 22.1C, 22.1D, 22.1E, 22.1F Cambridge Checkpoint Maths 3 Chapter 22 Ex. 22.1A, 22.1B Cambridge O Level Mathematics Volume 1 Chapter 4 Ex. 4.10, 4.11 Ex. 4.13, Questions 5, 6

Cambridge Checkpoint Maths 1 Chapter 22 Ex.22.2A, 22.2B 22.3 Cambridge Checkpoint Maths 2 Chapter 22 Ex. 22.2A, 22.2B Cambridge Checkpoint Maths 3 Chapter 22 Ex. 22.2A, 22.2B Cambridge O Level Mathematics Volume 1 Chapter 4 Ex. 4.12 Lesson Support Teaching Tips/Teaching Strategies:

Prior Knowledge: You have already learnt to:  use ratio to compare similar quantities;  express ratios in its simplest form;  express one quantity as a ratio of another in the form a : b;  find the ratio of two or more quantities; Words to Remember: Ratio, Rate, Equivalent ratio, Simplest form, Increase, Decrease, Reciprocal, Proportion, Direct, Inverse, Reciprocal

Basic task: Introduce proportion by using a recipe with quantities for four people, asking learners for the quantities needed for eight people, six people etc. This could be a traditional local recipe, or if you have looked at data from another country using the Census at School website, you could use a recipe from that region. (W) Do further work on proportion such as how many cans of paint are needed to paint a fence, knowing the area which can be painted using 1 litre. Include some inverse proportion, such as the fixed cost of hiring a coach, finding the cost per person if 50 people go in the coach or only 40 do. Move on to comparing quantities as ratios, using ratio notation. Include work on scales and scale drawings, following on from the work in Unit 3, using harder scales, including scales written in the form 1 : n. Do work on solving problems with ratios, including simplifying ratios and dividing a quantity in a given ratio. (W/G/I) Formally define speed and use it to solve problems involving constant speeds. Use problems involving other rates, for example the volume of water per minute that is flowing through a tap. (W/G/I)

Misconceptions/Facts to Remember:      

Ratio has no units. Ratio is expressed as a fraction of the first quantity to the other. Two quantities must have same units to be expressed as a ratio. Rate is a relationship between two quantities having different units. In case of direct proportion quantities increase or decrease together. In case of inverse proportion if one quantity increases the other quantity decreases and vice versa

Project/Bulletin Board Ideas/ Subject Integration: Online: An introductory lesson on ratio: www.mathsisfun.com/numbers/ratio.html Work on ratio and proportion and scale drawings: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkc15.pdf BBC Bitesize has materials on ratio: www.bbc.co.uk/schools/gcsebitesize/maths/number/ Recipes are widely available on websites. For instance there are links to over 500 sites giving Asian recipes at: www.cbel.com/asian_recipes/ Developing Proportional Reasoning, a resource from the UK Department for Education’s Standards Unit, asks learners to create and solve a variety of problems: www.nationalstemcentre.org.uk/elibrary/resource/1963/developing-proportional-reasoning-n6 Information about the ‘Golden section’: www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html Use unitary method to solve problems based on direct and inverse Proportion.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 ‘Proportion’ is a statement which shows that two ratios are equivalent

Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 paper 12 Q16 Jun 12 paper 21 Q7a Nov 12 paper 11 Q19 Nov 12 paper 12 Q24 Jun13 paper 21 Q 2a Jun 12 Paper 12 Q5 Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/Topic: Algebra Duration: 1.5weeks (6, 7.5 of 17) Objectives: In this unit you will learn to:

 substitute numbers for letters in formulae to find the unknown;  construct simple formulae using variables;  write algebraic expressions;  solve word problems

Prior Knowledge: You have learnt to recognize Algebraic expressions Words to Remember: Variable, Substitute, Formula, Construct a formula

Content Syllabus - D Book 1 Chapter 7 Ex. 7 d Q 1 – Q 12, Ex. 7 e Q 1 a – i Ex. 7 g , Ex. 7 h

Class: 7 Term: 2 Lessons: 12 Suggested Resources: Cambridge Checkpoint Maths 1 Chapter 23 Ex. 23.1A, 23.1B Cambridge Checkpoint Maths 2 Chapter 2 Ex. 2.1A, 2.1C, 2.2A Cambridge Checkpoint Maths 3 Chapter 2 Ex. 2.2A, 2.2B Cambridge O Level Mathematics Volume 1 Chapter 3 Ex. 3.1, 3.2

