Heinemann Maths Zone 9 VELS Edition: Teaching and Assessment ProgramThis Teaching and Assessment Program (TAP) is presented to assist teachers in planning their school’s courses, and to demonstrate that a
program incorporating the Victorian Essential Learning Standards (VELS) may be constructed using the curriculum package of resources
published by Heinemann. There are three versions (A, B and C) provided for Years 9 and 10, while the Years 7 and 8 format involves core,
background and extension. The TAPs for the other year levels are available on this website. The Heinemann Maths Zone 9 VELS Edition fully
integrates VELS Design Tasks, graphics calculator and computer material.
The following tables contain extracts from material produced by the Victorian Curriculum and Assessment Authority, Australia. Students and teachers should consult the Victorian Essential Learning Standards website, http://vels.vcaa.vic.edu.au, for more information. This material is copyright and cannot be reproduced in any form without written permission of the VCAA.
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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SummaryAll units are presented at three Levels: A, B and C. In some cases the content is different at different Levels. For ease of planning, all units are
the same length.
Unit no. Unit title Length in weeks
1 Mathematical techniques 3
2 Measurement 3
3 Pythagoras' Theorem 3
4 Expanding and factorising 3
5 Trigonometry 4
6 Linear equations, graphs and inequalities 4
7 Statistics 4
8 Geometry 4
9 Quadratic functions 4
10 Probability 4
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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Abbreviations
The following abbreviations have been used in the Year 9 TAP grids:
VELS standards
The appropriate part of the standards are included. The VELS correlation grid and the audit appear both on this website and at the front of
Heinemann Maths Zone 9 VELS Edition.
Standards that come from the non-discipline strands are titled in bold with the particular strand identified in italics.
Heinemann references
MZ9 refers to the textbook Heinemann Maths Zone 9 VELS Edition
Assessment
FT9 refers to questions on the Heinemann Maths Zone 9 VELS EDITION FlexiTest. Specific section references are provided.
SA stands for Short answer, MC stands for Multiple choice and A&A stands for Applications and analysis questions
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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Unit 1: Mathematical techniques Level: A Dimensions: Number Time: 3 weeks
VELS standards Course Heinemann references Assessment
Ratios, fractions and
percentages
They carry out exact arithmetic computations involving fractions and
irrational numbers such as square roots (e.g., ,
) and multiples and fractions of π (e.g. ).
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations
to a required accuracy in terms of decimal places and/or significant
figures.
Fractions, decimals, percentages
and ratios
MZ9 p 3 (1.1)
p 30 (Problem solving)
FT9 1.1 SA
FT9 1.1 MC
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Profit and loss (percentage on cost
or selling price)
MZ9 p 8 (1.2) FT9 1.2 SA
FT9 1.2 MC
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Discounts MZ9 p 8 (1.2) FT9 1.2 SA
FT9 1.2 MC
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
Cost of living MZ9 pxxii (Assignment 1)
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
functions and carry out symbolic manipulation.
Information and communications technology/ICT for visualising
thinking Students use a range of ICT tools and data types to
visualise their thinking strategies when solving problems, and
discriminate between such tools and strategies based on their
suitability for problem solving in new situations.
Number skills
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms. (one- or two-digit divisors in the case of division). They
perform computations involving very large or very small numbers in
scientific notation (e.g., 0.0045 × 0.000 028 = 4.5 × 10-3 × 2.8 × 10-5
= 1.26 × 10-7).
Multiplying and dividing in index
form
MZ9 p 17 (1.3 Q1–9) FT9 1.3 SA
FT9 1.3 MC
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms. (one- or two-digit divisors in the case of division). They
perform computations involving very large or very small numbers in
scientific notation (e.g., 0.0045 × 0.000 028 = 4.5 × 10-3 × 2.8 × 10-5
= 1.26 × 10-7).
Index laws MZ9 p 21 (1.4 Q1–7) FT9 1.4 SA (Q1–12)
FT9 1.4 MC (Q1–6)
Students use the Euclidean division algorithm to find the greatest
common divisor (highest common factor) of two natural numbers
(e.g., the greatest common divisor of 1071 and 1029 is 21 since 1071
= 1029 × 1 + 42, 1029 = 42 × 24 + 21 and 42 = 21 × 2 + 0).
Physical, Personal and Social Learning/Interpersonal
Euclidean division MZ9 p 16 (Investigation)
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
development/Working in teams Students respect and build on the
ideas and opinions of team members, reflect on the effectiveness of
learning in a team and develop strategies for improvement.
Thinking/Creativity Students experiment with innovative
possibilities within the parameters of a task. They take calculated
risks when defining tasks and generating solutions.
Incomes
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Earnings MZ9 p 24 (1.5)
p 31 (Maths in action)
MZ9 p 33 (VELS
Design task)
FT9 1.5 SA
FT9 1.5 MC
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Income tax MZ9 p 34 (1.6) FT9 1.6 SA
FT9 1.6 MC
FT9 1.6 A&A
Simple interest
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
Calculation of interest MZ9 p 37 (1.7) FT9 1.7 SA(Q1–6)
FT9 1.7 MC(Q1–9)
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
numbers, integers and finite decimals using mental and/or written
algorithms.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Deposit account interest MZ9 p 37 (1.7)
p 45 (Graphics calculator
investigation)
FT9 1.7 SA (Q1–6)
FT9 1.7 MC(Q1–9)
Payment options
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Interest-free payment methods MZ9 p 49 (1.8) FT9 1.8 SA
FT9 1.8 MC
FT9 1.8 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Payment methods with interest MZ9 p 52 (1.9 Q1–7) FT9 1.9 SA
FT9 1.9 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 9 of 84
Unit 1: Mathematical techniques Level: B Dimensions: Number Time: 3 weeks
VELS standards Course Heinemann references Assessment
Ratios, fractions and
percentages
Students carry out exact arithmetic computations involving fractions
and irrational numbers such as square roots (e.g. ,
) and multiples and fractions of π (e.g. ).
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations
to a required accuracy in terms of decimal places and/or significant
figures.
Fractions, decimals, percentages
and ratios
MZ9 p 3 (1.1)
p 30 (Problem solving)
FT9 1.1 SA
FT9 1.1 MC
FT9 1.1 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Profit and loss (percentage on cost
or selling price)
MZ9 p 8 (1.2) FT9 1.2 SA
FT9 1.2 MC
FT9 1.2 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Discounts MZ9 p 8 (1.2) FT9 1.2 SA
FT9 1.2 MC
FT9 1.2 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
They select and use technology in various combinations to assist in
Cost of living MZ9 pxxii (Assignment 1)
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Information and communications technology/ICT for visualising
thinking Students use a range of ICT tools and data types to
visualise their thinking strategies when solving problems, and
discriminate between such tools and strategies based on their
suitability for problem solving in new situations.
