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<ul><li><p>1</p><p>Teachers Resource Manual</p></li><li><p>Contents</p><p>Specific Instructional / Teaching Objectives .................................................................................................................... iv</p><p>Preface ................................................................................................................................................................................. xxii</p><p>Chapter 1: Congruence and Similarity ............................................................................................................................1</p><p>Chapter 2: Direct and Inverse Proportion ................................................................................................................... 19</p><p>Chapter 3: Expansion and Factorisation of Algebraic Expressions .......................................................................... 28</p><p>Chapter 4: Algebraic Manipulation and Formulae ..................................................................................................... 39</p><p>Chapter 5: Simultaneous Linear Equations .................................................................................................................. 51</p><p>Chapter 6: Pythagoras Theorem ................................................................................................................................... 59</p><p>Chapter 7: Volume and Surface Area ........................................................................................................................... 67</p><p>Chapter 8: Graphs of Linear Equations in Two Unknowns ...................................................................................... 79</p><p>Chapter 9: Graphs of Quadratic Functions .................................................................................................................. 86</p><p>Chapter 10: Set Language and Notation ......................................................................................................................... 98</p><p>Chapter 11: Statistics ....................................................................................................................................................... 109</p><p>Chapter 12: Probability ................................................................................................................................................... 124</p><p>iii</p></li><li><p>iv</p><p>Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths </p><p>InvestigationProblem Solving NE IT Resources</p><p>Term 1</p><p>Weeks1, 2, and 3</p><p>Chapter 1</p><p>Congruence and Similarity</p><p> Identify congruent figures and objects; use the correct notations to express congruency.</p><p> Find unknown values in a pair of congruent figures. Identify similar figures and objects; use the correct notations to express </p><p>similarity. State the properties of a pair of similar figures; use these properties to find the </p><p>unknowns in a pair of similar figures. Use similarity properties to make scale drawings of simple objects or places such </p><p>as a field or a school hall. Calculate the actual length and the actual area from a given scale model and vice </p><p>versa. Express the scale of a map as a representative fraction and vice versa; use it to </p><p>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 </p><p>vice versa. Solve map problems involving distance and area of a place.</p><p>1a</p><p>1a1b</p><p>1b</p><p>1c</p><p>Pg 4: What other living examples are there around you that are similar or congruent?</p><p>Pg 11, 15 Pg 3, 20, 21 Textbook</p><p>Term 1</p><p>Weeks4 and 5</p><p>Chapter 2</p><p>Direct and Inverse Proportion</p><p> Write down an equation connecting two quantities which are directly proportional to each other; use the rule to solve problems involving direct proportion.</p><p> Sketch the graph connecting two quantities which are directly proportional to each other.</p><p> Write down an equation connecting two quantities which are inversely proportional to each other; use the rule to solve problems involving inverse proportion.</p><p> Sketch the graph connecting two quantities which are inversely proportional to each other.</p><p> Solve simple problems involving direct or inverse proportions.</p><p>2a</p><p>2b, 2c</p><p>2d, 2e, 2f</p><p>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?</p><p>Pg 48, 53, 61 Pg 58, 66 Textbook</p><p>Term 1</p><p>Weeks5, 6, 7, and 8</p><p>Chapter 3</p><p>Expansion and Factorisation of Algebraic Expressions</p><p> Perform expansion of algebraic expressions of the form (a b)(c d) and (a b)(c d e).</p><p> State the identities for the expansion of perfect squares (a b)2, and the expansion of (a + b)(a b).</p><p> 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 </p><p>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 </p><p>by factorisation.