Lesson Support Teaching Tips/Teaching Strategies: While solving word problems based on algebra, highlight the key words and convert the wording to an algebraic expression or equation by using mathematical language. Basic task: Simplify expressions such as 4a + 3b − 6a + 5b, 4a × 3b. Use word formulae representing practical situations, such as costs – substitute numbers into these, then show that the same situation can be represented generally using letters to represent the variables. Move on to substituting numbers into formulae. Challenging task: Ask learners to try more using complex algebra, for example substituting negative values into expressions involving powers, e.g. 3x2 – x3 when x=-4. (G/I)

Project/Bulletin Board Ideas/ Subject Integration: Online: Work on directed numbers, simplifying and simple equations: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb10.pdf Two ‘Top Trumps’ games to practise substitution: www.tes.co.uk/ResourceDetail.aspx?storyCode=6027440 Work on formulae: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bka2.pdf

www.tes.co.uk//Resource Suggested Method of Assessment: Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 paper 11 Q4a Nov 12 paper 11Q18a Nov12 paper 12 Q7b andQ15a , Nov12 pap3er21 Q2ai Jun 13 paper 21 Q1a Jun 13 paper 22 Q3a Nov 13 paper 21 Q5bi Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Time Durations: 1 week (7.5, 8.5 of 17) Objective (s) • Calculate time in terms of the 12hour and 24-hour clock; read clocks, dials and timetables.

Content Syllabus - D Book 1 Chapter 10 Exercise 10f

Class: 7 Term: 2 Lessons: 8 Suggested Resources Cambridge Checkpoint Maths Book 1, Chapter 11, Exercise 11.1 A, 11.1 B Cambridge O Level Mathematics Volume 1 Chapter 4 Ex. 4.13, Questions 2, 4

Prior Knowledge

Words to Remember

Teaching Tips/ Teaching Strategies

• Convert 24 hour clock time to 12 hour and vice versa. • Find time difference between two cities given the local time in each city. • Calculate the local time in one city given the local time in another city and their time difference. • Calculate time intervals using digital and analogue times.

Duration, arrival time, departure time, timetable, analogue clock/time, digital clock/time, am, pm, earlier, later, hour, hands, minute, second, o’ clock, quarter to, quarter past, half past, before, after, 24-hour clock, 12-hour clock, am, pm, before, after, midday, midnight, noon, daytime, noon, afternoon, evening, midnight, night, am, pm, calendar, day, week, month, year, leap year, decade, century, millennium

Give learners practice in finding information from timetables. They could be challenged to use local timetables to plan an activity or holiday or to find the maximum distance they can travel in 24 hours with a given budget. (G/I) Calculate times, making sure that learners can convert between hours, minutes and seconds, as well as find the sum and difference of times. Using a timeline is recommended. (G/I)

Real World Connection

Misconceptions / Facts to Remember

Project / Bulletin Board Ideas / Subject Integration

Time is used in every activity of our life and reading and recording time helps to structure it, like meal time, prayer time, school timings, birth days and age, and timetables. It helps to organise life and be constructive. There is time duration for everything we do, be it in clock time or in calendar time. All our activities, in school or at home are time based. Also everything in the universe is controlled by time. We should learn how to use our time constructively. Time helps us structure our daily lives

Facts to remember: Conversion of Time

Practice in using timetables: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb8.pdf

minutes 1 5 10 60

seconds 60 5 x 60= 300 10 x 60= 600 60 x 60= 3600

hours 1 2 3 5

minutes 60 2 x 60 =120 3 x 60 =180 5 x 60 =300

seconds 3600 2 x 3600= 7200 3 x 3600= 10800 5 x 3600= 18000

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q13bi, Jun 12 Paper 12 Q17b, Nov 12 Paper 11 Q5a and Q26a, Nov 12 Paper 12 Q8b and Q27a Jun 13 Paper 12 Q7, Nov 13 paper 11 Q10c, Nov 13 Paper 12 Q4a and Q24a Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Volume and Surface Area Durations: 1.5 weeks (8.5, 10 of 17) Objective (s)  find volume, capacity and surface area of cubes and cuboids;  find total surface area when area of each surface is given;  find unknown sides when volume or total surface area is given