Number skills
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms. (one- or two-digit divisors in the case of division). They
perform computations involving very large or very small numbers in
scientific notation (e.g., 0.0045 × 0.000 028 = 4.5 × 10-3 × 2.8 × 10-5
= 1.26 × 10-7).
Multiplying and dividing in index
form
MZ9 p 17 (1.3) FT9 1.3 SA
FT9 1.3 MC
FT9 1.3 A&A
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms. (one- or two-digit divisors in the case of division). They
perform computations involving very large or very small numbers in
scientific notation (e.g., 0.0045 × 0.000 028 = 4.5 × 10-3 × 2.8 × 10-5
= 1.26 × 10-7).
Index laws MZ9 p 21 (1.4) FT9 1.4 SA
FT9 1.4 MC
FT9 1.4 A&A
Students use the Euclidean division algorithm to find the greatest
common divisor (highest common factor) of two natural numbers 9
(e.g., the greatest common divisor of 1071 and 1029 is 21 since 1071
= 1029 × 1 + 42, 1029 = 42 × 24 + 21 and 42 = 21 × 2 + 0).
Euclidean division MZ9 p 16 (Investigation)
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
Physical, Personal and Social Learning/Interpersonal
development/Working in teams Students respect and build on the
ideas and opinions of team members, reflect on the effectiveness of
learning in a team and develop strategies for improvement.
Thinking/Creativity Students experiment with innovative
possibilities within the parameters of a task. They take calculated
risks when defining tasks and generating solutions.
Incomes
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Earnings MZ9 p 24 (1.5)
p 31 (Maths in action)
MZ9 p 33 (VELS
Design task)
FT9 1.5 SA
FT9 1.5 MC
FT9 1.5 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Income tax MZ9 p 34 (1.6) FT9 1.6 SA
FT9 1.6 MC
FT9 1.6 A&A
Simple interest
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Calculation of interest MZ9 p 37 (1.7) FT9 1.7 SA
FT9 1.7 MC
FT9 1.7 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
Deposit account interest MZ9 p 37 (1.7)
p 45 (Graphics calculator
investigation)
FT9 1.17 SA
FT9 1.7 MC
FT9 1.7 A&A
Payment options
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Interest-free payment methods MZ9 p 49 (1.8) FT9 1.8 SA
FT9 1.8 MC
FT9 1.8 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
Payment methods with interest MZ9 p 52 (1.9) FT9 1.9 SA
FT9 1.9 MC
FT9 1.9 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 13 of 84
VELS standards Course Heinemann references Assessment
algorithms.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 14 of 84
Unit 1: Mathematical techniques Level: C Dimensions: Number Time: 3 weeks
VELS standards Course Heinemann references Assessment
Ratios, fractions and
percentages
They carry out exact arithmetic computations involving fractions and
irrational numbers such as square roots (e.g., , )
and multiples and fractions of π (e.g. ). They use
appropriate estimates to evaluate the reasonableness of the results of
calculations involving rational and irrational numbers, and the decimal
approximations for them. They carry out computations to a required
accuracy in terms of decimal places and/or significant figures.
Fractions, decimals, percentages
and ratios
MZ9 p 3 (1.1)
p 30 (Problem solving)
FT9 1.1 SA
FT9 1.1 MC
FT9 1.1 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Profit and loss (percentage on
cost or selling price)
MZ9 p 8 (1.2) FT9 1.2 SA
FT9 1.2 MC
FT9 1.2 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Discounts MZ9 p 8 (1.2) FT9 1.2 SA
FT9 1.2 MC
FT9 1.2 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 15 of 84
VELS standards Course Heinemann references Assessment
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Information and communications technology/ICT for visualising
thinking Students use a range of ICT tools and data types to visualise
their thinking strategies when solving problems, and discriminate
between such tools and strategies based on their suitability for
problem solving in new situations
Cost of living MZ9 pxxii (Assignment 1)
Number skills
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
(one- or two-digit divisors in the case of division). They perform
computations involving very large or very small numbers in scientific
notation (e.g., 0.0045 × 0.000 028 = 4.5 × 10-3 × 2.8 × 10-5 = 1.26 × 10-
7).
Multiplying and dividing in
index form
MZ9 p 17 (1.3) FT9 1.3 SA
FT9 1.3 MC
FT9 1.3 A&A
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
(one- or two-digit divisors in the case of division). They perform
computations involving very large or very small numbers in scientific
notation (e.g., 0.0045 × 0.000 028 = 4.5 × 10-3 × 2.8 × 10-5 = 1.26 × 10-
7).
Index laws MZ9 p 21 (1.4) FT9 1.4 SA
FT9 1.4 MC
FT9 1.4 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 16 of 84
VELS standards Course Heinemann references Assessment
Students use the Euclidean division algorithm to find the greatest
common divisor (highest common factor) of two natural numbers (e.g.,
the greatest common divisor of 1071 and 1029 is 21 since
1071 = 1029 × 1 + 42, 1029 = 42 × 24 + 21 and 42 = 21 × 2 + 0).
Physical, Personal and Social Learning/Interpersonal
development/Working in teams Students respect and build on the
ideas and opinions of team members, reflect on the effectiveness of
learning in a team and develop strategies for improvement
Thinking/Creativity Students experiment with innovative possibilities
within the parameters of a task. They take calculated risks when
defining tasks and generating solutions
Euclidean division MZ9 p 16 (Investigation)
Incomes
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
Earnings MZ9 p 24 (1.5)
p 31 (Maths in action)
MZ9 p 33 (VELS
Design task)
FT9 1.5 SA
FT9 1.5 MC
FT9 1.5 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
Income tax MZ9 p 34 (1.6) FT9 1.6 SA
FT9 1.6 MC
FT9 1.6 A&A
Simple interest
Students choose, use and develop mathematical models and Calculation of interest MZ9 p 37 (1.7) FT9 1.7 SA
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
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VELS standards Course Heinemann references Assessment
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
FT9 1.7 MC
FT9 1.7 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
Deposit account interest MZ9 p 37 (1.7)
p 45 (Graphics calculator
investigation)
FT9 1.7 SA
FT9 1.7 MC
FT9 1.7 A&A
Payment options
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Interest-free payment methods MZ9 p 49 (1.8) FT9 1.8 SA
FT9 1.8 MC
FT9 1.8 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
They select and use technology in various combinations to assist in
Payment methods with interest MZ9 p 52 (1.9) FT9 1.9 SA
FT9 1.9 MC
FT9 1.9 A&A
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Page 18 of 84
VELS standards Course Heinemann references Assessment
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 19 of 84
Unit 2: Measurement Level: A Dimensions: Measurement Time: 3 weeks
VELS standards Course Heinemann references Assessment
Units
They select and use appropriate units, converting between units as
required.
