Chapter 1
Chapter 1 Financial decisions Suggested time: 3.5 weeks
Strand: Number
Topic: Number concepts
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, |Technology applications |Learning outcomes |
| |activities, History of mathematics, Maths|Interactive games, |(CD-ROM) | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 18) | |SkillSHEETs (page 18) | |M 4.2 |
| | |1.1: Converting units of time | |Students calculate with time. |
| | |1.2: Finding a percentage of a quantity | |N 4.1 |
| | |(money) | |Students compare and order numbers and |
| | |1.3: Converting a percentage to a decimal| |fractions and make connections between |
| | |fraction | |key percentages and fractions. |
| | |1.5: Rounding money to the nearest 5 | |N5.3 |
| | |cents | |Students solve multiplication problems |
| | |1.6: Increasing a quantity by a | |involving percentages. |
| | |percentage | | |
|Wages and salaries (page 19) | |SkillSHEET 1.1: Converting units of time | |N 6.1 Ex 1A Q1–10 |
|WE 1a–c, 2 | |(page 20) | |Students analyse options and make |
|Ex 1A Wages and salaries (page 20) | | | |informed financial decisions. |
|Working overtime (page 21) |Maths Quest challenge: |SkillSHEET 1.2: Finding a percentage of a| |N 6.1 Ex 1B Q1–11 |
|WE 3 |Q1–2 (page 23) |quantity (money) (page 22) | |Students analyse options and make |
|Ex 1B Working overtime (page 21) |Career profile: Jo Mooney (page 23) | | |informed financial decisions. |
|Piecework (page 24) | |WorkSHEET 1.1 (page 26) | |N 6.1 Ex 1C Q1–12 |
|WE 4, 5, 6 | | | |Students analyse options and make |
|Ex 1C Piecework (page 25) | | | |informed financial decisions. |
|Commission and royalties (page 27) |Investigation: Earning money (page 29) |SkillSHEET 1.3: Converting a percentage |Excel: Converting percentages to |N 6.1 Ex 1D Q1–14 |
|WE 7, 8a–b, 9 |Code puzzle (page 30) |to a decimal fraction (page 28) |fractions or decimals (page 28) |Students analyse options and make |
|Ex 1D Commission and royalties (page 28) |Investigation: Investigating government |SkillSHEET 1.4: Finding a percentage of a|Excel: Finding the percentage of an |informed financial decisions. |
| |payments (page 31) |quantity (money) (page 28) |amount (page 28) | |
| | |Game time 001 (page 29) |Mathcad: Commission and royalties | |
| | | |(page 29) | |
|Gross and net pay (page 32) |Enrichment activity: Percentages in tests|WorkSHEET 1.2 (page 34) | |N 6.1 Ex 1E Q1–12 |
|WE 10, 11, 12 |(page 34) | | |Students analyse options and make |
|Ex 1E Gross and net pay (page 33) |Investigation: Working piece rate | | |informed financial decisions. |
| |(page 35) | | | |
| |10 Quick Questions 1 (page 36) | | | |
|Budgeting (page 37) | | | |N 6.1 Ex 1F Q1–12 |
|WE 13, 14, 15a–c, 16a–d | | | |Students analyse options and make |
|Ex 1F Budgeting (page 40) | | | |informed personal budgeting decisions. |
|Calculating GST and VAT (page 47) |Enrichment activity: Understanding |SkillSHEET 1.5: Rounding money to the | |N 5.1 Ex 1G Q1–11 |
|WE 17, 18, 19, 20 |percentages (page 51) |nearest 5 cents (page 49) | |Students analyse options and make |
|Ex 1G Calculating GST and VAT (page 49) |Investigation: Examining bank fees and |SkillSHEET 1.6: Increasing a quantity by | |informed financial decisions (regarding |
| |taxes (page 52) |a percentage (page 50) | |fees and charges). |
| |10 Quick Questions 2 (page 53) | | | |
|Compound interest (page 54) |Investigation: Compound interest |Game time 002 (page 58) |Excel: Interest (page 58) |N 6.1 Ex 1H Q1–16 |
|WE 21, 22, 23 |spreadsheets (page 58) |WorkSHEET 1.3 (page 58) | |Students analyse options and make |
|Ex 1H Compound interest (page 56) | | | |informed financial decisions (regarding |
| | | | |compound growth). |
|Summary (page 59) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 60) | |(page 62) | | |
| | |Topic tests (2) | | |
Chapter 2 Surds and indices Suggested time: 4.5 weeks
Strand: Number
Topics: Number concepts, Addition and subtraction, Multiplication and division
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests | | |
| |puzzles |(CD-ROM) | | |
|Are you ready? (page 64) | |SkillSHEETs (page 64) | |N 4.1 |
| | |2.1: Finding square roots, cube roots and| |Students compare and order whole numbers |
| | |other roots | |and common fractions. |
| | |2.2: Rounding to a given number of | |N 4.2 |
| | |decimal places | |Students identify and solve addition and |
| | |2.4: Expanding brackets | |subtraction problems involving common |
| | |2.5: Expanding a pair of brackets | |fractions. |
| | |2.6: Simplifying common fractions | |N 4.3 |
| | |2.9: Using a calculator to evaluate | |Students identify and solve |
| | |numbers in index form | |multiplication and division problems |
| | |2.10: Addition of common fractions | |involving common fractions. |
| | |2.11: Subtraction of common fractions | |N 5.1 |
| | |2.12: Multiplication of common fractions | |Students compare and order integers. |
| | | | |PA 6.2 |
| | | | |Students interpret and solve problems |
| | | | |using algebraic methods. (expanding and |
| | | | |simplifying expressions |
| | | | | |
|Irrational numbers (page 65) |GC tip – Casio: Calculating roots of |SkillSHEET 2.1: Finding square roots, |Mathcad: Irrational numbers (page 68) |N DB 6.1 Ex 2A Q1–11 |
|WE 1a–d, 2 |numbers (page 65) |cube roots and other roots (page 68) |Excel: Square roots DIY (page 69) |Students interpret and use the various |
|Ex 2A Irrational numbers (page 68) |GC tip – TI: Calculating roots of numbers|SkillSHEET 2.2: Rounding to a given | |sets of real numbers. |
| |(page 65) |number of decimal places (page 69) | | |
| |History of mathematics: Richard Dedekind | | | |
| |(page 67) | | | |
| |Investigation: Plotting irrational | | | |
| |numbers on the number line (page 70) | | | |
|Simplifying surds (page 71) |Maths Quest challenge Q1–2 (page 75) |SkillSHEET 2.3: Simplifying surds |Mathcad: Simplifying surds (page 74) |N DB 6.1 Ex 2B Q1–7 |
|WE 3a–b, 4, 5, 6a–c |Career profile: Peter Richardson |(page 74) |Excel: Simplifying surds (page 74) |Students interpret and use the various |
|Ex 2B Simplifying surds (page 74) |(page 75) | |GC program – Casio: Surds (page 74) |sets of real numbers. |
| |Investigation: Braking distances | |GC program – TI: Surds (page 74) | |
| |(page 76) | | | |
| |Code puzzle (page 77) | | | |
|Addition and subtraction of surds (page |Code puzzle (page 80) | |Mathcad: Addition and subtraction of |N DB 6.2 Ex 2C Q1–5 |
|78) | | |surds (page 78) |Students identify and solve addition and |
|WE 7a–b, 8 | | | |subtraction problems involving real |
|Ex 2C Addition and subtraction of surds | | | |numbers. |
|(page 78) | | | | |
|Multiplication and division of surds | |SkillSHEET 2.4: Expanding brackets |Mathcad: Multiplication and division of |N DB 6.3 Ex 2D Q1–9 |
|(page 81) | |(page 85) |surds (page 84) |Students identify and solve |
|WE 9a–c, 10a–c, 11, | |SkillSHEET 2.5: Expanding a pair of | |multiplication problems involving real |
|12a–b, 13 | |brackets (page 85) | |numbers. |
|Ex 2D Multiplication and division of | |Game time 001 (page 86) | | |
|surds (page 84) | | | | |