Content Syllabus - D Book 1 Chapter 9 Ex. 9 a Q 2- 7

Class: 7 Term: 2 Lessons: 12 Suggested Resources Cambridge Checkpoint workbook1 Exercise 25.1, 25.2 Mathematics Workbook 1 Q no 1-28 Cambridge O Level Mathematics Volume 1 Chapter 8 Ex. 8.5, Questions 1, 4 Ex. 8.6, Questions 1, 4, 5, 6

Lesson Support Words to Remember Teaching Tips/ Teaching Strategies

Prior Knowledge  find volume and surface area of a cube and a cuboid;  find each side of cube when volume is given;  find measurement of a side of a cuboid when measurements of other two sides and volume is given.

Cube, Cuboid, Dimensions, Length, Breadth, Height, Volume, Surface area, Mass, Capacity

Misconceptions / Facts to Remember Facts to remember 3

There are 1000 cm in 1 litre. Volume of an object is the amount of space occupied by it. Volume of a regular geometrical object is base area x height. Unit of volume is cm3 or m3. The total surface area is the sum of areas of all the faces of a 3D figure. Unit of surface area is cm2 or m2. 2

Surface area of a cube = 6 l Surface area of a solid cuboid = 2 [ (l x b) + (b xh) + (l x h) ] Misconceptions Surface area of a closed and open tank will be same.

Explain the difference in units of volume and surface area. Basic task: Draw the nets of some prisms and construct the prisms. If card is available, these could be decorated (easiest to do at the net stage) and made into gift or storage boxes, perhaps with separate lids. This activity leads naturally into calculations of surface area and volume. (It could be set as a task to design a storage box taking these elements into consideration.) (W/G/I)

Project / Bulletin Board Ideas / Subject Integration Boxes and bottles from Cre8ate Maths has some suggestions for some straightforward practical starter tasks: www.cre8atemaths.org.uk/food-and-drink/boxes-and-bottles Area and volume problems are at section 7.8: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb7.pdf Real World Connection Carpeting, Tiling, Packaging, Designing, Interior decoration, Architecture

Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Cambridge Checkpoint workbook2 Exercise 18.4 Quick Check: 4024 past examination papers:

Nov 12 Paper 21 Q5b, Nov 12 Paper 22 Q7a, Jun 13 Paper 21 Q9a and Q9b, Jun 13 Paper 22 Q12a, Nov 13 Paper 21 Q10b Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Class:7 Unit/Skill/ Topic: Lines and Angles/Geometrical Ideas and Properties Term: 2 Durations: 1 week (11 of 17) Lessons: 8 Objective (s) Content Suggested Resources Mathematics Workbook 1 Chapter 14 Q 12-32 Syllabus D  Find the unknown angles using Cambridge Checkpoint Maths Book 1 Chapter 17, properties of parallel lines and Book 1 Exercise 17.1, exercise 17.3 A,17.3 B, 17.3 C straight lines. Chapter 14 Cambridge O Level Mathematics Volume 1 Chapter 6 Ex. 6.2, Question 4a, c, e, f Ex. 6.5 Ex. 14 b Q 1, 2, 3 Lesson Support Prior Knowledge Words to Remember Teaching Tips/ Teaching Strategies Two equal corresponding angles lie on same side of the transversal; Complementary, one of them is an interior angle and the other one is an exterior angle. Supplementary, Vertically Two equal alternate angles lie on opposite side of the transversal and  Calculate angles at a point; opposite, Adjacent, both of them are interior angles. Perpendicular lines, Parallel  Calculate unknown angles: Complementary Interior angles lie on the same side of the transversal. lines, Transversal, Supplementary Adjacent and Vertically opposite; Corresponding, Alternate, Interior angle, Exterior angle Real World Connection Project / Bulletin Board Ideas / Subject Integration Architecture, Space Sciences, Sports, Physical exercises Online: Work on angles: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bka3.pdf Misconceptions / Facts to Remember BBC Bitesize has work on angles: www.bbc.co.uk/schools/gcsebitesize/maths/geometry/ Facts to remember Sum of adjacent angles on a straight line is 180 °. Other: Corresponding angles are equal. Alternate angles are equal. Learners can investigate angles using straws or even spaghetti. There is a description of an angles Interior angles add up to 180 °. investigation using spaghetti here: www.morethanmaths.com/teacher/2013/05/06/why-everyIf two lines are parallel then corresponding and alternate angles maths-teacher-should-keep-spaghetti-in-their-classroom/ will be equal and interior angles will be supplementary angles. If the corresponding and alternate angles are equal and interior angles are supplementary angles the lines will be parallel. Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Textbook 1 , Revision Exercise IV No.2 Q no 5 , Textbook 1 , Revision Exercise IV No.3 Q no 3 Cambridge Checkpoint Maths Workbook 1 Chapter 17,Exercise 17.1, exercise 17.3 , Quick Check: 4024 past examination papers: Nov 12 Paper 21 Q4, Nov 12 Paper 22 Q4a, Jun 13 Paper 21 Q2 bi or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Lines and Angles/Angle Properties of Triangles Durations: 1.5 weeks (12, 12.5 of 17) Objective (s) Content Syllabus - D  Find the unknown angles of a triangle using properties of Book 1 triangles; Chapter 15 Ex. 15 a, Q 2 – Q 7 Prior Knowledge  Calculate angles at a point;  Calculate unknown angles: Complementary Supplementary Adjacent and Vertically opposite

