1
WORK PROGRAM  MQ 9 NSW 5.1 pathway
Chapter 8 Pythagoras’ theorem
Strands: Measurement, Space and geometry, Number
Substrands and Outcomes:
Length
MS3.1 Selects and uses the appropriate unit and device to measure length, distances and perimeters
Perimeter and area
MS4.1 Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figures
composed of rectangles and triangles
Properties of geometrical figures
SGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals
Operations with whole numbers
NS4.1 Recognises the properties of special groups of whole numbers and applies a range of strategies to
aid computation
Fractions, decimals and percentages NS4.3 Operates with fractions, decimals, percentages, ratios and rates
Section
Are you ready? (page 284)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETS,
Technology applications
WorkSHEETS,
(CD–ROM)
Interactive games,
Test yourself, Topic tests
(CD–ROM)
SkillSHEETS (page 284)
8.1: Finding the square of
a number
8.2: Finding the square
root of a number
8.3: Rounding to a given
number of decimal places
8.4: Measuring the length
of a line
8.5: Constructing angles
with a protractor
8.6: Perimeter
8.8: Area of triangles
Learning outcomes
NS4.1
 using index notation to
express powers of
numbers
 using the notation for
square roots
 finding square roots of
numbers
NS4.3
 rounding decimals to a
given number of
decimal places
MS3.1
 measuring and
recording lengths or
2
Squares, square roots and
rounding (page 285)
WE 1a-b, 2a-b
Ex 8A Squares, square
roots and rounding
(page 286)
SkillSHEET 8.1: Finding
the square of a number
(page 286)
SkillSHEET 8.2: Finding
the square root of a
number (page 286)
SkillSHEET 8.3: Rounding
to a given number of
decimal places
(page 287)
Mathcad: Squares and
square roots (page 286)
Excel: Squares and square
roots (DIY) (page 286)
Right-angled triangles
(page 287)
Ex 8B Right-angled
triangles (page 288)
SkillSHEET 8.4:
Cabri geometry:
Measuring the length of a
Pythagoras’ theorem
line (page 288)
(page 289)
SkillSHEET 8.5:
Constructing angles with
a protractor (page 289)
distances
 calculating perimeters
of triangles
MS4.1
 using the formula for
the area of a triangle
SGS4.3
 constructing various
types of triangles using
geometrical
instruments given
different information
NS4.1
 using index notation to
express powers of
numbers
 using the notation for
square roots
 finding square roots of
numbers
 recognising the link
between squares and
square roots
MS4.1
 identifying the
hypotenuse as the
longest side in any
right-angled triangle
and also as the side
opposite the right
angle
 establishing the
3
Finding the hypotenuse
(page 290)
WE 3, 4
Ex 8C Finding the
hypotenuse (page 292)
10 Quick Questions 1
(page 294)
WorkSHEET 8.1
(page 293)
Excel: Finding the length
of the hypotenuse
(page 292)
Mathcad: Pythagoras’
theorem (page 292)
GC program – Casio:
Pythagoras’ theorem
(page 292)
GC program – TI:
Pythagoras’ theorem
relationship between
the lengths of the sides
of a right angledtriangle in practical
ways, including the
dissection of areas
 describing the
relationship between
the sides of a rightangles triangle
(Communicating)
SGS4.3
 constructing various
types of triangles using
geometrical
instruments given
different information
 recognising that the
longest side of a
triangle is always
opposite the largest
angle (Reasoning)
MS4.1
 using Pythagoras’
theorem to find the
length of sides in rightangled triangles
 solving problems using
Pythagoras’ theorem,
giving an exact answer
as a surd (eg 5 ) and
4
(page 292)
Finding a shorter side
(page 295)
WE 5, 6
Ex 8D Finding a shorter
side (page 296)
Code puzzle (page 298)
SkillSHEET 8.6: Perimeter
(page 297)
SkillSHEET 8.7: Area of
rectangles (page 297)
SkillSHEET 8.8: Area of
triangles (page 297)
Game time 001 (page 297)
WorkSHEET 8.2
(page 297)
Excel: Finding the length
of the shorter side
(page 296)
Mathcad: Pythagoras’
theorem (page 296)
GC program – Casio:
Pythagoras’ theorem
(page 296)
GC program – TI:
Pythagoras’ theorem
(page 296)
approximating the
answer using an
approximation of the
square root
 writing answers to a
specified or sensible
level of accuracy,
using the
‘approximately equals’
sign
 using Pythagoras’
theorem to solve
practical problems
involving right-angled
triangles (Applying
strategies)
MS4.1
 using Pythagoras’
theorem to find the
length of sides in rightangled triangles
 solving problems using
Pythagoras’ theorem,
giving an exact answer
as a surd (eg 5 ) and
approximating the
answer using an
approximation of the
square root
 writing answers to a
specified or sensible
5
The converse of
Pythagoras’ theorem
(page 299)
WE 7, 8
Ex 8E The converse of
Pythagoras’ theorem
(page 300)
Investigation: Pythagorean
triads (page 300)
10 Quick Questions 2
(page 301)
Investigation: Pythagoras
and the building industry
(page 302)
Game time 002 (page 300)
WorkSHEET 8.3
(page 300)
Excel: Right-angle tester
(page 300)
level of accuracy,
using the
‘approximately equals’
sign
 using Pythagoras’
theorem to solve
practical problems
involving right-angled
triangles (Applying
strategies)
 applying Pythagoras’
theorem to solve
problems involving
perimeter and area
(Applying strategies)
MS4.1
 identifying a
Pythagorean triad as a
set of three numbers
such that the sum of
the squares of the first
two equals the square
of the third
 using the converse of
Pythagoras’ theorem to
establish whether a
triangle has a right
angle
 using Pythagoras’
theorem to solve
practical problems
involving right-angled
6
triangles (Applying
strategies)
Summary (page 304)
Chapter review (page 305)
‘Test yourself’ multiple
choice questions
(page 306)
Topic tests (2)