Standard metric units MZ9 p 67 (2.1)
p 71 (Maths in action)
FT9 2.1 SA
FT9 2.1 MC
FT9 2.1 A&A
Measuring
Students decide on acceptable or tolerable levels of error in a given
situation.
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations to a
required accuracy in terms of decimal places and/or significant figures.
Errors and approximation MZ9 p 74 (2.2) FT9 2.2 SA
FT9 2.2 MC
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Real life measurement MZ9 pxxiii (Assignment 2)
Area
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Area of composite shapes MZ9 p 80 (2.3) p 91 (VELS Design
Task)
FT9 2.3 SA
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Page 20 of 84
VELS standards Course Heinemann references Assessment
FT9 2.3 MC
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Area of quadrilaterals MZ9 p 85 (2.4) FT9 2.4 SA
FT9 2.4 MC
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Total surface area MZ9 p 92 (2.5) FT9 2.5 SA
FT9 2.5 MC
FT9 2.5 A&A
Volume
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Volume and capacity MZ9 p 96 (2.6)
p 100 (Graphics calculator
investigation)
FT9 2.6 SA
FT9 2.6 MC
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Page 21 of 84
Unit 2: Measurement Level: B Dimensions: Measurement Time: 3 weeks
VELS standards Course Heinemann references Assessment
Units
They select and use appropriate units, converting between units as
required.
Standard metric units MZ9 p 67 (2.1)
p 71 (Maths in action)
FT9 2.1 SA
FT9 2.1 MC
FT9 2.1 A&A
Measuring
Students decide on acceptable or tolerable levels of error in a given
situation.
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations to a
required accuracy in terms of decimal places and/or significant figures.
Errors and approximation MZ9 p 74 (2.2) FT9 2.2 SA
FT9 2.2 MC
FT9 2.2 A&A
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Real life measurement MZ9 pxxiii (Assignment 2)
Area
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Area of composite shapes MZ9 p 80 (2.3) p 91 (VELS Design
Task)
FT9 2.3 SA
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Page 22 of 84
VELS standards Course Heinemann references Assessment
FT9 2.3 MC
FT9 2.3 A&A
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Area of quadrilaterals MZ9 p 85 (2.4) FT9 2.4 SA
FT9 2.4 MC
FT9 2.4 A&A
Total surface area
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Total surface area MZ9 p 92 (2.5) FT9 2.5 SA
FT9 2.5 MC
FT9 2.5 A&A
Volume
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Volume and capacity MZ9 p 96 (2.6)
p 100 (Graphics calculator
investigation)
FT9 2.6 SA
FT9 2.6 MC
FT9 2.6 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 23 of 84
Unit 2: Measurement Level: C Dimensions: Measurement Time: 3 weeks
VELS standards Course Heinemann references Assessment
Units
They select and use appropriate units, converting between units as
required.
Standard metric units MZ9 p 67 (2.1)
p 71 (Maths in action)
FT9 2.1 SA
FT9 2.1 MC
FT9 2.1 A&A
Measuring
Students decide on acceptable or tolerable levels of error in a given
situation.
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations to a
required accuracy in terms of decimal places and/or significant figures.
Errors and approximation MZ9 p 74 (2.2) FT9 2.2 SA
FT9 2.2 MC
FT9 2.2 A&A
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Real life measurement MZ9 pxxiii (Assignment 2)
Area
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Area of composite shapes MZ9 p 80 (2.3) p 91 (VELS Design
Task)
FT9 2.3 SA
FT9 2.3 MC
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VELS standards Course Heinemann references Assessment
FT9 2.3 A&A
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Area of quadrilaterals MZ9 p 85 (2.4) FT9 2.4 SA
FT9 2.4 MC
FT9 2.4 A&A
Total surface area
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Total surface area MZ9 p 92 (2.5) FT9 2.5 SA
FT9 2.5 MC
FT9 2.5 A&A
Volume
They interpret and use mensuration formulas for calculating the
perimeter, surface area and volume of familiar two- and three-
dimensional shapes and simple composites of these shapes.
Volume and capacity MZ9 p 96 (2.6)
p 100 (Graphics calculator
investigation)
FT9 2.6 SA
FT9 2.6 MC
FT9 2.6 A&A
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Page 25 of 84
Unit 3: Pythagoras’ Theorem Level: A Dimensions: Space Time: 3 weeks
VELS standards Course Heinemann references Assessment
Theorem of Pythagoras
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Introduction to the theorem and
right-angled triangles
MZ9 p 115 (3.1) FT9 3.1 SA
FT9 3.1 MC
Students comprehend the set of real numbers containing natural,
integer, rational and irrational numbers. They represent rational
numbers in both fractional and decimal (terminating and infinite
recurring) forms (e.g., , ). They comprehend
that irrational numbers have an infinite non-terminating decimal form.
They specify decimal rational approximations for square roots of
primes, rational numbers that are not perfect squares, the golden ratio
φ , and simple fractions of π correct to a required decimal place
accuracy.
Squares, square roots, surds and
approximations
MZ9 p 122 (3.2) FT9 3.2 SA
FT9 3.2 MC
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Pythagorean triads MZ9 p 126 (Maths in action)
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
They carry out computations to a required accuracy in terms of
decimal places and/or significant figures.
Finding unknown sides in right-
angled triangles, using the
theorem—both the hypotenuse
and a shorter side
MZ9 p 128 (3.3, 3.4) FT9 3.3 SA
FT9 3.3 MC
FT9 3.3 A&A (Q1–6)
FT9 3.4 SA
FT9 3.4 MC
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VELS standards Course Heinemann references Assessment
FT9 3.4 A&A (Q1–3)
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations to a
required accuracy in terms of decimal places and/or significant figures.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Using Pythagoras’ theorem MZ9 p 138 (3.5) MZ9 p 143 (VELS
Design task)
FT9 3.5 SA
FT9 3.5 MC
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Page 27 of 84
Unit 3: Pythagoras’ Theorem Level: B Dimensions: Number, Measurement, Algebra Time: 3 weeks
VELS standards Course Heinemann references Assessment
Theorem of Pythagoras
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Introduction to the theorem and
right-angled triangles
MZ9 p 115 (3.1) FT9 3.1 SA
FT9 3.1 MC
FT9 3.1 A&A
Students form and test mathematical conjectures; e.g., ‘What
relationship holds between the lengths of the three sides of a triangle?’.