Real World Connection Fashion and textile designing

Class: 7 Term: 2 Lessons: 12 Suggested Resources Mathematics Workbook 1 Chapter 15 Q no 1-15 Cambridge Check Point Maths Book 2 Chapter 17 Exercise 17.2 Cambridge O Level Mathematics Volume 1 Chapter 6 Ex. 6.4, Questions 1 and 3

Lesson Support Words to Remember Teaching Tips/ Teaching Strategies Polygons, Interior angle, Exterior Learners could investigate angle properties by drawing lines/shapes and angle, Vertically opposite angle, measuring the angles. (I) Adjacent angle, Quadrilaterals The class could make posters showing the angle and symmetry properties of special triangles and quadrilaterals. (G) Make sure the learners know the angle properties of angles on a straight line, angles at a point, vertically opposite angles, angles formed on parallel lines then move on to solve angle problems for each of types , asking the learners to give their reasons for each calculation. (I) Misconceptions / Facts to Project / Bulletin Board Ideas / Subject Integration Remember Facts to remember Work on angles: Sum of interior angles of a triangle is www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bka3.pdf 180°. Exterior angle of a triangle is BBC Bitesize has work on angles: equal to the sum of the opposite www.bbc.co.uk/schools/gcsebitesize/maths/geometry/ interior angles.

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Cambridge Check Point Maths Workbook 2 Chapter 17 Exercise 17.2 Quick Check: 4024 past examination papers:

Nov 12 Paper 21 Q4, Nov 12 Paper 22 Q4a, Jun 13 Paper 21 Q2bi Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Class: 7 Unit/Skill/ Topic: Shapes and Polygon/Angle properties of polygons Term: 2 Durations: 1 week (12.5, 13.5 of 17) Lessons: 8 Objective (s) Content Suggested Resources Syllabus D Mathematics Workbook 1 Chapter 15 Q no 41-55  Find number of sides of a polygon when sum of interior or exterior angles is given and vice versa. Cambridge O Level Mathematics Volume 1 Chapter 6 Ex. 6.9 Book 1 Chapter 15 Ex. 15 c Lesson Support Prior Knowledge Words to Remember Teaching Tips/ Teaching Strategies 

Know names and properties of common 2D shapes and polygons;

Polygons, Interior angle, Exterior angle, Vertically opposite angle, Adjacent angle, regular and irregular polygons, pentagons, hexagons octagons, decagons.

Real World Connection Fashion and textile designing, Architecture

Islamic designs are a rich source of examples of use of polygons as are tiled floors in some public buildings. Use a picture of a tiled design including triangles, quadrilaterals and other polygons to ask learners what shapes they can identify. Move on to introducing the names of different polygons and identifying line and rotational symmetries (met in Unit 2) of regular and some irregular polygons. (W) One approach to considering interior angles is to divide the polygon into triangles. Having deduced key ideas about exterior and interior angles, learners should apply these to finding missing angles in both regular and irregular polygons. (I)

Misconceptions / Facts to Remember Facts to remember Sum of angles of a triangle is 180°. Exterior angle of a triangle is equal to the sum of the opposite interior angles.

