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Teachers Resource Manual

Contents

Specific Instructional / Teaching Objectives .................................................................................................................... iv

Preface ................................................................................................................................................................................. xxii

Chapter 1: Congruence and Similarity ............................................................................................................................1

Chapter 2: Direct and Inverse Proportion ................................................................................................................... 19

Chapter 3: Expansion and Factorisation of Algebraic Expressions .......................................................................... 28

Chapter 4: Algebraic Manipulation and Formulae ..................................................................................................... 39

Chapter 5: Simultaneous Linear Equations .................................................................................................................. 51

Chapter 6: Pythagoras Theorem ................................................................................................................................... 59

Chapter 7: Volume and Surface Area ........................................................................................................................... 67

Chapter 8: Graphs of Linear Equations in Two Unknowns ...................................................................................... 79

Chapter 9: Graphs of Quadratic Functions .................................................................................................................. 86

Chapter 10: Set Language and Notation ......................................................................................................................... 98

Chapter 11: Statistics ....................................................................................................................................................... 109

Chapter 12: Probability ................................................................................................................................................... 124

iii

iv

Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths

InvestigationProblem Solving NE IT Resources

Term 1

Weeks1, 2, and 3

Chapter 1

Congruence and Similarity

Identify congruent figures and objects; use the correct notations to express congruency.

Find unknown values in a pair of congruent figures. Identify similar figures and objects; use the correct notations to express

similarity. State the properties of a pair of similar figures; use these properties to find the

unknowns in a pair of similar figures. Use similarity properties to make scale drawings of simple objects or places such

as a field or a school hall. Calculate the actual length and the actual area from a given scale model and vice

versa. Express the scale of a map as a representative fraction and vice versa; use it to

calculate the distance between two places. Calculate the actual dimensions of a place on a map, and vice versa. Calculate the actual area of a place such as a park, a villages, etc., on a map, and

vice versa. Solve map problems involving distance and area of a place.

1a

1a1b

1b

1c

Pg 4: What other living examples are there around you that are similar or congruent?

Pg 11, 15 Pg 3, 20, 21 Textbook

Term 1

Weeks4 and 5

Chapter 2

Direct and Inverse Proportion

Write down an equation connecting two quantities which are directly proportional to each other; use the rule to solve problems involving direct proportion.

Sketch the graph connecting two quantities which are directly proportional to each other.

Write down an equation connecting two quantities which are inversely proportional to each other; use the rule to solve problems involving inverse proportion.

Sketch the graph connecting two quantities which are inversely proportional to each other.

Solve simple problems involving direct or inverse proportions.

2a

2b, 2c

2d, 2e, 2f

Pg 37: Oral discussion about the need for rules when using the library. What new rules would be useful for a more effective use of the library?

Pg 48, 53, 61 Pg 58, 66 Textbook

Term 1

Weeks5, 6, 7, and 8

Chapter 3

Expansion and Factorisation of Algebraic Expressions

Perform expansion of algebraic expressions of the form (a b)(c d) and (a b)(c d e).

State the identities for the expansion of perfect squares (a b)2, and the expansion of (a + b)(a b).

Perform expansions of algebraic expressions using the rules above. Evaluate numerical expressions using the identities learnt earlier. Factorise algebraic expressions by picking out the common factor. Factorise expressions using the algebraic identities involving perfect squares and

difference of squares learnt earlier. Evaluate numerical expressions using factorisation. Factorise quadratic expressions. Solve quadratic equations by factorisation. Express word problems in the form of quadratic equation; solve these problems

by factorisation.

3b

3c3c3d3e

3e3f3g3h

Pg 84: Find out more about Pascal Triangle using the Internet.

Pg 74, 100, 103, 107

Textbook

v

Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths

InvestigationProblem Solving NE IT Resources

Term 1

Weeks1, 2, and 3

Chapter 1

Congruence and Similarity

Identify congruent figures and objects; use the correct notations to express congruency.

Find unknown values in a pair of congruent figures. Identify similar figures and objects; use the correct notations to express

similarity. State the properties of a pair of similar figures; use these properties to find the

unknowns in a pair of similar figures. Use similarity properties to make scale drawings of simple objects or places such

as a field or a school hall. Calculate the actual length and the actual area from a given scale model and vice

versa. Express the scale of a map as a representative fraction and vice versa; use it to

calculate the distance between two places. Calculate the actual dimensions of a place on a map, and vice versa. Calculate the actual area of a place such as a park, a villages, etc., on a map, and

vice versa. Solve map problems involving distance and area of a place.

1a

1a1b

1b

1c

Pg 4: What other living examples are there around you that are similar or congruent?

Pg 11, 15 Pg 3, 20, 21 Textbook

Term 1

Weeks4 and 5

Chapter 2

Direct and Inverse Proportion

Write down an equation connecting two quantities which are directly proportional to each other; use the rule to solve problems involving direct proportion.

Sketch the graph connecting two quantities which are directly proportional to each other.

Write down an equation connecting two quantities which are inversely proportional to each other; use the rule to solve problems involving inverse proportion.

Sketch the graph connecting two quantities which are inversely proportional to each other.

Solve simple problems involving direct or inverse proportions.

2a

2b, 2c

2d, 2e, 2f

Pg 37: Oral discussion about the need for rules when using the library. What new rules would be useful for a more effective use of the library?

Pg 48, 53, 61 Pg 58, 66 Textbook

Term 1

Weeks5, 6, 7, and 8

Chapter 3

Expansion and Factorisation of Algebraic Expressions

Perform expansion of algebraic expressions of the form (a b)(c d) and (a b)(c d e).

State the identities for the expansion of perfect squares (a b)2, and the expansion of (a + b)(a b).

Perform expansions of algebraic expressions using the rules above. Evaluate numerical expressions using the identities learnt earlier. Factorise algebraic expressions by picking out the common factor. Factorise expressions using the algebraic identities involving perfect squares and

difference of squares learnt earlier. Evaluate numerical expressions using factorisation. Factorise quadratic expressions. Solve quadratic equations by factorisation. Express word problems in the form of quadratic equation; solve these problems

by factorisation.

3b

3c3c3d3e

3e3f3g3h

Pg 84: Find out more about Pascal Triangle using the Internet.

Pg 74, 100, 103, 107

Textbook

vi

Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths

InvestigationProblem Solving NE IT Resources

Term 1

Weeks9 and 10

&

Term 2

Weeks1 and 2

Chapter 4

Algebraic Manipulation and Formulae

State the two important rules in the manipulation of fractions: , .

andba

b ca c

ba

b ca b''= =

Simplify simple algebraic fractions involving single terms using the rules shown above.

Simplify algebraic fractions with polynomials, using factorisation and using the rules learnt above.

Perform multiplication and division of simple algebraic fractions. Find the HCF and LCM of algebraic expressions. Perform addition and subtraction of simple algebraic expressions. Solve simple equations involving algebraic fractions. Express problems that involve algebraic fractions in the form of equations, and