Students formulate and test conjectures, generalisations and arguments
in natural language and symbolic form (e.g., ‘if m2 is even then m is
even, and if m2 is odd then m is odd’). They follow formal
mathematical arguments for the truth of propositions (e.g., ‘the sum of
three consecutive natural numbers is divisible by 3’).
Proof of the theorem MZ9 p 120 (Investigation)
Students comprehend the set of real numbers containing natural,
integer, rational and irrational numbers. They represent rational
numbers in both fractional and decimal (terminating and infinite
recurring) forms (e.g., , ). They comprehend
that irrational numbers have an infinite non-terminating decimal form.
They specify decimal rational approximations for square roots of
primes, rational numbers that are not perfect squares, the golden ratio
φ , and simple fractions of π correct to a required decimal place
accuracy.
Squares, square roots, surds and
approximations
MZ9 p 122 (3.2) FT9 3.2 SA
FT9 3.2 MC
FT9 3.2 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine, Pythagorean triads MZ9 p 126 (Maths in action)
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Page 28 of 84
VELS standards Course Heinemann references Assessment
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
They carry out computations to a required accuracy in terms of
decimal places and/or significant figures.
Finding unknown sides in right-
angled triangles, using the
theorem—both the hypotenuse
and a shorter side
MZ9 p 128 (3.3, 3.4) FT9 3.3 SA
FT9 3.3 MC
FT9 3.3 A&A
FT9 3.4 SA
FT9 3.4 MC
FT9 3.4 A&A
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations to a
required accuracy in terms of decimal places and/or significant figures.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles
Using Pythagoras’ theorem MZ9 p 138 (3.5) MZ9 p 143 (VELS
Design task)
FT9 3.5 SA
FT9 3.5 MC
FT9 3.5 A&A
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Page 29 of 84
Unit 3: Pythagoras’ Theorem Level: C Dimensions: Number, Measurement, Algebra Time: 3 weeks
VELS standards Course Heinemann references Assessment
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Introduction to the theorem and
right-angled triangles
MZ9 p 115 (3.1) FT9 3.1 SA
FT9 3.1 MC
FT9 3.1 A&A
Students form and test mathematical conjectures; e.g., ‘What
relationship holds between the lengths of the three sides of a triangle?’
Students formulate and test conjectures, generalisations and arguments
in natural language and symbolic form (e.g., ‘if m2 is even then m is
even, and if m2 is odd then m is odd’). They follow formal
mathematical arguments for the truth of propositions (e.g., ‘the sum of
three consecutive natural numbers is divisible by 3’).
Proof of the theorem MZ9 p 120 (Investigation)
Students comprehend the set of real numbers containing natural,
integer, rational and irrational numbers. They represent rational
numbers in both fractional and decimal (terminating and infinite
recurring) forms (e.g., , ). They comprehend
that irrational numbers have an infinite non-terminating decimal form.
They specify decimal rational approximations for square roots of
primes, rational numbers that are not perfect squares, the golden ratio
φ , and simple fractions of π correct to a required decimal place
accuracy.
Squares, square roots, surds and
approximations
MZ9 p 122 (3.2) FT9 3.2 SA
FT9 3.2 MC
FT9 3.2 A&A
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VELS standards Course Heinemann references Assessment
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Pythagorean triads MZ9 p 126 (Maths in action)
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
They carry out computations to a required accuracy in terms of
decimal places and/or significant figures.
Finding unknown sides in right-
angled triangles, using the
theorem—both the hypotenuse
and a shorter side
MZ9 p 128 (3.3, 3.4) FT9 3.3 SA
FT9 3.3 MC
FT9 3.3 A&A
FT9 3.4 SA
FT9 3.4 MC
FT9 3.4 A&A
They use appropriate estimates to evaluate the reasonableness of the
results of calculations involving rational and irrational numbers, and
the decimal approximations for them. They carry out computations to a
required accuracy in terms of decimal places and/or significant figures.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles
Using Pythagoras’ theorem MZ9 p 138 (3.5) MZ9 p 143 (VELS
Design task)
FT9 3.5 SA
FT9 3.5 MC
FT9 3.5 A&A
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Page 31 of 84
Unit 4: Expanding and factorising Level: A Dimensions: Structure Time: 3 weeks
VELS standards Course Heinemann references Assessment
Substitution
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Substituting into expressions MZ9 p 153 (4.1 Q1–9)
p 156 (Maths@Work)
FT9 4.1 SA
FT9 4.1 MC
Expansion
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Expanding of the type a(b + c) MZ9 p 157 (4.2 Q1–8) FT9 4.2 SA
FT9 4.2 MC
FT9 4.2 A&A
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VELS standards Course Heinemann references Assessment
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Expanding two factors of the
type (a + b)(c + d)
MZ9 p 163 (4.3 Q1–6)
p 165 (Investigation)
FT9 4.3 SA
FT9 4.3 MC
FT9 4.3 A&A
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Page 33 of 84
Unit 4: Expanding and factorising Level: B Dimensions: Structure Time: 3 weeks
VELS standards Course Heinemann references Assessment
Substitution
Students carry out arithmetic computations involving natural numbers,
integers and finite decimals using mental and/or written algorithms.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Substituting into expressions MZ9 p 153 (4.1 )
p 156 (Maths @Work)
FT9 4.1 SA
FT9 4.1 MC
FT9 4.1 A&A
Expansion
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Expanding of the type a(b + c) MZ9 p 157 (4.2) FT9 4.2 SA
FT9 4.2 MC
FT9 4.2 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
Expanding two factors of the
type (a + b)(c + d)
MZ9 p 163 (4.3)
p 165 (Investigation)
FT9 4.3 SA
FT9 4.3 MC
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Page 34 of 84
VELS standards Course Heinemann references Assessment
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
FT9 4.3 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Perfect squares and difference
of two squares
MZ9 p 166 (4.4) p 171 VELS Design
Task
FT9 4.4 SA
FT9 4.4 MC
FT9 4.4 A&A
Factorisation
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 − 12a +
Factorising using common
factors
MZ9 p 171 (4.5) FT9 4.5 SA
FT9 4.5 MC
FT9 4.5 A&A
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Page 35 of 84
VELS standards Course Heinemann references Assessment
9; (3w)3 = 27w3; ; ).