|Writing surd fractions with a rational |10 Quick Questions 1 (page 89) |SkillSHEET 2.6: Simplifying common |Mathcad: Rationalising denominators |N DB 6.3 Ex 2E Q1–6 |
|denominator (page 86) | |fractions (page 88) |(page 88) |Students identify and solve |
|WE 14a–b, 15 | |SkillSHEET 2.7: Conjugate pairs (page 88)| |multiplication problems involving real |
|Ex 2E Writing surd fractions with a | |SkillSHEET 2.8: Applying the difference | |numbers. |
|rational denominator (page 88) | |of two squares rule to expressions with | | |
| | |surds (page 88) | | |
| | |WorkSHEET 2.1 (page 88) | | |
|Review of the index laws (page 89) | |SkillSHEET 2.9: Using a calculator to |Excel: Index laws (page 92) |N 5.1 Ex 2F Q1–7 |
|WE 16a–c, 17a–b, 18a–c | |evaluate numbers in index form (page 92) |Mathcad: Index laws (page 92) |Students use and interpret index |
|Ex 2F Review of the index laws (page 92) | | | |notation. |
|Negative indices (page 93) |Maths Quest challenge Q1–3 (page 97) |Game time 002 (page 97) |Mathcad: Negative indices (page 96) |N DB 6.1 Ex 2G Q1–5 |
|WE 19a–c, 20a–c, 21, 22 | | |Excel: Index laws (page 96) |Students interpret and use integer |
|Ex 2G Negative indices (page 96) | | | |powers. |
|Fractional indices (page 98) |10 Quick Questions 2 (page 103) |SkillSHEET 2.10: Addition of common |Mathcad: Fractional indices (page 101) |N DB 6.1 Ex 2H Q1–10 |
|WE 23a–b, 24a–b, 25a–c |Career profile: Jim Elliot (page 104) |fractions (page 102) |Excel: Index laws (page 101) |Students interpret and use fractional |
|Ex 2H Fractional indices (page 101) |Enrichment activity: Standard paper sizes|SkillSHEET 2.11: Subtraction of common | |powers. |
| |(page 105) |fractions (page 102) | | |
| | |SkillSHEET 2.12: Multiplication of common| | |
| | |fractions (page 102) | | |
| | |SkillSHEET 2.13: Writing roots as | | |
| | |fractional indices (page 103) | | |
| | |WorkSHEET 2.2 (page 103) | | |
|Further use of the index laws (page 106) | | |Mathcad: Further use of index laws |N DB 6.1 Ex 2I Q1–9 |
|WE 26a–c, 27a–b | | |(page 108) |Students interpret and use the various |
|Ex 2I Further use of the index laws | | | |sets of real numbers and integer and |
|(page 108) | | | |fractional powers. |
|Scientific notation (standard form) |Investigation: Alpha Centauri (page 114) |WorkSHEET 2.3 (page 114) |Excel: Scientific notation (DIY) |N 6.1 Ex 2J Q1–10 |
|(page 110) | | |(page 113) |Students interpret and use scientific |
|WE 28a–b, 29a–b, 30 | | |Mathcad: Scientific notation (page 113) |notation. |
|Ex 2J Scientific notation (page 113) | | | | |
|Summary (page 115) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 116) | |(page 118) | | |
| | |Topic tests (2) | | |
Chapter 3 Ratio and proportion Suggested time: 3 weeks
Strand: Number
Topic: Multiplication and division
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests | | |
| |puzzles |(CD-ROM) | | |
|Are you ready? (page 120) | |SkillSHEETs (page 120) | |N 4.1 |
| | |3.1: Equivalent fractions I | |Students compare and order decimal |
| | |3.2: Equivalent fractions II | |fractions and common fractions. |
| | |3.3: Highest common factor | |PA 5.1 |
| | |3.4: Rounding to a given number of | |Students solve problems related to linear|
| | |decimal places | |functions. |
| | |3.5: Finding the gradient given two | |PA 5.2 |
| | |points | |Students interpret and solve linear |
| | |3.6: Predicting the value of x in | |equations using algebraic methods. |
| | |equations of the type y = kx + c | | |
| | |3.7: Expressing minutes as fractions of | | |
| | |an hour | | |
| | |3.8: Predicting the value of x in | | |
| | |equations of the type y = [pic] | | |
|Direct proportion (page 121) |GC tip – Casio: Checking for direct |SkillSHEET 3.1: Equivalent fractions I |Mathcad: Direct proportion checker |N 6.3 Ex 3A Q1–7 |
|WE 1a–b |proportion (page 123) |(page 125) |(page 124) |Students identify and solve |
|Ex 3A Direct proportion (page 124) |GC tip – TI: Checking for direct |SkillSHEET 3.2: Equivalent fractions II |Mathcad: Direct proportion equation |multiplication and division problems |
| |proportion (page 123) |(page 125) |(page 125) |involving direct proportion. |
| |Maths Quest challenge Q1–3 (page 126) |SkillSHEET 3.3: Highest common factor | | |
| | |(page 125) | | |
|Direct proportion ― the constant of |Maths Quest challenge Q1–5 (page 129) | |Mathcad: Direct proportion (page 128) |N 6.3 Ex 3B Q1–12 |
|proportionality (page 126) |10 Quick Questions 1 (page 129) | | |Students identify and solve |
|WE 2, 3 | | | |multiplication and division problems |
|Ex 3B Direct proportion ― the constant of| | | |involving direct proportion. |
|proportionality (page 128) | | | | |
|Direct proportion and ratio or rate (page|Investigation: Leonardo’s observations |SkillSHEET 3.4: Rounding to a given | |N 6.3 Ex 3C Q1–9 |
|130) |(page 134) |number of decimal places (page 133) | |Students identify and solve |
|WE 4a–b, 5, 6a–b |Enrichment activity: What’s our money |Game time 001 (page 134) | |multiplication and division problems |
|Ex 3C Direct proportion and ratio or rate|worth overseas? (page 135) |WorkSHEET 3.1 (page 134) | |involving rates, ratio and direct |
|(page 133) | | | |proportion. |
|Partial proportion (page 136) |Investigation: Many hands make light |SkillSHEET 3.5: Finding the gradient |Excel: Partial proportion (page 138) |N 6.3 Ex 3D Q1–9 |
|WE 7, 8a-c |work! (page 139) |given two points (page 138) | |Students identify and solve |
|Ex 3D Partial proportion (page 138) | |SkillSHEET 3.6: Predicting the value of x| |multiplication and division problems |
| | |in equations of the type y = kx + c | |involving direct proportion. |
| | |(page 138) | | |
|Inverse proportion (page 140) |Investigation: The building problem |SkillSHEET 3.7: Expressing minutes as |Mathcad: Inverse proportion (page 142) |N 6.3 Ex 3E Q1–11 |
|WE 9a–b, 10a–d |(page 144) |fractions of an hour (page 143) |Excel: Inverse proportion (page 142) |Students identify and solve |
|Ex 3E Inverse proportion (page 142) |Code puzzle (page 145) |SkillSHEET 3.8: Predicting the value of x| |multiplication and division problems |
| |10 Quick Questions 2 (page 146) |in equations of the type y = [pic] | |involving inverse proportion. |
| |Investigation: Focus on proportion | (page 143) | | |
| |(page 146) |Game time 002 (page 144) | | |
| | |WorkSHEET 3.2 (page 144) | | |
|Identifying the type of proportion |Career profile: Anna Wojcik (page 149) |WorkSHEET 3.3 (page 148) | |N 6.3 Ex 3F Q1 |
|(page 147) | | | |Students identify and solve problems |
|WE 11a–b | | | |involving direct and inverse proportion |
|Ex 3F Identifying the type of proportion | | | |using a range of computation methods and |
|(page 148) | | | |strategies. |
|Summary (page 150) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 151) | |(page 152) | | |
| | |Topic tests (2) | | |
Chapter 4 Algebraic operations Suggested time: 4.5 weeks
Strand: Patterns and algebra
Topic: Equivalence and equations
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests | | |
| |puzzles |(CD-ROM) | | |
|Are you ready? (page 154) | |SkillSHEETs (page 154) | |N 4.2 |
| | |4.1: Expanding brackets | |Students identify and solve addition and |