Project / Bulletin Board Ideas / Subject Integration Work on polygons in section 3.5: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bka3.pdf A PowerPoint presentation containing some images of Islamic designs: www.dropbox.com/s/fhcxdie5f9stmvt/islamic-patterns.pptx BBC Bitesize has work on polygons, including angle properties: www.bbc.co.uk/schools/gcsebitesize/maths/geometry/

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 12 Q16,Jun 12 Paper 21 Q7a,Nov 12 Paper 11 Q19,Nov 12 Paper 12 Q24,Jun 13 Paper 21 Q2a,Nov 13 Paper 11 Q18 Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Lines and Angles/Geometrical Construction Durations: 1 week (13.5, 14.5 of 17) Objective (s) Content Syllabus - D  Construct a perpendicular bisectors and angle bisectors using protractors Book 1 or set squares as necessary. Chapter 16 page 383-387

Class: 7 Term: 2 Lessons: 8 Suggested Resources Cambridge Checkpoint Maths Book 2 Chapter 10 Exercise 10.3 and 10.4

Lesson Support Prior Knowledge Words to Remember Teaching Tips/ Teaching Strategies Draw, Construct ,Bisector, Angle Give learners practice in constructing triangles from different data, given bisector, Perpendicular bisector three sides, a side and two angles, or two sides and an angle. Include  draw circles with different radii also construction of some other geometrical figures, such as some quadrilaterals. (G/I) Misconceptions / Facts to Remember Project / Bulletin Board Ideas / Subject Integration Facts to remember Links for teachers about constructions, giving background and ideas: An angle bisector divides the angle in two equal parts. www.mathforum.org/library/topics/constructions A line (perpendicular) bisector divides the line in two equal parts (at an angle of 900) Suggested Method of Assessment Assessment for Learning: Skill Check: Cambridge Checkpoint Maths Workbook 2 Chapter 10 Exercise 10.3 and 10.4 Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Quick Check: 4024 past examination papers:

Jun 12 Paper 21 Q8a, Jun 12 Paper 22 Q4, Nov 12 Paper 11 Q10 and Q26b, Nov 12 Paper 12 Q8a and Q27b,Jun 13 Paper 12 Q12a ,Jun 13 Paper 21 Q4a, Nov 13 Paper 11 Q10a and Q10b, Nov 13 Paper 21 Q2a Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Symmetry Durations: 1 week (14.5, 15.5 of 17) Objective (s)  Identify the order of rotational symmetry in plane figures.

Prior Knowledge  Identify and draw line/s of symmetry in two dimensions;

Class: 7 Term: 2 Lessons: 8 Suggested Resources Cambridge checkpoint Maths 2 Chapter 3 Exercise3.3 Cambridge O Level Mathematics Volume 1 Chapter 6 Ex. 6.6

Content Syllabus - D Book 1 Addendum Ex. 1 a, Ex. 1 b

Lesson Support Words to Remember Teaching Tips/ Teaching Strategies Show learners pictures of shapes and logos which have line or rotational symmetry Symmetrical, Line of symmetry, and ask them to identify how many lines of symmetry the shape has and what its Mirror image, Rotational symmetry, Order of order of rotational symmetry is. Move on to the symmetry properties of isosceles and symmetry equilateral triangles and special quadrilaterals. (W)

Real World Connection Symmetry in nature and Architecture

Misconceptions / Facts to Remember Facts to remember Line of symmetry divides the shape into two equal parts such that each one of them is the mirror image of the other. When a figure can be rotated to fit the outline of its original position, we say that the figure possess a rotational symmetry. The order of symmetry is the number of times the figure has been rotated to fit the original figure. Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Project / Bulletin Board Ideas / Subject Integration BBC Bitesize has work on properties of shapes and interactive symmetry activities: www.bbc.co.uk/schools/gcsebitesize/maths/geometry/ The Victoria and Albert Museum has created some teachers’ resources linked to the mathematical properties of Islamic designs: www.vam.ac.uk/content/articles/t/teachers-resource-maths-andislamic-art-and-design/

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q1, Jun 12 Paper 12 Q3, Nov 12 Paper 21 Q5c, Jun 13 Paper 11 Q11, Nov 13 Paper 11 Q15 Nov 13 Paper 12 Q5 Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Position and Movement/Functions and Graphs Durations: 1 week (15.5, 16.5 of 17) Objective (s) Content Syllabus - D  Plot graphs of linear equations.  Find value of ’x’ and ’y’ from the graph. Book 1  Find the gradient of the linear function. Chapter 12 Ex. 12 b, Prior Knowledge Write down coordinates of the given point. Plot points on a graph.

