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1 WORK PROGRAM Chapter 7 The right-angled triangle Clusters: Measurement, Space Section Are you ready? (page 270) Suggested time: 4 weeks GC tips, Investigations, Rich tasks, History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles SkillSHEETs, WorkSHEETs, Interactive games, Test yourself, Topic tests (CD-ROM) SkillSHEETs (page 270) 7.1: Using a calculator to evaluate numbers in index form 7.2: Using a calculator to evaluate square roots and cube roots 7.3: Rounding to a given number of decimal places 7.4: Conversion of units of length 7.5: Measuring angles 7.6: Measuring length 7.8: Solving equations of x the type a to find x b 7.9: Solving equations of b the type a to find x x Technology applications (CD-ROM) Learning outcomes N 8.6 Calculate Calculates with positive numbers and decimals using integral powers. N 6a.5 Understand numbers Reads, writes, says and understands the meaning, order and relative magnitude of decimal numbers. M 9a.5 Understand units Uses the relationship between metric prefixes to move between units. M 9b.4 Direct measure Measures length and angle by reading whole number scales. A 19.6 Equivalence, equations and inequalities Solves linear equations using analytical methods. 2 Right-angled triangles (page 271) Pythagoras’ theorem (page 272) WE 1, 2 Ex 7A Pythagoras’ theorem (page 276) Investigation: Pythagoras’ theorem (page 272) History of mathematics: Pythagoras (c. 580 – c. 500 BC) (page 273) Maths Quest challenge: Q1–2 (page 277) Investigation: Electrical cable (page 278) Finding the length of a shorter side (page 278) WE 3, 4 Ex 7B Finding the length of a shorter side (page 279) Investigation: Shortest path (page 281) SkillSHEET 7.1: Using a calculator to evaluate numbers in index form (page 276) SkillSHEET 7.2: Using a calculator to evaluate square roots and cube roots (page 276) SkillSHEET 7.3: Rounding to a given number of decimal places (page 276) Game time 001 (page 277) Excel: Finding the length of the hypotenuse (page 276) Mathcad: Pythagoras’ theorem (page 276) GC program — Casio: Pythagoras’ theorem (page 276) GC program — TI: Pythagoras’ theorem (page 276) Excel: Finding the length of the shorter side (page 280) Mathcad: Pythagoras’ theorem (page 280) GC program — Casio: Pythagoras’ theorem (page 280) GC program — TI: Pythagoras’ theorem (page 280) M 10b.6 Scale Understands and uses Pythagoras’ theorem to solve problems involving triangles. AM 2.5 Contextualise mathematics Describes how some familiar mathematical ideas are, or have been, used by people to represent, describe and explain their world. WM 3.5 Mathematical strategies Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches. M 10b.6 Scale Understands and uses Pythagoras’ theorem to solve problems involving triangles. WM 3.5 Mathematical strategies Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches. WM 4.5 Apply and verify Checks working and reasoning and whether answers fit specifications and make sense in the original situation. 3 Composite shapes (page 283) WE 5, 6, 7 Ex 7C Composite shapes (page 285) Investigation: Will the house stand up? (page 288) Code puzzle (page 289) Career profile: Rob Benson (page 290) Rich task: Ernie’s didgeridoo (page 290) 10 Quick Questions 1 (page 291) SkillSHEET 7.4: Conversion of units of length (page 285) WorkSHEET 7.1 (page 288) Excel: Pythagoras’ theorem (page 285) Mathcad: Pythagoras’ theorem (page 285) Mathcad: Pythagoras’ theorem (DIY) (page 285) M 10b.6 Scale Understands and uses Pythagoras’ theorem to solve problems involving triangles. AM 2.5 Contextualise mathematics Describes how some familiar mathematical ideas are, or have been, used by people to represent, describe and explain their world. WM 3.5 Mathematical strategies Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches. WM 4.5 Apply and verify Checks working and reasoning and whether answers fit specifications and make sense in the original situation. 4 What is trigonometry? Investigation: The tangent (page 291) ratio (page 295) Naming the sides of a Maths Quest challenge: right-angled triangle Q1–3 (page 298) (page 292) WE 8, 9, 10a–c Ex 7D Naming the sides of a right-angled triangle (page 296) The tangent ratio (page 299) WE 11, 12a–b, 13 Ex 7E The tangent ratio (page 302) Finding side lengths (page 304) WE 14, 15, 16 Ex 7F Finding side lengths (page 308) GC tip — Casio: Finding the tan of an angle (page 301) Maths Quest challenge: Q1 (page 304) Maths Quest challenge: Q1–2 (page 310) SkillSHEET 7.5: Measuring angles (page 296) SkillSHEET 7.6: Measuring length (page 296) Game time 002 (page 298) Cabri geometry: Investigating the tangent ratio (page 293) Cabri geometry: Investigating the tangent ratio (page 295) SkillSHEET 7.7: Labelling sides of a triangle (page 302) WorkSHEET 7.2 (page 303) SkillSHEET 7.8: Solving equations of the type x a to find x b (page 308) SkillSHEET 7.9: Solving equations of the type b a to find x x (page 308) GC tip — TI: Finding the tan of an angle (page 301) Excel: Introducing the tangent ratio (page 303) Excel: Using tangent (page 308) Mathcad: Finding side lengths (page 308) M 10b.7 Scale Understands and uses similarity relationships in and between figures, including the trigonometric ratios. WM 3.5 Mathematical strategies Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches. M 10b.7 Scale Understands and uses similarity relationships in and between figures, including the trigonometric ratios. M 10b.7 Scale Understands and uses similarity relationships in and between figures, including the trigonometric ratios. S 15a.5 Represent location Uses bearings on maps in descriptions of locations and paths. 5 Finding the size of an angle (page 310) WE 17, 18, 19 Ex 7G Finding the size of an angle (page 313) GC tip — Casio: Using WorkSHEET 7.3 the inverse tangent (page 315) function (page 311) 10 Quick Questions 2 (page 316) Investigation: Using an inclinometer to measure inaccessible heights (page 316) GC tip — TI: Using the inverse tangent function (page 311) Excel: Finding the angle (page 314) Excel: Universal trigonometric calculator (page 314) Applications of Pythagoras’ theorem and trigonometry (page 317) WE 20 Ex 7H Applications of Pythagoras’ theorem and trigonometry (page 319) Investigation: Length of shadows (page 322) Code puzzle (page 323) Excel: Universal trigonometric calculator (page 319) Summary (page 324) Chapter review (page 325) ‘Test yourself’ multiple choice questions (page 328) Topic tests (2) M 9b.4 Direct measure Measures angle by reading whole number scales. M 10b.7 Scale Understands and uses similarity relationships in and between figures, including the trigonometric ratios. WM 3.5 Mathematical strategies Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches. M 10b.6 Scale Understands and uses Pythagoras’ theorem to solve problems involving triangles. M 10b.7 Scale Understands and uses similarity relationships in and between figures, including the trigonometric ratios. S 15a.5 Represent location Uses bearings on maps in descriptions of locations and paths.