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Factorising by grouping MZ9 p 177 (4.6) FT9 4.6 SA
FT9 4.6 MC
FT9 4.6 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 − 12a +
9; (3w)3 = 27w3; ; ).
Factorising using difference of
two squares
MZ9 p 178 (4.7) FT9 4.7 SA
FT9 4.7 MC
FT9 4.7 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 − 12a +
Factorising using the perfect
square rule
MZ9 p 181 (4.8) FT9 4.8 SA
FT9 4.8 MC
FT9 4.8 A&A
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Page 36 of 84
VELS standards Course Heinemann references Assessment
9; (3w)3 = 27w3; ; ).
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent, and
reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Factorising quadratic trinomials MZ9 p 184 (4.9 Q1–3, 5–8) FT9 4.9 SA
FT9 4.9 MC
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Page 37 of 84
Unit 4: Expanding and factorising Level: C Dimensions: Structure Time: 3 weeks
VELS standards Course Heinemann references Assessment
Substitution
Students carry out arithmetic computations involving natural
numbers, integers and finite decimals using mental and/or written
algorithms
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
Substituting into expressions MZ9 p153 (4.1 )
p 156 (Maths @Work)
FT9 4.1 SA
FT9 4.1 MC
FT9 4.1 A&A
Expansion
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
12a + 9; (3w)3 = 27w3; ; ).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
Expanding of the type a(b + c) MZ9 p 157 (4.2) FT9 4.2 SA
FT9 4.2 MC
FT9 4.2 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
Expanding two factors of the type
(a + b)(c + d)
MZ9 p 163 (4.3)
p 165 (Investigation)
FT9 4.3 SA
FT9 4.3 MC
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Page 38 of 84
VELS standards Course Heinemann references Assessment
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
12a + 9; (3w)3 = 27w3; ; ).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
FT9 4.3 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
12a + 9; (3w)3 = 27w3; ; ).
Perfect squares and difference of
two squares
MZ9 p 166 (4.4) p171 VELS Design
Task
FT9 4.4 SA
FT9 4.4 MC
FT9 4.4 A&A
Factorisation
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
Factorising using common factors MZ9 p 171 (4.5) FT9 4.5 SA
FT9 4.5 MC
FT9 4.5 A&A
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Page 39 of 84
VELS standards Course Heinemann references Assessment
12a + 9; (3w)3 = 27w3; ; ).
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
12a + 9; (3w)3 = 27w3; ; ).
Factorising by grouping MZ9 p 177 (4.6) FT9 4.6 SA
FT9 4.6 MC
FT9 4.6 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
12a + 9; (3w)3 = 27w3; ; ).
Factorising using difference of
two squares
MZ9 p 178 (4.7) FT9 4.7 SA
FT9 4.7 MC
FT9 4.7 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 −
Factorising using the perfect
square rule
MZ9 p 181 (4.8) FT9 4.8 SA
FT9 4.8 MC
FT9 4.8 A&A
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Page 40 of 84
VELS standards Course Heinemann references Assessment
12a + 9; (3w)3 = 27w3; ; ).
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (e.g., 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2 =
4a2 − 12a + 9; (3w)3 = 27w3; ; ).
Factorising quadratic trinomials MZ9 p 184 (4.9)
p 187 (Problem solving)
FT9 4.9 SA
FT9 4.9 MC
FT9 4.9 A&A
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Page 41 of 84
Unit 5: Trigonometry Level: A Dimensions: Measurement Time: 4 weeks
VELS standards Course Heinemann references Assessment
Looking at triangles
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Identifying sides and angles in
triangles
MZ9 p 197 (5.1) FT9 5.1 SA
FT9 5.1 MC
FT9 5.1 A&A
Trigonometric ratios
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Introduction to sin, cos, tan MZ9 p 201 (5.2, 5.3) FT9 5.2 SA
FT9 5.2 MC
FT9 5.3 SA
FT9 5.3 MC
FT9 5.3 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
The use of sin, cos or tan for
finding lengths of sides of right-
angled triangles (using angles
given in whole degrees)
MZ9 p 212 (5.4 Q1–4) FT9 5.4 SA
FT9 5.4 MC
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Use of sin, cos or tan for finding
angles (to the nearest degree, or
decimal degrees only)
MZ9 p 218 (5.5) FT9 5.5 SA
FT9 5.5 MC
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
Angles of elevation and
depression, found using
trigonometric methods
MZ9 p 226 (5.6 Q 1–4) FT9 5.6 SA
FT9 5.6 MC
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VELS standards Course Heinemann references Assessment
practical, theoretical and historical contexts
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 43 of 84
Unit 5: Trigonometry Level: B Dimensions: Measurement Time: 4 weeks
VELS standards Course Heinemann references Assessment
Looking at triangles
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Identifying sides and angles in
triangles
MZ9 p 197 (5.1) FT9 5.1 SA
FT9 5.1 MC
FT9 5.1 A&A
Trigonometric ratios
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Introduction to sin, cos, tan MZ9 p 201 (5.2, 5.3) FT9 5.2 SA
FT9 5.2 MC
FT9 5.2 A&A
FT9 5.3 SA
FT9 5. 3 MC
FT9 5.3 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
The use of sin, cos or tan for
finding lengths of sides of right-
angled triangles (using angles
given in whole degrees)
MZ9 p 212 (5.4)
p 217 (Problem solving)
FT9 5.4 SA
FT9 5.4 MC
FT9 5.4 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Use of sin, cos or tan for finding
angles (to the nearest degree, or
decimal degrees only)
MZ9 p 218 (5.5)
p 222 (Problem solving)
FT9 5.15 SA
FT9 5.5 MC
FT9 5.5 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Angles of elevation and
depression, found using
trigonometric methods
MZ9 p 226 (5.6 Q 1–7)
p 231 (Maths@Work)
MZ9 p 230 (VELS
Design Task)
FT9 5.6 SA
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 44 of 84
VELS standards Course Heinemann references Assessment
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
FT9 5.6 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 45 of 84
Unit 5: Trigonometry Level: C Dimensions: Measurement Time: 4 weeks
VELS standards Course Heinemann references Assessment
Looking at triangles
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Identifying sides and angles in
triangles
MZ9 p 197 (5.1) FT9 5.1 SA
FT9 5.1 MC
FT9 5.1 A&A
Trigonometric ratios
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Introduction to sin, cos, tan MZ9 p 201 (5.2, 5.3) FT9 5.2 SA
FT9 5.2 MC
FT9 5.2 A&A
FT9 5.3 SA
FT9 5.3 MC
FT9 5.3 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
The use of sin, cos or tan for
finding lengths of sides of right-
angled triangles (using angles
given in whole degrees)
MZ9 p 212 (5.4)
p 217 (Problem solving)
FT9 5.4 SA
FT9 5.4 MC
FT9 5.4 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Use of sin, cos or tan for finding
angles (to the nearest degree, or
decimal degrees only)
MZ9 p 218 (5.5)
p 222 (Problem solving)
FT9 5.5 SA
FT9 5.5 MC
FT9 5.5 A&A
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Angles of elevation and
depression, found using
trigonometric methods
MZ9 p 226 (5.6)
p 231 (Maths@Work)
MZ9 p 230 (VELS
Design Task)
FT9 5.6 SA
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 46 of 84
VELS standards Course Heinemann references Assessment
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
FT9 5.6 MC
FT9 5.6 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 47 of 84
Unit 6: Linear equations, graphs and inequalities Level: A Dimensions: Structure Time: 4 weeks
VELS standards Course Heinemann references Assessment
Linear relationships
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Linear relationships, recognising
and plotting from points
MZ9 p 245 (6.1 Q 1–6) FT9 6.1 SA
FT9 6.1 MC
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Understanding gradient MZ9 p 248 (6.2 Q 1–6) FT9 6.2 SA
FT9 6.2 MC
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Sketching straight line graphs
using a table
MZ9 p 258 (6.3 Q 1–6) FT9 6.3 SA
FT9 6.3 MC
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Sketching straight line graphs
using y-intercept and gradient
MZ9 p 262 (6.4 Q 1–8) FT9 6.4 SA
FT9 6.4 MC
FT9 6.4 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
Sketching linear graphs using the
x- and y-intercepts
MZ9 p 267 (6.5 Q 1–2) FT9 6.5 SA
FT9 6.5 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 48 of 84
VELS standards Course Heinemann references Assessment
variables, domain and range.