</p><p>3b</p><p>3c3c3d3e</p><p>3e3f3g3h</p><p>Pg 84: Find out more about Pascal Triangle using the Internet.</p><p>Pg 74, 100, 103, 107</p><p>Textbook</p></li><li><p>v</p><p>Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths </p><p>InvestigationProblem Solving NE IT Resources</p><p>Term 1</p><p>Weeks1, 2, and 3</p><p>Chapter 1</p><p>Congruence and Similarity</p><p> Identify congruent figures and objects; use the correct notations to express congruency.</p><p> Find unknown values in a pair of congruent figures. Identify similar figures and objects; use the correct notations to express </p><p>similarity. State the properties of a pair of similar figures; use these properties to find the </p><p>unknowns in a pair of similar figures. Use similarity properties to make scale drawings of simple objects or places such </p><p>as a field or a school hall. Calculate the actual length and the actual area from a given scale model and vice </p><p>versa. Express the scale of a map as a representative fraction and vice versa; use it to </p><p>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 </p><p>vice versa. Solve map problems involving distance and area of a place.</p><p>1a</p><p>1a1b</p><p>1b</p><p>1c</p><p>Pg 4: What other living examples are there around you that are similar or congruent?</p><p>Pg 11, 15 Pg 3, 20, 21 Textbook</p><p>Term 1</p><p>Weeks4 and 5</p><p>Chapter 2</p><p>Direct and Inverse Proportion</p><p> Write down an equation connecting two quantities which are directly proportional to each other; use the rule to solve problems involving direct proportion.</p><p> Sketch the graph connecting two quantities which are directly proportional to each other.</p><p> Write down an equation connecting two quantities which are inversely proportional to each other; use the rule to solve problems involving inverse proportion.</p><p> Sketch the graph connecting two quantities which are inversely proportional to each other.</p><p> Solve simple problems involving direct or inverse proportions.</p><p>2a</p><p>2b, 2c</p><p>2d, 2e, 2f</p><p>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?</p><p>Pg 48, 53, 61 Pg 58, 66 Textbook</p><p>Term 1</p><p>Weeks5, 6, 7, and 8</p><p>Chapter 3</p><p>Expansion and Factorisation of Algebraic Expressions</p><p> Perform expansion of algebraic expressions of the form (a b)(c d) and (a b)(c d e).</p><p> State the identities for the expansion of perfect squares (a b)2, and the expansion of (a + b)(a b).</p><p> 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 </p><p>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 </p><p>by factorisation.</p><p>3b</p><p>3c3c3d3e</p><p>3e3f3g3h</p><p>Pg 84: Find out more about Pascal Triangle using the Internet.</p><p>Pg 74, 100, 103, 107</p><p>Textbook</p></li><li><p>vi</p><p>Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths </p><p>InvestigationProblem Solving NE IT Resources</p><p>Term 1</p><p>Weeks9 and 10 </p><p>&</p><p>Term 2</p><p>Weeks1 and 2</p><p>Chapter 4</p><p>Algebraic Manipulation and Formulae</p><p> State the two important rules in the manipulation of fractions: , .</p><p> andba</p><p>b ca c</p><p>ba</p><p>b ca b''= =</p><p> Simplify simple algebraic fractions involving single terms using the rules shown above.</p><p> Simplify algebraic fractions with polynomials, using factorisation and using the rules learnt above.</p><p> 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 </p><p>solve them. Change the subject of a simple formula. Changing the subject of a formula involving squares, square roots, cubes and </p><p>cube roots etc. Finding the unknown in a formula.</p><p>4a</p><p>4b</p><p>4c, 4d</p><p>4e, 4f4g4h</p><p>4i4j</p><p>4k</p><p>Pg 125 Pg 121, 127, 128, 133, 138, 139, 143</p><p>Textbook</p><p>Term 2</p><p>Weeks3 and 4</p><p>Chapter 5</p><p>Simultaneous Linear Equations</p><p> Solve a pair of simultaneous equations by the elimination method. Solve a pair of simultaneous linear equations, adjusting the coefficients of one </p><p>similar variable of both equations so that they are equal before elimination. Solve a pair of simultaneous linear equations by using the substitution method. Solve a pair of simultaneous linear equations using either the elimination or the </p><p>substitution method. Express word problems into the form of a pair of simultaneous linear equations; </p><p>use either the elimination or substitution method to solve the problem. </p><p>5a5b</p><p>5c</p><p>5c</p><p>5d</p><p> Pg 170 Pg 164165</p><p>Pg 157, 171</p><p>Textbook</p><p>Term 2</p><p>Weeks5, 6, and 7</p><p>Chapter 6</p><p>Pythagoras Theorem</p><p> Identify a right-angled triangle and its hypotenuse. Define Pythagoras theorem and its converse. Use proper symbols to express the </p><p>relationship. Apply the Pythagoras theorem to find the unknown side of a right-angled </p><p>triangle when the two other sides are given. Solve word problems involving right-angled triangles using Pythagoras </p><p>theorem.