| | |4.2: Collecting like terms | |subtraction problems involving common |
| | |4.3: Expanding a pair of brackets | |fractions. |
| | |4.5: Finding the highest common factor | |PA 6.2 |
| | |4.7: Factorising by taking out the | |Students interpret and solve problems |
| | |highest common factor | |using algebraic methods. (expanding, |
| | |4.12: Simplification of algebraic | |simplifying and factorising expressions) |
| | |fractions | | |
| | |4.15: Addition and subtraction of common | | |
| | |fractions | | |
|Expanding algebraic expressions | |SkillSHEET 4.1: Expanding brackets |Excel: Expanding |PA 6.2 Ex 4A Q 1–12 |
|(page 155) | |(page 159) |a(bx + c) (page 159) |Students interpret and solve problems |
|WE 1, 2a–b, 3, 4, 5a–b, | |SkillSHEET 4.2: Collecting like terms |Excel: Expanding |using algebraic methods. (expanding and |
|6a-b | |(page 159) |(ax + b)(cx + d) (page 159) |simplifying expressions) |
|Ex 4A Expanding algebraic expressions | |SkillSHEET 4.3: Expanding a pair of |Mathcad: Expanding algebraic expressions | |
|(page 159) | |brackets (page 159) |(page 159) | |
| | |SkillSHEET 4.4: Recognising expansion |Excel: Expanding | |
| | |patterns (page 159) |(ax + b)2 (page 159) | |
| | |Game time 001 (page 160) |Excel: Expanding | |
| | | |(ax + b)(ax ( b) (page 159) | |
|Factorising using common factors (page |Code puzzle (page163) |SkillSHEET 4.5: Finding the highest |Mathcad: Factorising (page 162) |PA 6.2 Ex 4B Q1–6 |
|160) | |common factor (page 162) | |Students interpret and solve problems |
|WE 7a–b, 8a–b | |SkillSHEET 4.6: Division of algebraic | |using algebraic methods. (factorising) |
|Ex 4B Factorising using common factors | |terms (page 162) | | |
|(page 162) | |SkillSHEET 4.7: Factorising by taking out| | |
| | |the highest common factor (page 162) | | |
| | |SkillSHEET 4.8: Factorising by taking out| | |
| | |a common binomial factor (page 162) | | |
|Factorising expressions with two or four |Maths Quest challenge Q1–5 (page 168) |SkillSHEET 4.9: Factorising by taking out|Excel: Factorising ax2 + bx (page 166) |PA 6.2 Ex 4C Q1–13 |
|terms (page 164) | |the highest common factor (page 166) |Excel: Difference of two squares |Students interpret and solve problems |
|WE 9a–c, 10a–b | |SkillSHEET 4.10: Factorising by taking |(page 166) |using algebraic methods. (factorising) |
|Ex 4C Factorising expressions with two or| |out a common binomial factor (page 166) |Mathcad: Factorising two or four terms | |
|four terms (page 166) | |WorkSHEET 4.1 (page 167) |(page 166) | |
|Factorising expressions with three terms |Investigation: Mouse pad dimensions |SkillSHEET 4.11: Finding a factor pair |Excel: Factorising |PA 6.2 Ex 4D Q1–50 |
|(page 168) |(page 172) |that adds to a given number (page 171) |x2 + bx+ c (page 171) |Students interpret and solve problems |
|WE 11a–d |10 Quick Questions 1 (page 172) | |Mathcad: Factorising |using algebraic methods. (factorising) |
|Ex 4D Factorising expressions with three | | |x2 + bx+ c (page 171) | |
|terms (page 171) | | | | |
|Factorising more complex expressions with|Maths Quest challenge Q1–2 (page 175) |Game time 002 (page 175) |Excel: Factorising |PA 6.2 Ex 4E Q1–3 |
|three terms (page 173) |Code puzzle (page176) | |ax2 + bx+ c (page 175) |Students interpret and solve problems |
|WE 12a–b, 13a–c | | |Mathcad: Factorising |using algebraic methods. (factorising) |
|Ex 4E Factorising more complex | | |ax2 + bx+ c (page 175) | |
|expressions with three terms (page 175) | | | | |
|Mixed factorising practice (page 177) | |WorkSHEET 4.2 (page 177) |Mathcad: Mixed factorising (page 177) |PA 6.2 Ex 4E Q1–40 |
|Ex 4F Mixed factorising practice | | | |Students interpret and solve problems |
|(page 177) | | | |using algebraic methods. (factorising) |
|Simplifying algebraic fractions (page |Investigation: Equal or not equal? |SkillSHEET 4.12: Simplification of |Mathcad: Simplifying algebraic fractions |PA 6.2 Ex 4G Q1–3 |
|177) |(page 182) |algebraic fractions (page 181) |(page 181) |Students interpret and solve problems |
|WE 14a–b, 15a–c, 16a–b |Investigation: What’s the problem? |SkillSHEET 4.13: Multiplication of common| |using algebraic methods. (factorising and|
|Ex 4G Simplifying algebraic fractions |(page 182) |fractions (page 182) | |simplifying) |
|(page 181) | |SkillSHEET 4.14: Division of common | |PA DB 6.2 Ex 4G Q1–3 |
| | |fractions (page 182) | |Students manipulate expressions. |
|Adding and subtracting algebraic |10 Quick Questions 2 (page 188) |SkillSHEET 4.15: Addition and subtraction|Mathcad: Adding and subtracting algebraic|PA 6.2 Ex 4H Q1–7 |
|fractions (page 183) |Investigation: Musical notes (page 188) |of common fractions (page 185) |fractions (page 185) |Students interpret and solve problems |
|WE 17a–b, 18a–b, 19 |Enrichment activity: Converting recurring|SkillSHEET 4.16: Writing equivalent | |using algebraic methods. (simplifying) |
|Ex 4H Adding and subtracting algebraic |decimal fractions to common fractions |algebraic fractions with lowest common | |PA DB 6.2 Ex 4H Q1–7 |
|fractions (page 185) |(page 189) |denominator (page 185) | |Students manipulate expressions. |
| | |SkillSHEET 4.17: Algebraic fractions: | | |
| | |finding and converting to the lowest | | |
| | |common denominator (page 187) | | |
|Algebraic applications (page 190) | |WorkSHEET 4.3 (page 194) | |PA DB 6.2 Ex 4I Q1–8 |
|WE 20a–d, 21a–d | | | |Students manipulate expressions and solve|
|Ex 4I Algebraic applications (page 192) | | | |equations. |
|Summary (page 195) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 196) | |(page 198) | | |
| | |Topic tests (2) | | |
Chapter 5 Linear equations Suggested time: 2.5 weeks
Strand: Patterns and algebra
Topics: Equivalence and equations
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 200) | |SkillSHEETs (page 200) | |PA 5.1 |
| | |5.1: Substitution into a rule | |Students interpret and compare different |
| | |5.2: Solving linear equations that arise | |representations of linear functions and |
| | |when finding x- and y-intercepts | |solve the related problems. |
| | |5.3: Graphing linear equations using the | | |
| | |x- and y-intercept method | | |
| | |5.4: Finding the gradient of a line from | | |
| | |its equation | | |
| | |5.6: Transposing linear equations to make| | |
| | |x or y the subject | | |
|Graphical solution of simultaneous |GC tip – Casio: Solving simultaneous |SkillSHEET 5.1: Substitution into a rule |Mathcad: Simultaneous equations ― |PA 6.2 Ex 5A Q1–7 |
|equations (page 202) |equations graphically (page 205) |(page 208) |graphical (page 206) |Students solve mathematical models using |
|WE 1, 2, 3 |GC tip – TI: Solving simultaneous |SkillSHEET 5.2: Solving linear equations |Excel: Simultaneous equations ― graphical|graphical methods. |
|Ex 5A Graphical solution of simultaneous |equations graphically (page 205) |that arise when finding x- and |(page 206) | |
|equations (page 206) |Investigation: How many cockatoos and |y-intercepts (page 208) | | |
| |kangaroos? (page 209) |SkillSHEET 5.3: Graphing linear equations| | |
| |Enrichment activity: Cat and mouse |using the x- and y-intercept method | | |
| |problem (page 209) |(page 208) | | |
| | |SkillSHEET 5.4: Finding the gradient of a| | |