Words to Remember Coordinates, Cartesian coordinates, Axis, Horizontal axis, x – axis, Vertical axis, y– axis, Origin, Ordered pair, Gradient, Intercept, x – intercept, y – intercept, Slope Linear equation, Simultaneous, Solution

Class: 7 Term: 2 Lessons: 8 Suggested Resources Cambridge Checkpoint Maths 1 Chapter 9 Ex.9.3 Cambridge O Level Mathematics Volume 1 Chapter 7 Ex. 7.2

Lesson Support Teaching Tips/ Teaching Strategies Begin with graph of the equations of the form: x = a, y = c, y = mx and y = mx + c The measure of the steepness is called the gradient. The gradient of a straight line is the measure of the ratio of the vertical change to the horizontal change. Basic task: Show the learners how to construct tables of values and use them to draw a straight line graph. (W) Activity: Ask groups of learners to draw families of graphs and compare the results, e.g. one group to draw y = x, , y = 2x, y = 3x etc., one to draw y = x, y = x + 1, y = x − 2, one to draw y = 2x, y = −0.5x , y = −4x, y = 0.25x etc. as a lead in to work on the equation of a straight line, gradient, intercept, and parallel (and perpendicular) lines. If possible, use computers for this activity, using graph-drawing programs such as GeoGebra, Autograph or Omnigraph. (G/I)

Misconceptions / Facts to Remember

Project / Bulletin Board Ideas / Subject Integration Software for graphing and constructions may be downloaded from: www.geogebra.org/ Work on straight line graphs: www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8_14.pdf

Facts to Remember Lines parallel to y – axis are of the form x = a. Lines parallel to x – axis are of the form y =c. Lines of the form y = mx always pass through the origin and has the gradient ‘m . Line of the form y = mx + c, cuts the y-axis at the point (0, c) and has the gradient ‘m’. Misconceptions There is no difference in writing the ordered pair as (x , y) or (y , x).

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Jun 12 Paper 11 Q20, Jun 12 Paper 12 Q14,Jun 12 Paper 21 Q6a,Jun 12 Paper 22 Q1c and Q1d, Nov 12 Paper 12 Q20a,Jun 13 Paper 11 Q23a,Jun 13 Paper 12 Q4,Jun 13 Paper 22 Q8a,Nov 13 Paper 12 Q11 Or questions from the suggested resources. Written Work: please refer to “Content Section”.

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Mathematics Curriculum 2017-18 Subject: Mathematics Unit/Skill/ Topic: Data Handling Durations: 1.5 weeks (16.5, 17 of 17) Objective (s)

Content Syllabus - D Book 1 Chapter 13, examples and exercises and online worksheets and activities Syllabus - D Book 1 Chapter 13 Ex. 13 b Q 1 – Q 8 Ex. 13 c Syllabus - D Book 2 Chapter 11 Ex. 11 b Q 1, Q 2 a, Q 2 d, Q 3, Q 4, Q 5 c, Q 6,

 Collect, classify, tabulate and interpret ungrouped data  Construct a frequency table of a grouped data

Construct and interpret pie charts and line graphs

Calculate median and mode of the given (ungrouped) data; Lesson Support Prior Knowledge 

Construct and interpret bar graph  Calculate percentages  Find averages Ref. Book 1, Chapter 13, Ex 13 a and 13c and Book 2, Chapter 11

Words to Remember Data, Mean, Average, Mode, most occurring value, Set of data, Bar graph, Pie chart, Represent, Table, Interpret, Most popular, Most common, Least popular, Least common, Maximum, Minimum, Mean, Average

Class: 7 Term: 2 Lessons: 12 Suggested Resources Cambridge Checkpoint Maths 2 Chapter 5 Ex. 5.1, 5.2, 5.3A Cambridge O Level Mathematics Volume 1 Chapter 11 Ex. 11.1, Questions 1, 2, 3a, 4a, 5

