Teacher's Resource Book 2.pdf

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  • 1

    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