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Sketching lines parallel to axes
and other graphs
MZ9 p 270 (6.6 Q 1, 4, 5) FT9 6.6 SA
FT9 6.6 MC
Solving linear equations
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
Using backtracking to solve
linear equations
MZ9 p 275 (6.7 Q1–5) FT9 6.7 SA
FT9 6.7 MC
FT9 6.7 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Solving word problems MZ9 p 288 (6.10 Q 1–3) FT9 6.10 SA
FT9 6.10 MC
Inequalities
Level 5 They recognise and use inequality symbols. They solve
simple inequalities such as y ≤ 2x + 4 and decide whether inequalities
such as x2 > 2y are satisfied or not for specific values of x and y.
Representation of simple
inequalities on number lines
MZ9 p 293 (6.12) FT9 6.12 SA
FT9 6.12 MC
FT9 6.12 A&A
Level 5 They recognise and use inequality symbols. They solve
simple inequalities such as y ≤ 2x + 4 and decide whether inequalities
such as x2 > 2y are satisfied or not for specific values of x and y.
Solving linear inequalities MZ9 p 296 (6.13 Q1–3) FT9 6.13 SA
FT9 6.13 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 49 of 84
Unit 6: Linear equations, graphs and inequalities Level: B Dimensions: Structure Time: 4 weeks
VELS standards Course Heinemann references Assessment
Linear relationships
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Linear relationships, recognising
and plotting from points
MZ9 p 245 (6.1) FT9 6.1 SA
FT9 6.1 MC
FT9 6.1 A&A
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Understanding gradient MZ9 p 248 (6.2 Q 1–8)
p 255 (Investigation)
p 256 (CAS investigation)
FT9 6.2 SA
FT9 6.2 MC
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Sketching straight line graphs
using a table
MZ9 p 258 (6.3 Q 1–10) FT9 6.3 SA
FT9 6.3 MC
FT9 6.3 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Sketching straight line graphs
using y-intercept and gradient
MZ9 p 262 (6.4) FT9 6.4 SA
FT9 6.4 MC
FT9 6.4 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
Sketching linear graphs using the
x- and y-intercepts
MZ9 p 267 (6.5 Q 1–3) FT9 6.5 SA
FT9 6.5 MC
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Page 50 of 84
VELS standards Course Heinemann references Assessment
variables, domain and range.
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Sketching lines parallel to axes
and other graphs
MZ9 p 270 (6.6 Q 1–5) FT9 6.6 SA
FT9 6.6 MC
FT9 6.6 A&A
Solving linear equations
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Solving linear equations MZ9 p 275 (6.7, 6.8 Q 1–3)
p 281 (Maths in Action)
p 283 (6.9 Q 1–9)
p 277 (VELS Design
Task)
FT9 6.7 SA
FT9 6.7 MC
FT9 6.7 A&A
FT9 6.8 SA
FT9 6.8 MC
FT9 6.9 SA
FT9 6.9 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 51 of 84
VELS standards Course Heinemann references Assessment
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
Solving word problems MZ9 p 288 (6.10 Q 1–11) FT9 6.10 SA
FT9 6.10 MC
FT9 6.10 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
Formulae MZ9 p 290 (6.11 Q 1–4) FT9 6.11 SA
FT9 6.11 MC
Inequalities
Level 5 They recognise and use inequality symbols. They solve
simple inequalities such as y ≤ 2x + 4 and decide whether inequalities
such as x2 > 2y are satisfied or not for specific values of x and y.
Representation of simple
inequalities on number lines
MZ9 p 293 (6.12) FT9 6.12 SA
FT9 6.12 MC
FT9 6.12 A&A
Level 5 They recognise and use inequality symbols. They solve
simple inequalities such as y ≤ 2x + 4 and decide whether inequalities
such as x2 > 2y are satisfied or not for specific values of x and y.
Solving linear inequalities MZ9 p 296 (6.13 Q1–5)
p 299 (Graphics calculator
investigation)
FT9 6.13 SA
FT9 6.13 MC
FT9 6.13 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 52 of 84
Unit 6: Linear equations, graphs and inequalities Level: C Dimensions: Structure Time: 4 weeks
VELS standards Course Heinemann references Assessment
Linear relationships
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Linear relationships, recognising
and plotting from points
MZ9 p 245 (6.1) FT9 6.1 SA
FT9 6.1 MC
FT9 6.1 A&A
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Understanding gradient MZ9 p 248 (6.2)
p 254 (Problem solving)
p 255 (Investigation)
p 256 (CAS investigation)
FT9 6.2 SA
FT9 6.2 MC
FT9 6.2 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Sketching straight line graphs
using a table
MZ9 p 258 (6.3)
p 262 (Problem solving)
FT9 6.3 SA
FT9 6.3 MC
FT9 6.3 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Sketching straight line graphs
using y-intercept and gradient
MZ9 p 262 (6.4) FT9 6.4 SA
FT9 6.4 MC
FT9 6.4 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
Sketching linear graphs using the
x- and y-intercepts
MZ9 p 267 (6.5) FT9 6.5 SA
FT9 6.5 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 53 of 84
VELS standards Course Heinemann references Assessment
coordinate system) with consideration of independent and dependent
variables, domain and range.