| | |line from its equation (page 208) | | |
| | |Game time 001 (page 208) | | |
|Algebraic solution of simultaneous |Maths Quest challenge Q1–2 (page 214) |SkillSHEET 5.5: Addition of simultaneous |Mathcad: Simultaneous equations ― |PA DB 6.2 Ex 5B Q1–5 |
|equations ― elimination method (page 209)|Code puzzle (page 215) |equations (page 213) |elimination (page 213) |Students solve simultaneous equations. |
|WE 4, 5, 6, 7 |10 Quick Questions 1 (page 216) |WorkSHEET 5.1 (page 214) |Excel: Simultaneous equations ― ax + by =| |
|Ex 5B Algebraic solution of simultaneous |Investigation: Simultaneous equations in | |c form (page 214) | |
|equations ― elimination method (page 213)|3 unknowns (page 216) | |Excel: Simultaneous equations ― | |
| | | |elimination (page 214) | |
|Algebraic solution of simultaneous |Investigation: Cramer’s rule for |SkillSHEET 5.6: Transposing linear |Mathcad: Simultaneous equations |PA DB 6.2 Ex 5C Q1–3 |
|equations ― substitution method |simultaneous equations (page 220) |equations to make x or y the subject |substitution (page 220) |Students solve simultaneous equations. |
|(page 217) | |(page 220) |Excel: Simultaneous equations ― | |
|WE 8, 9, 10 | |Game time 002 (page 220) |substitution (page 220) | |
|Ex 5C Algebraic solution of simultaneous | |WorkSHEET 5.2 (page 220) | | |
|equations ― substitution method | | | | |
|(page 220) | | | | |
|Problem solving using simultaneous |Maths Quest challenge Q1–3 (page 225) |WorkSHEET 5.3 (page 225) |Excel: Simultaneous equations (page 223) |PA DB 6.2 Ex 5D |
|equations (page 221) |10 Quick Questions 2 (page 225) | |GC program – Casio: Simultaneous |Q1–18 |
|WE 11, 12 |Investigation: Concert hall seating | |equations (page 223) |Students solve simultaneous equations. |
|Ex 5D Problem solving using simultaneous |(page 226) | |GC program – TI: Simultaneous equations | |
|equations (page 223) | | |(page 223) | |
|Summary (page 227) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 228) | |(page 228) | | |
| | |Topic tests (2) | | |
Chapter 6 Quadratic equations Suggested time: 3.5 weeks
Strand: Patterns and algebra
Topics: Patterns and functions, Equivalence and equations
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 230) | |SkillSHEETs (page 230) | |N 5.1 |
| | |6.1: Factorising by taking out the | |Students compare and order integers. |
| | |highest common factor | |N DB 6.1 |
| | |6.2: Finding a factor pair that adds to a| |Students interpret and use the various |
| | |given number | |sets of real numbers (simplify surds). |
| | |6.6: Simplifying surds | |PA 5.1 |
| | |6.7: Substituting into quadratic | |Students interpret different |
| | |equations | |representations of linear and non-linear |
| | |6.8: Equation of a vertical line | |functions and solve the related problems.|
| | | | |PA 6.2 |
| | | | |Students interpret and solve problems |
| | | | |using algebraic methods. (factorising) |
|Solving quadratic equations by | |SkillSHEET 6.1: Factorising by taking out|GC program – Casio: Solving quadratic |PA DB 6.2 Ex 6A |
|factorising (page 231) | |the highest common factor (page 233) |equations (page 233) |Q1–16 |
|WE 1, 2a–d, 3 | |SkillSHEET 6.2: Finding a factor pair |GC program – TI: Solving quadratic |Students manipulate expressions and solve|
|Ex 6A Solving quadratic equations by | |that adds to a given number (page 234) |equations (page 233) |quadratic equations. |
|factorising (page 233) | |SkillSHEET 6.3: Solving quadratic |Mathcad: Solving quadratic equations | |
| | |equations of the type ax2 + bx + c = 0, |(page 233) | |
| | |where a = 1 (page 234) |Excel: Solving | |
| | |SkillSHEET 6.4: Solving quadratic |ax2 + bx = 0 (page 233) | |
| | |equations of the type ax2 + bx + c = 0, |Excel: Solving ax2 + c = 0 (page 233) | |
| | |where a ≠ 1 (page 234) |Excel: Solving | |
| | |Game time 001 (page 235) |x2 + bx + c = 0 (page 234) | |
| | | |Excel: Solving | |
| | | |ax2 + bx + c = 0 (page 234) | |
|Solving quadratic equations using the | |SkillSHEET 6.5: Substituting into the |Mathcad: Quadratic formula (page 238) |PA DB 6.2 Ex 6B Q1–6 |
|quadratic formula (page 236) | |quadratic formula (page 237) |Excel: Quadratic formula (page 238) |Students solve quadratic equations |
|WE 4a–b | |SkillSHEET 6.6: Simplifying surds | | |
|Ex 6B Solving quadratic equations using | |(page 237) | | |
|the quadratic formula (page 237) | |WorkSHEET 6.1 (page 238) | | |
|Using the discriminant (page 238) |Maths Quest challenge Q1–5 (page 241) | |Mathcad: Using the discriminant |PA DB 6.2 Ex 6C Q1–6 |
|WE 5a–d |Investigation: Flying dolphin (page 242) | |(page 241) |Students solve quadratic equations. |
|Ex 6C Using the discriminant (page 241) |10 Quick Questions 1 (page 242) | | | |
|Plotting parabolas (page 243) |GC tip – Casio: Drawing graphs (page 246)|SkillSHEET 6.7: Substituting into |Mathcad: Parabolas of the form y = x2 + c|PA 6.1 Ex 6D Q1–12 |
|WE 6, 7a–c |GC tip – TI: Drawing graphs (page 246) |quadratic equations (page 248) |(page 248) |Students use tables to draw non-linear |
|Ex 6D Plotting parabolas (page 248) | |SkillSHEET 6.8: Equation of a vertical |Mathcad: Parabolas of the form y = (x – |graphs. |
| | |line (page 248) |b)2 (page 248) | |
| | |WorkSHEET 6.2 (page 249) | | |
|Sketching parabolas using the basic graph|Maths Quest challenge Q1–3 (page 255) | |Mathcad: Parabolas of the form y = x2 + c|PA DB 6.1 Ex 6E Q1–7 |
|of y = x2 (page 249) |10 Quick Questions 2 (page 255) | |(page 250) |Students identify and interpret the |
|WE 8a–b, 9a–b, 10a–b, 11a–b, 12a–b | | |Mathcad: Parabolas of the form y = (x – |properties of various families of |
|Ex 6E Sketching parabolas using the basic| | |b)2 (page 250) |functions (quadratic graphs). |
|graph of | | |Mathcad: Parabolas of the form y = ax2 | |
|y = x2 (page 254) | | |(page 251) | |
|Sketching parabolas of the form y = ax2 +|Code puzzle (page 262) |Game time 002 (page 261) |Excel : Solving |PA DB 6.1 Ex 6F Q1–8 |
|bx + c (page 256) |Investigation: Finding intercepts and |WorkSHEET 6.3 (page 261) |ax2 + bx + c = 0 (page 259) |Students identify and interpret the |
|WE 13, 14 |turning points using a graphics | |GC program – Casio: Solving |properties of various families of |
|Ex 6F Sketching parabolas of the form |calculator (page 263) | |ax2 + bx + c = 0 (page 259) |functions (quadratic graphs). |
|y = ax2 + bx + c (page 259) |Investigation: Catch this! (page 265) | |GC program – TI: Solving | |
| | | |ax2 + bx + c = 0 (page 259) | |
| |Enrichment activity: The game of golf | |Excel: Parabolas of the form y = ax2 + bx| |
| |(page 265) | |+ c (page 259) | |
| |Investigation: Bicycle helmets (page 267)| |Mathcad: Parabolas of the form y = ax2 + | |
| | | |bx + c (page 259) | |
|Summary (page 268) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 269) | |(page 270) | | |
| | |Topic tests (2) | | |
Chapter 7 Length, area and volume Suggested time: 2.5 weeks
Strands: Measurement and Space
Topics: Length, mass, area and volume, Shape and line
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 272) | |SkillSHEETs (page 272) | |M 5.1 |
| | |7.1: Conversion of area units | |Students use formulae to calculate areas |
