1

WORK PROGRAM

Chapter 7 The right-angled triangle

Clusters: Measurement, SpaceSuggested time: 4 weeks

Section

/ 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) / Technology applications
(CD-ROM) /

Learning outcomes

Are you ready? (page 270) / 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 the type to find x
7.9: Solving equations of the type to find x / 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.
Right-angled triangles (page271)
Pythagoras’ theorem (page272)
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) / 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 (page276)
Game time 001 (page 277) / Excel: Finding the length of the hypotenuse (page276)
Mathcad: Pythagoras’ theorem (page 276)
GC program — Casio: Pythagoras’ theorem (page 276)
GC program — TI: Pythagoras’ theorem (page 276) / 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.
Finding the length of a shorter side (page 278)
WE 3, 4
Ex 7B Finding the length of a shorter side (page279) / Investigation: Shortest path (page 281) / Excel: Finding the length of the shorter side (page280)
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.
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.
Composite shapes (page283)
WE 5, 6, 7
Ex 7C Composite shapes (page 285) / Investigation: Will the house stand up? (page288)
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 (page288) / 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.
What is trigonometry? (page 291)
Naming the sides of a right-angled triangle (page292)
WE 8, 9, 10a–c
Ex 7D Naming the sides of a right-angled triangle (page 296) / Investigation: The tangent ratio (page 295)
Maths Quest challenge: Q1–3 (page 298) / SkillSHEET 7.5: Measuring angles (page296)
SkillSHEET 7.6: Measuring length (page296)
Game time 002 (page298) / Cabri geometry: Investigating the tangent ratio (page293)
Cabri geometry: Investigating the tangent ratio (page 295) / 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.
The tangent ratio (page299)
WE 11, 12a–b, 13
Ex 7E The tangent ratio (page 302) / GC tip — Casio: Finding the tan of an angle (page301)
Maths Quest challenge: Q1 (page 304) / SkillSHEET 7.7: Labelling sides of a triangle (page302)
WorkSHEET 7.2 (page303) / GC tip — TI: Finding the tan of an angle (page301)
Excel: Introducing the tangent ratio (page 303) / M 10b.7 Scale
Understands and uses similarity relationships in and between figures, including the trigonometric ratios.
Finding side lengths (page304)
WE 14, 15, 16
Ex 7F Finding side lengths (page 308) / Maths Quest challenge: Q1–2 (page 310) / SkillSHEET 7.8: Solving equations of the type to find x (page308)
SkillSHEET 7.9: Solving equations of the type to find x (page308) / Excel: Using tangent (page308)
Mathcad: Finding side lengths (page 308) / 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.
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 the inverse tangent function (page311)
10 Quick Questions 2 (page 316)
Investigation: Using an inclinometer to measure inaccessible heights (page 316) / WorkSHEET 7.3 (page315) / GC tip — TI: Using the inverse tangent function (page311)
Excel: Finding the angle (page 314)
Excel: Universal trigonometric calculator (page 314) / 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.
Applications of Pythagoras’ theorem and trigonometry (page317)
WE 20
Ex 7H Applications of Pythagoras’ theorem and trigonometry (page319) / Investigation: Length of shadows (page 322)
Code puzzle (page 323) / Excel: Universal trigonometric calculator (page 319) / 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.
Summary (page 324)
Chapter review (page 325) / ‘Test yourself’ multiple choice questions
(page 328)
Topic tests (2)