Cambridge Checkpoint Maths 2 Chapter 5 Ex. 5.3C, 5.3E Cambridge O Level Mathematics Volume 1 Chapter 11 Ex. 11.3

Cambridge Checkpoint Maths 2 Chapter 12 Ex. 12.1 Cambridge O Level Mathematics Volume 1 Chapter 11 Ex. 11.4

Teaching Tips/ Teaching Strategies 

Mode is the most occurring value. Median is the middle value (of the data arranged in ascending/descending order)  Concepts of sum of angles in a circle is 360°, to be used to find angles of individual sector in a pie chart Basic task: Look at a chart of each type which has been drawn already. For each one, ask questions about the information which has been shown. Draw attention to the title, labels on axes / bars / sectors and to the key for a pictogram. Ask ‘Which is the mode?’ for each diagram. Ask ‘How many...?’ for each diagram, ensuring that learners then realise that a pie chart does not show this, just relative proportions. (W) Give the learners a list of data with repeats, say 30 items, and ask them to calculate the mean. Whilst they do this, put the data into a frequency distribution on the board and add an extra column. Alternatively, ask each learner to write a piece of data, for example their age or shoe size on a piece of paper. The learners hold up their sheet of paper so that everyone can see it. Ask them to find the mean, you may need to suggest that they organise themselves into groups in order to do this more efficiently. Then show them how to get their result using the frequency distribution. Then for the next example, just give the data in the form of a frequency distribution and ask them to calculate the mean. (W)

Misconceptions / Facts to Remember Sum of angles in a circle is 360° Mean is equal to the sum of the product of x and f divided by sum of f;

Project / Bulletin Board Ideas / Subject Integration Project: Students will collect data on the number of hours students spend on face book by 5 students in the class. They will then present the data in the form of percentages on pie charts.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 𝑋̅ =

∑ 𝑓𝑥 ∑𝑓

where f= frequency and x is the measure of e.g age/ marks etc. depending upon the type of data. The median for an odd number of data is the middle value; while that of an even number of data it is equal to the sum of the two middle values divided by 2. Mode is the most frequent value in the given data

Bulletin Board Ideas: Along with the vocabulary words, Tally charts can be put on bulletin board after each Math lesson about its understanding

Online: BBC Bitesize has work on charts, diagrams and statistical calculations: www.bbc.co.uk/schools/gcsebitesize/maths/statistics/ Work on tables and charts at: www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkb8.pdf Two worksheets on interpreting athletics data are available at: www.cimt.plymouth.ac.uk/resources/res1/dint1.htm and www.cimt.plymouth.ac.uk/resources/res1/dint2.htm , with links to the data relevant files. If you do not have printed charts that you can show, you could draw them yourself on Excel or using GeoGebra, perhaps using an extract of data from www.censusatschool.ntu.ac.uk/ Global and regional statistics, e.g. the populations for different districts in a country are available at: www.geohive.com/

Suggested Method of Assessment Assessment for Learning: Topic Quiz daily/ weekly. One question per day based on prior knowledge or on the current topic to be written on board and students trained to solve it within a limited time (using mini whiteboards)/ self and peer assessment. Lesson Starters / Plenary: Increase the level of difficulty gradually and reduce work time by encouraging students to use simple Mental Math strategies. Keep a record of the progress of each student.

Skill Check: Quick Check: 4024 past examination papers:

Nov 12 Paper 11 Q11 Nov 12 Paper 12 Q9 Jun 13 Paper 12 Q19 Jun 13 Paper 21 Q4b and Q12 b Jun 13 Paper 22 Q10b Nov 13 Paper 22 Q2a, Q2bi and Q2bii Or questions from the suggested resources. Written Work: please refer to “Content Section”.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18