| | |7.2: Using a formula to find the area of | |and volume. |
| | |a common shape | |N 6.1 |
| | |7.3: Total surface area of cubes and | |Students use scientific notation. |
| | |rectangular prisms | | |
| | |7.5: Conversion of volume units | | |
| | |7.6: Volume of cubes and rectangular | | |
| | |prisms | | |
|Perimeter (page 273) |Maths Quest challenge Q1–2 (page 278) | |Mathcad: Perimeter (page 276) |M5.1 Ex 7A Q1–2 |
|WE 1a–c, 2a–b, 3, 4 | | |GC program – Casio: Measurement |Students use formulae to calculate |
|Ex 7A Perimeter (page 276) | | |(page 276) |lengths of boundaries. |
| | | |GC program – TI: Measurement (page 276) |M 6.1 Ex 7A Q1–7 |
| | | |Excel: Length converter (page 276) |Students solve measurement problems and |
| | | |Excel: Perimeter and area (page 276) |justify selections and applications of |
| | | |Cabri geometry: Circumference and area of|formulae. |
| | | |a circle (page 276) |M DB 6.1 Ex 7A Q8–15 |
| | | | |Students use combinations of procedures |
| | | | |and formulae to solve multi-step |
| | | | |problems. |
|Area (page 279) |Maths Quest challenge Q1–3 (page 286) |SkillSHEET 7.1: Conversion of area units |Excel: Area converter (DIY) (page 279) |M 6.1 Ex 7B Q1–6 |
|WE 5a–b, 6a–b |10 Quick Questions 1 (page 286) |(page 279) |Mathcad: Area (page 283) |Students solve measurement problems and |
|Ex 7B Area (page 283) |Enrichment activity: Teardrops (page 287)|SkillSHEET 7.2: Using a formula to find |GC program – Casio: Measurement |justify selections and applications of |
| | |the area of a common shape (page 283) |(page 283) |formulae. |
| | |Game time 001 (page 285) |GC program – TI: Measurement (page 283) |M DB 6.1 Ex 7B Q7–10 |
| | |WorkSHEET 7.1 (page 285) |Excel: Perimeter and area (page 283) |Students use combinations of procedures |
| | | |Excel: Heron’s formula DIY (page 284) |and formulae to solve multi-step |
| | | |Cabri geometry: Area of a sector |problems. |
| | | |(page 284) | |
|Total surface area (page 287) |Code puzzle (page 296) |SkillSHEET 7.3: Total surface area of |Mathcad: Total surface area (page 293) |M 6.1 Ex 7C Q1–7 |
|WE 7a–b, 8, 9, 10, 11a–b | |cubes and rectangular prisms (page 287) |GC program – Casio: Measurement |Students solve measurement problems and |
|Ex 7C Total surface area (page 293) | |SkillSHEET 7.4: Total surface area of |(page 293) |justify selections and applications of |
| | |cubes and rectangular prisms (page 293) |GC program – TI: Measurement (page 293) |formulae. |
| | | |Excel: Total surface area and volume |M DB 6.1 Ex 7C Q8–12 |
| | | |(page 293) |Students use combinations of procedures |
| | | | |and formulae to solve multi-step |
| | | | |problems. |
|Volume and capacity (page 297) |Investigation: Comparing volumes of |SkillSHEET 7.5: Conversion of volume |Mathcad: Volume (page 302) |M 6.1 Ex 7D Q1–8 |
|WE 12a–b, 13, 14a–b, 15, 16 |pyramids and prisms (page 299) |units (page 297) |GC program – Casio: Measurement |Students solve measurement problems and |
|Ex 7D Volume and capacity (page 302) |Investigation: Volume and capacity |SkillSHEET 7.6: Volume of cubes and |(page 302) |justify selections and applications of |
| |(page 301) |rectangular prisms (page 297) |GC program – TI: Measurement (page 302) |formulae. |
| |Investigation: Water tank worries |SkillSHEET 7.7: Volume of cubes and |Excel: Total surface area and volume |M DB 6.1 Ex 7D Q9–15 |
| |(page 305) |rectangular prisms (page 302) |(page 302) |Students use combinations of procedures |
| |Career profile: Mike Matheson (page 305) |Game time 002 (page 304) | |and formulae to solve multi-step |
| |Code puzzle (page 307) |WorkSHEET 7.2 (page 304) | |problems. |
| |10 Quick Questions 2 (page 308) | | | |
|Length, area and volume changes with | |WorkSHEET 7.3 (page 316) |Cabri geometry: Dilation (page 313) |M 6.1 Ex 7E Q4, 6–16 |
|dilations (page 309) | | |Cabri geometry: Dilation and area (page |Students solve measurement problems and |
|WE 17, 18, 19, 20a–b, | | |314) |justify selections and applications of |
|21a–c | | | |formulae. |
|Ex 7E Length, area and volume changes | | | |S 5.1 Ex 7E Q1–3, 5 |
|with dilations (page 313) | | | |Students create representations of |
| | | | |geometric objects that satisfy design |
| | | | |specifications. |
| | | | |S 6.1 Ex 7E Q1–3, 5 |
| | | | |Students use deductive reasoning to |
| | | | |generalise about the properties of shapes|
| | | | |(use scale factors in changes to 2D and |
| | | | |3D shapes). |
|Summary (page 317) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 318) | |(page 320) | | |
| | |Topic tests (2) | | |
Chapter 8 Trigonometry and its applications Suggested time: 4 weeks
Strands: Measurement and Space
Topics: Length, mass, area and volume, Location, direction and movement
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 322) | |SkillSHEETs (page 322) | |M 6.1 |
| | |8.1: Labelling the sides of a | |Students interpret measurement problems |
| | |right-angled triangle | |(labelling sides of a triangle). |
| | |8.2: Rounding to a given number of | |N 4.1 |
| | |decimal places | |Students compare and order numbers. |
| | |8.3: Rounding the size of an angle to the| |S 5.2 |
| | |nearest minute and second | |Students describe (by drawings) movements|
| | |8.5: Rearranging formulas | |using compass bearings and distance. |
| | |8.6: Drawing a diagram from given | | |
| | |directions | | |
|Trigonometric ratios (page 323) |Investigation: The cosine ratio |SkillSHEET 8.1: Labelling the sides of a |Cabri geometry: Investigating the sine |M 6.1 Ex 8A Q1–7 |
|WE 1a–c, 2, 3a–b |(page 325) |right-angled triangle (page 328) |ratio (page 323) |Students interpret, analyse and solve |
|Ex 8A Trigonometric ratios (page 328) | | |Cabri geometry: Investigating the cosine |measurement problems and justify |
| | | |ratio (page 325) |selections and applications of formulae |
| | | |Mathcad: Trigonometric ratios (page 328) |(tangent). |
| | | |Excel: Introducing the trigonometric |M DB 6.1 Ex 8A Q1–7 |
| | | |ratios (page 329) |Students apply trigonometric ratios to |
| | | | |particular situations involving |
| | | | |triangles. |
|Using a calculator (page 330) |GC tip – Casio: Finding sin, cos or tan |SkillSHEET 8.2: Rounding to a given |Excel: Converting angles (page 333) |M DB 6.1 Ex 8B Q1–13 |
|WE 4, 5a–b, 6, 7a–b |of an angle (page 331) |number of decimal places (page 335) |Excel: Converting angles (page 335) |Students apply trigonometric ratios to |
|Ex 8B Using a calculator (page 335) |GC tip – TI: Finding sin, cos or tan of |SkillSHEET 8.3: Rounding the size of an | |particular situations involving |
| |an angle (page 331) |angle to the nearest minute and second | |triangles. |
| |GC tip – Casio: Entering angles expressed|(page 335) | | |
| |in degrees, minutes and seconds | | | |
| |(page 332) | | | |
| |GC tip – TI: Entering angles expressed in| | | |
| |degrees, minutes and seconds (page 332) | | | |
| |GC tip – Casio: Converting degrees in | | | |
| |decimal form to degrees, minutes and | | | |
| |seconds (page 334) | | | |
| |GC tip – TI: Converting degrees in | | | |
| |decimal form to degrees, minutes and | | | |
| |seconds (page 334) | | | |