FT9 6.5 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Sketching lines parallel to axes
and other graphs
MZ9 p 270 (6.6) FT9 6.6 SA
FT9 6.6 MC
FT9 6.6 A&A
Solving linear equations
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Solving linear equations MZ9 p 275 (6.7, 6.8)
p 281 (Maths in Action)
p 283 (6.9 )
p 277 (VELS Design
Task)
FT9 6.7 SA
FT9 6.7 MC
FT9 6.7 A&A
FT9 6.8 SA
FT9 6.8 MC
FT9 6.8 A&A
FT9 6.9 SA
FT9 6.9 MC
FT9 6.9 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 54 of 84
VELS standards Course Heinemann references Assessment
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Solving word problems MZ9 p 288 (6.10) FT9 6.10 SA
FT9 6.10 MC
FT9 6.10 A&A
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulas, rearrange and simplify algebraic
expressions involving real variables.
Formulae MZ9 p 290 (6.11)
p 292 (Investigation)
FT9 6.11 SA
FT9 6.11 MC
FT9 6.11 A&A
Inequalities
Level 5 They recognise and use inequality symbols. They solve
simple inequalities such as y ≤ 2x + 4 and decide whether inequalities
such as x2 > 2y are satisfied or not for specific values of x and y.
Representation of simple
inequalities on number lines
MZ9 p 293 (6.12) FT9 6.12 SA
FT9 6.12 MC
FT9 6.12 A&A
Level 5 They recognise and use inequality symbols. They solve
simple inequalities such as y ≤ 2x + 4 and decide whether inequalities
such as x2 > 2y are satisfied or not for specific values of x and y.
Solving linear inequalities MZ9 p 296 (6.13)
p 299 (Graphics calculator
investigation)
FT9 6.13 SA
FT9 6.13 MC
FT9 6.13 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 55 of 84
Unit 7: Statistics Level: A Dimensions: Measurement, chance and data Time: 4 weeks
VELS standards Course Heinemann references Assessment
Types of data
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts
Data types MZ9 p 311 (7.1) FT9 7.1 SA
FT9 7.1 MC
Averages
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Mean, median, mode MZ9 p 313 (7.2 Q 1–4)
p 318 (Investigation)
FT9 7.2 SA
FT9 7.2 MC
Organisation and presentation
of data
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Stem-and-leaf plots MZ9 p 320 (7.3 Q 1–11) FT9 7.3 SA
FT9 7.3 MC
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Box-and-whisker plots MZ9 p 325 (7.4 Q 1–7) FT9 7.4 SA
FT9 7.4 MC
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Histograms and frequency
polygons
MZ9 p 340 (7.6 Q1–9) FT9 7.6 SA
FT9 7.6 MC
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Page 56 of 84
VELS standards Course Heinemann references Assessment
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Lines of best fit MZ9 p 347 (7.7 Q1–2) FT9 7.7 SA
FT9 7.7 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 57 of 84
Unit 7: Statistics Level: B Dimensions: Measurement, chance and data Time: 4 weeks
VELS standards Course Heinemann references Assessment
Types of data
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Data types MZ9 p 311 (7.1) FT9 7.1 SA
FT9 7.1 MC
FT9 7.1 A&A
Averages
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Mean, median, mode MZ9 p 313 (7.2 Q 1–7)
p 318 (Problem solving)
p 318 (Investigation)
FT9 7.2 SA
FT9 7.2 MC
FT9 7.2 A&A
Organisation and presentation
of data
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Stem-and-leaf plots MZ9 p 320 (7.3) FT9 7.3 SA
FT9 7.3 MC
FT9 7.3 A&A
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Box-and-whisker plots MZ9 p 325 (7.4 Q 1–9)
p 332 (Graphics calculator
investigation)
FT9 7.4 SA
FT9 7.4 MC
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Histograms and frequency
polygons
MZ9 p 340 (7.6 ) FT9 7.6 SA
FT9 7.6 MC
FT9 7.6 A&A
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Page 58 of 84
VELS standards Course Heinemann references Assessment
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Lines of best fit MZ9 p 347 (7.7 Q1–4)
p 353 (CAS investigation)
p 356 (Computer
investigation)
FT9 7.7 SA
FT9 7.7 MC
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot). They
distinguish informally between association and causal relationship in
bi-variate data, and make predictions based on an estimated line of
best fit for scatter-plot data with strong association between two
variables.
Comparing data MZ9 p 333 (7.5 Q1–13) p 339 (VELS Design
task)
FT9 7.5 SA
FT9 7.5 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 59 of 84
Unit 7: Statistics Level: C Dimensions: Measurement, chance and data Time: 4 weeks
VELS standards Course Heinemann references Assessment
Types of data
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Data types MZ9 p 311 (7.1) FT9 7.1 SA
FT9 7.1 MC
FT9 7.1 A&A
Averages
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Mean, median, mode MZ9 p 313 (7.2)
p 318 (Problem solving)
p 318 (Investigation)
FT9 7.2 SA
FT9 7.2 MC
FT9 7.2 A&A
Organisation and presentation
of data
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Stem-and-leaf plots MZ9 p 320 (7.3) FT9 7.3 SA
FT9 7.3 MC
FT9 7.3 A&A
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Box-and-whisker plots MZ9 p 325 (7.4 )
p 332 (Graphics calculator
investigation)
FT9 7.4 SA
FT9 7.4 MC
FT9 7.4 A&A
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Histograms and frequency
polygons
MZ9 p 340 (7.6 ) FT9 7.6 SA
FT9 7.6 MC
FT9 7.6 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 60 of 84
VELS standards Course Heinemann references Assessment
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Lines of best fit MZ9 p 347 (7.7)
p 353 (CAS investigation)
p 356 (Computer
investigation)
FT9 7.7 SA
FT9 7.7 MC
FT9 7.7 A&A
They calculate summary statistics for centrality (mode, median and
mean), spread (box plot, inter-quartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot). They
distinguish informally between association and causal relationship in
bi-variate data, and make predictions based on an estimated line of
best fit for scatter-plot data with strong association between two
variables.