The Project

Subject: Mathematics

Grade

Term I

UNIT PLAN Topic: Number Sequence Project

7

Week

6

Meaningful Learning Environment

Active

Unit Summary Number Sequence Project Creativity and Critical Thinking (School Achievement Day ) Students will organise School Achievement day where they will invite teachers, school management and other students. In groups they will plan out the finances/arrangements of 3 major components of this plan. Trophy: its size will vary with the increase and decrease of triangles Seating Plan: in terms of shape of a table and number of chairs for the number of guests. Décor: Carpet: you need to buy a red carpet for the ceremony. Calculate carpet cost, delivery charges and the size of a carpet in meters. (any other number sequence factor can be added by the teacher) Students will present their findings in the form of a proposal (MS Word). Curriculum Objectives 21st Century Skills This project will enable students to:  ICT Literacy recognize simple patterns from various number sequences; ☐ Cognitive Skills continue a given number sequence and find its general term ☐ Interpersonal Skills  Self and Task Management ☐ Research and Information Fluency  Creativity and Innovation ☐ Personal Characteristics Unit Plan (Suggested Timeline) Unit Plan Output Pre-Unit Tasks 4 lessons - Topic research from the internet. - MS Word 2 lessons : Critical thinking and - Online social media platform to share and collaborate - Photocopy of Collaboration with TCS network. project cards for 2 lessons : Proposal (Lab work) - Presentation every group. Resources Required Pre-Requisites Internet to do research Project cards for the students Project proposal templates for students.

Project Guidelines -

Teacher will divide the class in either 3 or 6 groups. Project plan and individual group project cards with be shared with the students. Students will plan the décor, seating arrangement and trophy design according to their group project card.

Students will prepare two most suitable, economical and effective proposals on MS Word. (Lab Work). Students will present their findings in the form of a proposal (MS. Word). Unit Extension Students will share their experience, findings, plan and analysis with the class in the form of a presentation through SKYPE or broadcasting with other schools of TCS.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18 Carpet Décor

Seating Arrangements

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

31

Mathematics Curriculum 2017-18 Trophy

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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Mathematics Curriculum 2017-18

Subject: Mathematics Class

7

UNIT PLAN Topic: Number Sequence Project Week

3 , 4

Term II

Meaningful Learning Environment

Active

Unit Summary Students will work in pairs to record a variety of measurements of various parts of their bodies. Students will be given an activity sheet (see “Investigate the Golden Ratio”) that will direct them what measurements students should take. This activity will give students the opportunity to engage in both whole-group discussion and small-group collaboration. Students will use proportional reasoning to make sense of the varying amount of impact caused by small errors in measurement. Curriculum Objectives 21st Century Skills  ICT Literacy  Use ratio to compare similar quantities; ☐ Interpersonal Skills  Express ratios in its simplest form;  Express one quantity as a ratio of another in the form a : b;  Self and Task Management  Find the ratio of two or more quantities; ☐ Research and Information Fluency  Solve word problems involving rates.  Creativity and Innovation Unit Plan (Suggested Timeline) Unit Plan Output Pre-Unit Tasks - Data presentation report 5 lessons - Teacher must have read “Are we Golden” - Report sharing through PBWorks 2 lessons : data collection (Class Work) document 1 lesson : data presentation (Lab Work) - Photocopy of Activity Sheet for each pair 2 lessons : project collaboration (Lab Work) of students. Resources Required Pre-Requisites Document: “Are we Golden?” - Students must be well versed with ratios. Activity Sheet “Investigate the Golden Ratio” - Students should be familiar with PBWorks software solution. http://vimeo.com/3206907 (Golden Ratio and Miracle of Islam)

Project Guidelines -

Project idea will be shared with students (in pairs) by their Mathematics teachers. (Reference: “Are We Golden?”.) Teacher will follow the guidelines given in the reference document. If possible, teachers should share salient features of “Golden Ratio” with the students. Students in pairs will take their measurements as per the activity sheet. Students will try to avoid curve measurement error by replacing it with linear measurement (Reference: “Are We Golden?”). Students will share their experience, findings, plan and analysis with the class in form of a presentation through PBWorks. Moreover, students will share their experience by commenting on each other’s presentations. Bulletin Board: Skeleton as given in the activity sheet along with students’ findings and Golden ratio information.

“Am I Golden?” Project Output: Report based on the activity sheet. Display of reports in the class next to the interactive bulletin board.

Unit Extension Research work can be given to the students to explore more about this Golden Ratio concept. Video http://vimeo.com/3206907 refers to the golden ratio and the golden mean can be shared with the students.

This document is the intellectual property of The City School and any unauthorised use is prohibited. Any amendments in this document shall be controlled by the Studies Department only.

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