|Using trigonometric ratios to find side |Code puzzle (page 342) |SkillSHEET 8.4: Selecting an appropriate |Cabri geometry: Investigating the sine |M DB 6.1 Ex 8C |
|lengths (page 336) | |trigonometric ratio based on the given |ratio (page 337) |Q1–9 |
|WE 8a-b, 9 | |information (page 340) |Cabri geometry: Investigating the cosine |Students apply trigonometric ratios to |
|Ex 8C Using trigonometric ratios to find | |SkillSHEET 8.5: Rearranging formulas |ratio (page 337) |particular situations involving |
|side lengths (page 340) | |(page 340) |Cabri geometry: Investigating the tangent|triangles. |
| | |WorkSHEET 8.1 (page 341) |ratio (page 337) | |
| | | |Cabri geometry: Sine, cosine, tangent | |
| | | |(page 337) | |
| | | |Excel: Introducing the trigonometric | |
| | | |ratios (page 337) | |
| | | |Mathcad: Finding side lengths (page 340) | |
| | | |Excel: Using sine (page 340) | |
| | | |Excel: Using cosine (page 340) | |
| | | |Excel: Using cosine (DIY) (page 340) | |
| | | |Excel: Using tangent (page 340) | |
| | | |Excel: Using tangent (DIY) (page 340) | |
| | | |Excel: Universal trigonometric calculator| |
| | | |(page 341) | |
|Using trigonometric ratios to find angles|Maths Quest challenge Q1–2 (page 348) |Game time 001 (page 347) |Mathcad: Finding angles (page 346) |M DB 6.1 Ex 8D Q1–8 |
|(page 343) |10 Quick Questions 1 (page 348) | |Excel: Finding angles (page 346) |Students apply trigonometric ratios to |
|WE 10a–b, 11a–b |Code puzzle (page 349) | | |particular situations involving |
|Ex 8D Using trigonometric ratios to find | | | |triangles. |
|angles (page 346) | | | | |
|Applications of trigonometry (page 350) |Maths Quest challenge Q1-2 (page 356) |WorkSHEET 8.2 (page 355) |Excel: Universal trigonometric calculator|M DB 6.1 Ex 8E Q1–20 |
|WE 12a–c, 13 |Investigation: Satellite height | |(page 353) |Students apply trigonometric ratios to |
|Ex 8E Applications of trigonometry |(page 356) | | |particular situations involving |
|(page 353) |Enrichment activity: Patchwork sewing | | |triangles. |
| |(page 357) | | | |
|Trigonometry and bearings (page 357) |Investigation: Which way do I go? |SkillSHEET 8.6: Drawing a diagram from |Cabri geometry: Bearings (page 365) |M DB 6.1 Ex 8F Q5–12 |
|WE 14a–b, 15a–b, 16a–c, 17a–c |(page 365) |given directions (page 363) | |Students apply trigonometric ratios to |
|Ex 8F Trigonometry and bearings (page |10 Quick Questions 2 (page 366) |Game time 002 (page 365) | |particular situations involving |
|363) | | | |triangles. |
| | | | |S 6.2 Ex 8F Q1–12 |
| | | | |Students provide directions based on |
| | | | |bearings and distances. |
|Graphs of y = sin θ and |GC tip – Casio: Investigating the graphs |WorkSHEET 8.3 (page 368) |Mathcad: Graphs of |M DB 6.1 Ex 8G Q1–11 |
|y = cos θ (page 367) |of y = sin θ and y = cos θ (page 368) | |y = sin θ and y = cos θ |Students apply trigonometric ratios and |
|Ex 8G Graphs of y = sin θ and y = cos θ |GC tip – TI: Investigating the graphs of | |(page 367) |use combinations of procedures to solve |
|(page 367) |y = sin θ and y = cos θ (page 369) | |Excel: Graphs of y = sin θ and y = cos θ |multi-step problems. |
| | | |(page 367) | |
|Summary (page 370) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 372) | |(page 374) | | |
| | |Topic tests (2) | | |
Chapter 9 Dealing with data Suggested time: 3.5 weeks
Strand: Chance and data
Topic: Data
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 376) | |SkillSHEETs (page 376) | |N 5.3 |
| | |9.1: Determining suitability of questions| |Students solve problems involving |
| | |for a survey | |percentages. |
| | |9.2: Finding proportions | |CD 4.2 |
| | |9.3: Distinguishing between types of data| |Students choose and construct appropriate|
| | |9.4: Reading bar graphs | |displays and make comparisons about the |
| | |9.5: Calculating the angle in a pie graph| |data. |
| | |9.6: Expressing one quantity as a | |CD 6.2 |
| | |percentage of another | |Students interpret data to identify the |
| | |9.8: Determining independent and | |nature of variations and relationships. |
| | |dependent variables | | |
|Collecting data (page 377) |Investigation: Problems collating data |SkillSHEET 9.1: Determining suitability |Excel: Generating random numbers |CD 6.2 Ex 9A Q1–8 |
|WE 1a–b, 2 |(page 377) |of questions for a survey (page 382) |(page 379) |Students decide which data collection |
|Ex 9A Collecting data (page 382) |GC tip – Casio: Generating random numbers|SkillSHEET 9.2 Finding proportions | |processes are appropriate for various |
| |using a calculator (page 379) |(page 383) | |purposes to provide representative |
| |GC tip – TI: Generating random numbers | | |samples. |
| |using a calculator (page 379) | | | |
| |Investigation: Non-random sampling | | | |
| |(page 383) | | | |
|Presenting categorical and discrete data |Maths Quest challenge (page 395) |SkillSHEET 9.3: Distinguishing between |Mathcad: Displaying data (page 392) |CD 5.2 Ex 9B Q1–14 |
|(page 384) |Code puzzle (page 396) |types of data (page 392) |Excel: Column graphs (DIY) (page 392) |Students produce and compare data |
|WE 3, 4, 5, 6, 7 | |SkillSHEET 9.4 Reading bar graphs |Excel: Bar graphs (DIY) (page 392) |displays of discrete and categorical |
|Ex 9B Presenting categorical and discrete| |(page 393) |Excel: Sector or pie graphs (DIY) |data. |
|data (page 392) | |SkillSHEET 9.5 Calculating the angle in a|(page 394) | |
| | |pie graph (page 394) |Excel: Dot-plots (DIY) (page 395) | |
| | |SkillSHEET 9.6: Expressing one quantity | | |
| | |as a percentage of another (page 394) | | |
| | |Game time 001 (page 395) | | |
|Representing data grouped into class |GC tip – Casio: Entering data and drawing|SkillSHEET 9.7 Organising data into class|GC program – Casio: UV statistics |CD 5.2 Ex 9C Q1–5 |
|intervals (page 397) |histograms (page 399) |intervals (page 400) |(page 400) |Students produce and compare data |
|WE 8, 9a–b |GC tip – TI: Entering data and drawing |WorkSHEET 9.1 (page 402) |GC program – TI: UV statistics (page 400)|displays involving grouping. |
|Ex 9C Representing data grouped into |histograms (page 400) | |Excel: Histograms and frequency polygons | |
|class intervals (page 400) |Maths Quest challenge (page 402) | |(page 401) | |
| |Investigation: Misuse of graphs | |Excel: Histograms and frequency polygons | |
| |(page 403) | |(DIY) (page 401) | |
| |10 Quick Questions 1 (page 403) | | | |
|Measures of central tendency (page 404) |GC tip – Casio: Finding the mean and | |Mathcad: Measures of central tendency |CD 5.2 Ex 9D Q1–10 |
|WE 10a–c, 11a–c, 12a–c |median of ungrouped data (page 405) | |(page 410) |Students produce data displays involving |
|Ex 9D Measures of central tendency |GC tip – TI: Finding the mean and median | |Excel: Finding the median (page 410) |grouping and compare measures of |
|(page 410) |of ungrouped data (page 405) | |Excel: Finding the median (DIY) |location. |
| |GC tip – Casio: Finding the mean (and | |(page 410) | |
| |other key statistics) of data in a | |Excel: Finding the mode (page 410) | |
| |frequency distribution table (page 407) | |Excel: Finding the mode (DIY) (page 410) | |
