Download Chapter 7 Work program

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.