</p><p>6a6a</p><p>6b</p><p>6b</p><p>Pg 178</p><p>Pg 181: Find out how mathematics and music are related, how computer music is made, etc.</p><p>Pg 185: Find out more about Pythagorean Triples.</p><p>Textbook</p><p>Term 3</p><p>Weeks1, 2, and 3</p><p>Chapter 7</p><p>Volume and Surface Area</p><p> State the formula for the volume of a pyramid and use it to solve related problems. Sketch a pyramid, draw its net, and use the net to find the surface area of a </p><p>pyramid. State the formulae for the volume, curved surface area, and the total surface area </p><p>of a cone; use these formulae to solve related problems. State the formulae for the volume and surface area of a sphere; use them to solve </p><p>related problems. Solve problems involving cones, prisms, pyramids, cylinders, and/or spheres.</p><p>7a7a7b</p><p>7c</p><p>Pg 199201, 211, 220221, 223</p><p>Pg 233ReviewQuestions 7,Q11, and Q12</p><p>Textbook</p></li><li><p>vii</p><p>Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths </p><p>InvestigationProblem Solving NE IT Resources</p><p>Term 1</p><p>Weeks9 and 10 </p><p>&</p><p>Term 2</p><p>Weeks1 and 2</p><p>Chapter 4</p><p>Algebraic Manipulation and Formulae</p><p> State the two important rules in the manipulation of fractions: , .</p><p> andba</p><p>b ca c</p><p>ba</p><p>b ca b''= =</p><p> Simplify simple algebraic fractions involving single terms using the rules shown above.</p><p> Simplify algebraic fractions with polynomials, using factorisation and using the rules learnt above.</p><p> 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 </p><p>solve them. Change the subject of a simple formula. Changing the subject of a formula involving squares, square roots, cubes and </p><p>cube roots etc. Finding the unknown in a formula.</p><p>4a</p><p>4b</p><p>4c, 4d</p><p>4e, 4f4g4h</p><p>4i4j</p><p>4k</p><p>Pg 125 Pg 121, 127, 128, 133, 138, 139, 143</p><p>Textbook</p><p>Term 2</p><p>Weeks3 and 4</p><p>Chapter 5</p><p>Simultaneous Linear Equations</p><p> Solve a pair of simultaneous equations by the elimination method. Solve a pair of simultaneous linear equations, adjusting the coefficients of one </p><p>similar variable of both equations so that they are equal before elimination. Solve a pair of simultaneous linear equations by using the substitution method. Solve a pair of simultaneous linear equations using either the elimination or the </p><p>substitution method. Express word problems into the form of a pair of simultaneous linear equations; </p><p>use either the elimination or substitution method to solve the problem. </p><p>5a5b</p><p>5c</p><p>5c</p><p>5d</p><p> Pg 170 Pg 164165</p><p>Pg 157, 171</p><p>Textbook</p><p>Term 2</p><p>Weeks5, 6, and 7</p><p>Chapter 6</p><p>Pythagoras Theorem</p><p> Identify a right-angled triangle and its hypotenuse. Define Pythagoras theorem and its converse. Use proper symbols to express the </p><p>relationship. Apply the Pythagoras theorem to find the unknown side of a right-angled </p><p>triangle when the two other sides are given. Solve word problems involving right-angled triangles using Pythagoras </p><p>theorem.</p><p>6a6a</p><p>6b</p><p>6b</p><p>Pg 178</p><p>Pg 181: Find out how mathematics and music are related, how computer music is made, etc.</p><p>Pg 185: Find out more about Pythagorean Triples.</p><p>Textbook</p><p>Term 3</p><p>Weeks1, 2, and 3</p><p>Chapter 7</p><p>Volume and Surface Area</p><p> State the formula for the volume of a pyramid and use it to solve related problems. Sketch a pyramid, draw its net, and use the net to find the surface area of a </p><p>pyramid. State the formulae for the volume, curved surface area, and the total surface area </p><p>of a cone; use these formulae to solve related problems. State the formulae for the volume and surface area of a sphere; use them to solve </p><p>related problems. Solve problems involving cones, prisms, pyramids, cylinders, and/or spheres.</p><p>7a7a7b</p><p>7c</p><p>Pg 199201, 211, 220221, 223</p><p>Pg 233ReviewQuestions 7,Q11, and Q12</p><p>Textbook</p></li><li><p>viii</p><p>Week Topic Specific Instructional Objectives Exercises Maths CommunicationMaths </p><p>InvestigationProblem Solving NE IT Resources</p><p>Term 3</p><p>Weeks4, 5, and 6</p><p>Chapter 8</p><p>Graphs of Linear Equations in Two Unknowns</p><p> Select appropriate scales for drawing graphs. Construct a table of values for x and y for a given linear equation. Plot the points given/found on a Cartesian plane. Identify y = c as the equation of a straight line graph drawn passing through a point </p><p>(h, c) where h is any constant, and parallel to the x-axis. Identify x = a as the equation of a straight line graph drawn passing through a </p><p>point (a, k) where k is any constant and parallel to the y-axis. Identify y = mx as the equation of a straight line graph passing through the origin </p><p>(...</p></li></ul>