| |GC tip – TI: Finding the mean (and other | |Excel: Calculating the mean from a | |
| |key statistics) of data in a frequency | |frequency table (page 411) | |
| |distribution table (page 407) | |Excel: Calculating the mean from a | |
| |GC tip – Casio: Finding the mean (or | |frequency table DIY (page 411) | |
| |other key statistics) for grouped data | |GC program – Casio: UV statistics | |
| |(page 409) | |(page 411) | |
| |GC tip – TI: Finding the mean (or other | |GC program – TI: UV statistics (page 411)| |
| |key statistics) for grouped data | | | |
| |(page 409) | | | |
| |Career profile: Graham de Hoedt | | | |
| |(page 414) | | | |
|Measures of spread (page 415) |GC tip – Casio: Finding the range and |Game time 002 (page 423) |Mathcad: Measures of spread (page 422) |CD 6.2 Ex 9E Q1–8 |
|WE 13, 14, 15a–b, 16a–b |interquartile range (page 416) |WorkSHEET 9.2 (page 423) |GC program – Casio: UV statistics |Students interpret data to identify the |
|Ex 9E Measures of spread (page 422) |GC tip – TI: Finding the range and | |(page 422) |nature of variations and relationships. |
| |interquartile range (page 417) | |GC program – TI: UV statistics (page 422)|CD DB 6.2 Ex 9E |
| |GC tip – Casio: Drawing a boxplot and | |Excel: Boxplots (page 423) |Q4–8 |
| |finding the five-number summary | | |Students interpret box and whisker plots |
| |(page 418) | | |and use them to compare sets of data. |
| |GC tip – TI: Drawing a boxplot and | | | |
| |finding the five-number summary | | | |
| |(page 419) | | | |
| |GC tip – Casio: Drawing a boxplot with | | | |
| |outliers (page 421) | | | |
| |GC tip – TI: Drawing a boxplot with | | | |
| |outliers (page 421) | | | |
| |Investigation: Standard deviation | | | |
| |(page 424) | | | |
| |Investigation: Conducting a statistical | | | |
| |inquiry (page 425) | | | |
| |Enrichment task: Who owns the gold coins?| | | |
| |(page 426) | | | |
|Bivariate data (page 428) |GC tip – Casio: Drawing scatterplots |SkillSHEET 9.8: Determining independent |Mathcad: Scatterplots (page 433) |CD 6.2 Ex 9F Q1-11 |
|WE 17, 18, 19a-b |(page 429) |and dependent variables (page 433) |Excel: Scatterplots (DIY) (page 433) |Students interpret data (presented as |
|Ex 9F Bivariate data (page 433) |GC tip – TI: Drawing scatterplots |SkillSHEET 9.9: Determining the type of | |scatterplots) to identify the nature of |
| |(page 429) |correlation (page 434) | |variations and relationships. |
| |10 Quick Questions 2 (page 438) | | | |
|Lines of best fit (page 439) |Investigation: A pulsating problem |WorkSHEET 9.3 (page 444) |Mathcad: Lines of best fit (page 442) |CD 6.2 Ex 9G Q1-8 |
|WE 20a-c |(page 445) | | |Students interpret data (presented as |
|Ex 9G Lines of best fit (page 442) |Investigation: A long jump to the top | | |scatterplots) to identify the nature of |
| |(page 445) | | |variations and relationships. |
|Summary (page 446) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 448) | |(page 450) | | |
| | |Topic tests (2) | | |
Chapter 10 Probability Suggested time: 3 weeks
Strand: Chance and data
Topic: Chance
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 452) | |SkillSHEETs (page 452) | |N 4.1 |
| | |10.1: Set notation | |Students compare common fractions. |
| | |10.2: Simplifying common fractions | |N 4.2 |
| | |10.6: Determining complementary events | |Students identify and solve addition and |
| | |10.7: Addition and subtraction of common | |subtraction problems involving common |
| | |fractions | |fractions. |
| | |10.9: Multiplying common fractions for | |N 4.3 |
| | |calculating probabilities | |Students identify and solve |
| | | | |multiplication problems involving common |
| | | | |fractions. |
| | | | |CD 5.1 |
| | | | |Students determine probabilities for |
| | | | |single events to justify statements and |
| | | | |decisions. |
|Probability of single events (page 453) |Maths Quest challenge Q1–3 (page 465) |SkillSHEET 10.1: Set notation (page 457) |Mathcad: Probability revision (page 461) |CD 5.1 Ex 10A Q1–18 |
|WE 1a–b, 2a–b, 3a–b, |Enrichment activity: Explain these tricks|SkillSHEET 10.2: Simplifying common |Excel: Converting odds (page 465) |Students model and determine |
|4a–b, 5a–c |(page 466) |fractions (page 461) | |probabilities for single events to |
|Ex 10A Probability of single events | |SkillSHEET 10.3: Working with Venn | |justify statements and decisions. |
|(page 461) | |diagrams (page 464) | | |
| | |SkillSHEET 10.4: Writing odds as | | |
| | |probabilities (page 465) | | |
| | |SkillSHEET 10.5: Writing probabilities as| | |
| | |odds (page 465) | | |
| | |Game time 001 (page 465) | | |
|Complementary events (page 467) |Maths Quest challenge Q1–3 (page 471) |SkillSHEET 10.6: Determining |Mathcad: Complementary events (page 468) |CD 5.1 Ex 10B Q1–12 |
|WE 6a–b, 7 |10 Quick Questions 1 (page 471) |complementary events (page 468) | |Students model and determine |
|Ex 10B Complementary events (page 468) |Code puzzle (page 472) |WorkSHEET 10.1 (page 470) | |probabilities for single events to |
| | | | |justify statements and decisions. |
|Mutually exclusive events (page 473) | |SkillSHEET 10.7: Adding and subtracting |Mathcad: Mutually exclusive events |CD 6.1 Ex 10C Q1–10 |
|WE 8, 9a–c | |fractions (page 475) |(page 475) |Students model and determine |
|Ex 10C Mutually exclusive events | |SkillSHEET 10.8: Distinguishing between | |probabilities for compound events and |
|(page 475) | |complementary and mutually exclusive | |justify decisions. |
| | |events (page 477) | |CD DB 6.1 Ex 10C Q1-10 |
| | | | |Students use addition property to assist |
| | | | |in finding probabilities. |
|Two-way tables and tree diagrams (page | |SkillSHEET 10.9: Multiplying common |Excel: Tree diagrams (page 486) |CD 6.1 Ex 10D Q1–16 |
|477) | |fractions for calculating probabilities |Mathcad: Tree diagrams (page 486) |Students model and determine |
|WE 10a–b, 11a–c, 12a–d, 13a–c | |(page 485) | |probabilities for multi-outcome and |
|Ex 10D Two-way tables and tree diagrams | |Game time 002 (page 487) | |compound events and justify decisions. |
|(page 485) | |WorkSHEET 10.2 (page 487) | |CD DB 6.1 Ex 10D Q1–16 |
| | | | |Students use addition property to assist |
| | | | |in finding probabilities. |
|Independent and dependent events |Investigation: Footy card collecting | |Mathcad: Independent and dependent events|CD 6.1 Ex 10E Q1–13 |
|(page 487) |(page 493) | |(page 490) |Students model and determine |
|WE 14a–c, 15 |Investigation: Hit or sit? (page 493) | | |probabilities for compound events and |
|Ex 10E Independent and dependent events |10 Quick Questions 2 (page 494) | | |justify decisions. |
|(page 490) | | | |CD DB 6.1 Ex 10E Q1–13 |
| | | | |Students use multiplication property to |
| | | | |assist in finding probabilities. |
|Subjective probability (page 495) |Maths Quest challenge Q1-2 (page 496) |WorkSHEET 10.3 (page 496) | |CD 6.1 Ex 10F Q1–4 |
|WE 16 | | | |Students justify decisions to support |
|Ex 10F Subjective probability (page 495) | | | |their predictions. |
|Summary (page 497) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 498) | |(page 500) | | |
| | |Topic tests (2) | | |
Chapter 11 Circle geometry Suggested time: 2.5 weeks
Strands: Space and Measurement
Topics: Shape and line, Location, direction and movement, Length, mass, area and volume
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activity, History of mathematics, Maths |games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 502) | |SkillSHEETs (page 502) | |M 6.1 |
| | |11.1: Pythagoras’ theorem | |Students interpret, analyse and solve |
| | |11.2: Angles in a triangle | |measurement problems (use Pythagoras’ |
| | |11.3: Naming angles | |theorem and calculate arc length). |
| | |11.4: Angles and parallel lines | |S 5.1 |
| | |11.5: Angle relations | |Students analyse the relationships |
| | |11.6: Angle sum of a quadrilateral | |between the properties of shapes, lines |
| | |11.7: Calculation of arc length | |and angles. |
|Circles, chords and tangents (page 503) |Investigation: Constructing a tangent |SkillSHEET 11.1: Pythagoras’ theorem |Cabri geometry: Tangents (page 505) |S DB 6.1 Ex 11A Q1–8 |
|WE 1, 2, 3 |(page 504) |(page 508) |Cabri geometry: Intersecting tangents |Students use deductive reasoning to |
|Ex 11A Circles, chords and tangents |Maths Quest challenge Q1–3 (page 508) | |(page 505) |establish theorems associated with |
|(page 507) |Enrichment activity: Chords and triangles| |Cabri geometry: Chords (page 505) |circles. |
| |in circles (page 508) | | |M 6.1 Ex 11A Q3–8 |
| |Investigation: Angles in a circle | | |Students interpret, analyse and solve |
| |(page 509) | | |measurement problems (use Pythagoras’ |
| |History of mathematics: They couldn’t do | | |theorem). |
| |it (page 510) | | | |
|Angles in a circle (page 511) |10 Quick Questions 1 (page 516) |SkillSHEET 11.2: Angles in a triangle |Cabri geometry: Angles at the centre and |S 5.1 Ex 11B Q3 |
|WE 4, 5, 6, 7 |Code puzzle (page 517) |(page 514) |the circumference (page 511) |Students analyse the relationships |
|Ex 11B Angles in a circle (page 514) |Investigation: Quadrilaterals in circles |SkillSHEET 11.3: Naming angles (page 515)|Cabri geometry: Angles subtended by the |between the properties of shapes, lines |
| |(page 518) |SkillSHEET 11.4: Angles and parallel |same arc (page 511) |and angles to explain congruence. |
| | |lines (page 516) | |S DB 6.1 Ex 11B Q1–8 |
| | |SkillSHEET 11.5: Angle relations | |Students use deductive reasoning to |
| | |(page 516) | |establish theorems associated with |
| | |SkillSHEET 11.6: Angle sum of a | |circles. |
| | |quadrilateral (page 516) | | |
| | |WorkSHEET 11.1 (page 516) | | |
|Cyclic quadrilaterals (page 518) |Maths Quest challenge Q1–2 (page 522) |Game time 001 (page 521) |Cabri geometry: Cyclic quadrilaterals 1 |S DB 6.1 Ex 11C Q1–5 |
|WE 8, 9, 10 | |WorkSHEET 11.2 (page 521) |(page 518) |Students use deductive reasoning to |
|Ex 11C Cyclic quadrilaterals (page 520) | | |Cabri geometry: Cyclic quadrilaterals 2 ―|establish theorems associated with |
| | | |proof (page 518) |circles and quadrilaterals. |
| | | |Cabri geometry: Exterior angles of cyclic| |
| | | |quadrilaterals (page 519) | |
|Great circles (page 522) |Investigation: Greenwich Mean Time |SkillSHEET 11.7: Calculation of arc |Mathcad: Arc length (page 526) |S 6.2 Ex 11D Q1–10 |
|WE 11, 12, 13 |(page 523) |length (page 526) | |Students identify lines of latitude and |
|Ex 11D Great circles (page 526) |Maths Quest challenge Q1–2 (page 527) |Game time 002 (page 527) | |longitude to explain distances between |
| |10 Quick Questions 2 (page 527) |WorkSHEET 11.3 (page 527) | |locations. |
| |Investigation: SOS! (page 528) | | |M 6.1 Ex 11D Q1–10 |
| |Enrichment activity: How big is our | | |Students interpret, analyse and solve |
| |Earth? (page 529) | | |measurement problems (based on arc |
| | | | |length). |
|Summary (page 530) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 531) | |(page 534) | | |
| | |Topic tests (2) | | |
Chapter 12 Networks Suggested time: 3 weeks
Strand: Space
Topic: Location, direction and movement
|Section |GC tips, Investigations, Enrichment |SkillSHEETs, WorkSHEETs, Interactive |Technology applications (CD-ROM) |Learning outcomes |
| |activities, History of mathematics, Maths|games, | | |
| |Quest challenge, 10 Quick Questions, Code|Test yourself, Topic tests (CD-ROM) | | |
| |puzzles | | | |
|Are you ready? (page 536) | |SkillSHEETs (page 536) | |S 5.1 |
| | |12.1: The degree of a vertex | |Students analyse the relationships |
| | |12.2: Vertices, edges and regions of a | |between the properties of shapes, lines |
| | |network | |and angles. |
| | |12.4: Paths in networks | | |
|What is a network? (page 537) |Code puzzle (page 542) | | |S DB 6.2 Ex 12A Q1–10 |
|WE 1, 2, 3 | | | |Students analyse simple network diagrams.|
|Ex 12A What is a network? (page 541) | | | | |
|Basic properties of networks (page 543) |Investigation: Traversable or not |SkillSHEET 12.1: The degree of a vertex |Mathcad: Euler’s rule (page 552) |S DB 6.2 Ex 12B Q1–13 |
|WE 4a–b, 5, 6, 7 |traversable? (page 544) |(page 551) | |Students analyse simple network diagrams.|
|Ex 12B Basic properties of networks (page|Maths Quest Challenge: Q1–2 (page 552) |SkillSHEET 12.2: Vertices, edges and | | |
|549) |History of mathematics: Leonhard Euler |regions of a network (page 552) | | |
| |(page 553) |SkillSHEET 12.3: Euler’s formula for | | |
| |10 Quick Questions 1 (page 554) |planar networks (page 552) | | |
| | |Game time 001 (page 552) | | |
| | |WorkSHEET 12.1 (page 552) | | |
|Application of networks to |Enrichment activity: How many paths in a | |Excel: Handshake counter (page 558) |S DB 6.2 Ex 12C Q1–2 |
|problem-solving (page 555) |network? (page 559) | | |Students analyse simple network diagrams.|
|WE 8, 9 | | | | |
|Ex 12C Application of networks to | | | | |
|problem-solving (page 558) | | | | |
|Paths and circuits ― part I (page 560) | |SkillSHEET 12.4: Paths in networks | |S DB 6.2 Ex 12D Q1–8 |
|WE 10, 11a–b | |(page 563) | |Students analyse simple network diagrams |
|Ex 12D Paths and circuits ― part I | |Game time 002 (page 563) | |to determine optimal pathways in a |
|(page 563) | | | |system. |
|Paths and circuits ― part II (page 564) |Investigation: Sprouts (page 567) |SkillSHEET 12.5: Traversable networks | |S DB 6.2 Ex 12E Q1–7 |
|WE 12, 13 |Investigation: The bridges of Konigsberg |(page 566) | |Students analyse simple network diagrams |
|Ex 12E Paths and circuits ― part II |(page 568) |WorkSHEET 12.2 (page567) | |to determine optimal pathways in a |
|(page 566) |10 Quick Questions 2 (page 568) | | |system. |
|Networks and maps (page 569) |Maths Quest Challenge: (page 574) |WorkSHEET 12.3 (page 574) | |S DB 6.2 Ex 12F Q1–5 |
|WE 14, 15 |Investigation: Tourist attractions | | |Students analyse simple network diagrams |
|Ex 12F Networks and maps (page 572) |(page 575) | | |to determine optimal pathways in a |
| |Investigation: Four colour problem (page | | |system. |
| |576) | | | |
|Summary (page 578) | |‘Test yourself’ multiple-choice questions| | |
|Chapter review (page 579) | |(page 580) | | |
| | |Topic tests (2) | | |
-----------------------
WORK PROGRAM
Maths Quest for Queensland Book 3
ISBN: 0-7314-0053-4 RRP: $46.95 Available: August 2004
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