Comparing data MZ9 p 333 (7.5) p 339 (VELS Design
task)
FT9 7.5 SA
FT9 7.5 MC
FT9 7.5 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 61 of 84
Unit 8: Geometry Level: A Dimensions: Space Time: 4 weeks
VELS standards Course Heinemann references Assessment
Angle relations
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
Polygons MZ9 p 373 (8.1)
p 375 (Investigation)
FT9 8.1 SA
FT9 8.1 MC
FT9 8.1 A&A
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Angles in triangles, external
angles of triangles
MZ9 p 377 (8.2 Q1–4, 8.3
Q1–4)
FT9 8.2 SA
FT9 8.2 MC
FT9 8.3 SA
FT9 8.3 MC
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Quadrilaterals, angles in
quadrilaterals
MZ9 p 385 (8.4 Q1–9, 8.5
Q1–5)
FT9 8.4 SA
FT9 8.4 MC
FT9 8.5 SA
FT9 8.5 MC
Tessellations and
constructions
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Tessellations of shapes MZ9 p 392 (8.6) FT9 8.6 SA
FT9 8.6 MC
FT9 8.6 A&A
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VELS standards Course Heinemann references Assessment
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Use tessellations in designs and
Escher-type drawings
MZ9 p 394 (Investigation)
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
Compass constructions MZ9 p 395 (8.7) FT9 8.7 SA
FT9 8.7 MC
Enlargement (or reduction)
They apply isometric and similarity transformations of geometric
shapes in the plane.
Using scale factors and scale
diagrams to solve problems
MZ9 p 397 (8.8 Q1–3) FT9 8.8 SA
FT9 8.8 MC
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
They apply isometric and similarity transformations of geometric
shapes in the plane.
Enlarging or reducing shapes MZ9 p 402 (8.9 Q1–3) FT9 8.9 SA
FT9 8.9 MC
Congruent and similar
triangles
Students use the conditions for shapes to be congruent or similar. Congruent triangles MZ9 p 404 (8.10 Q1–3) FT9 8.10 SA
FT9 8.10 MC
Students use the conditions for shapes to be congruent or similar. Similar triangles MZ9 p 407 (8.11 Q1–4)
p 412 (Computer
investigation)
FT9 8.11 SA
FT9 8.11 MC
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VELS standards Course Heinemann references Assessment
Investigating shapes
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Design, creativity and technology/ Investigating and designing They
seek information to help their design thinking and identify the needs of
a variety of client groups. When designing, they generate a range of
alternative possibilities and justify their preferred option, explaining
how it provides a solution to the problem, need or opportunity.
Design, creativity and technology/Producing They make
products/systems that meet the quality, aesthetic, functionality and
performance requirements outlined in the design brief.
Design, creativity and technology/Analysing and evaluating They use
a range of suitable testing methods to analyse and evaluate their
products/systems.
Investigation of shapes MZ9 p 412 (VELS Design
Task)
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Page 64 of 84
Unit 8: Geometry Level: B Dimensions: Space Time: 4 weeks
VELS standards Course Heinemann references Assessment
Angle relations
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
Polygons MZ9 p 373 (8.1)
p 375 (Investigation)
p 376 (Problem solving)
FT9 8.1 SA
FT9 8.1 MC
FT9 8.1 A&A
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Angles in triangles, external
angles of triangles
MZ9 p 377 (8.2 , 8.3 Q1–6)
p 384 (Computer
investigation)
FT9 8.2 SA
FT9 8.2 MC
FT9 8.2 A&A
FT9 8.3 SA
FT9 8.3 MC
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Quadrilaterals, angles in
quadrilaterals
MZ9 p 385 (8.4 Q1–9, 8.5
Q1–5)
FT9 8.4 SA
FT9 8.4 MC
FT9 8.5 SA
FT9 8.5 MC
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Exterior angle sum of a polygon MZ9 p 390 (Investigation)
Tessellations and
constructions
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VELS standards Course Heinemann references Assessment
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Tessellations of shapes MZ9 p 392 (8.6) FT9 8.6 SA
FT9 8.6 MC
FT9 8.6 A&A
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Use in designs and Escher-type
drawings
MZ9 p 394 (Investigation)
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
Compass constructions MZ9 p 395 (8.7) FT9 8.7 SA
FT9 8.7 MC
FT9 8.7 A&A
Enlargement (or reduction)
They apply isometric and similarity transformations of geometric
shapes in the plane.
Using scale factors and scale
diagrams to solve problems
MZ9 p 397 (8.8 Q1–6)
p 400 (Maths@Work)
FT9 8.8 SA
FT9 8.8 MC
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
They apply isometric and similarity transformations of geometric
shapes in the plane.
Enlarging or reducing shapes MZ9 p 402 (8.9) FT9 8.9 SA
FT9 8.9 MC
FT9 8.9 A&A
Congruent and similar
triangles
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Page 66 of 84
VELS standards Course Heinemann references Assessment
Students use the conditions for shapes to be congruent or similar. Congruent triangles MZ9 p 404 (8.10) FT9 8.10 SA
FT9 8.10 MC
FT9 8.10 A&A
Students use the conditions for shapes to be congruent or similar. Similar triangles MZ9 p 407 (8.11 Q1–7)
p 412 (Computer
investigation)
FT9 8.11 SA
FT9 8.11 MC
Investigating shapes
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Design, creativity and technology/ Investigating and designing They
seek information to help their design thinking and identify the needs of
a variety of client groups. When designing, they generate a range of
alternative possibilities and justify their preferred option, explaining
how it provides a solution to the problem, need or opportunity.
Design, creativity and technology/Producing They make
products/systems that meet the quality, aesthetic, functionality and
performance requirements outlined in the design brief.
Design, creativity and technology/Analysing and evaluating They use
a range of suitable testing methods to analyse and evaluate their
products/systems.
Investigation of shapes MZ9 p 412 (VELS Design
Task)
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Page 67 of 84
Unit 8: Geometry Level: C Dimensions: Space Time: 4 weeks
VELS standards Course Heinemann references Assessment
Angle relations
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
Polygons MZ9 p 373 (8.1)
p 375 (Investigation)
p 376 (Problem solving)
FT9 8.1 SA
FT9 8.1 MC
FT9 8.1 A&A
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Angles in triangles, external
angles of triangles
MZ9 p 377 (8.2 , 8.3)
p 384 (Computer
investigation)
FT9 8.2 SA
FT9 8.2 MC
FT9 8.2 A&A
FT9 8.3 SA
FT9 8.3 MC
FT9 8.3 A&A
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Quadrilaterals, angles in
quadrilaterals
MZ9 p 385 (8.4, 8.5) FT9 8.4 SA
FT9 8.4 MC
FT9 8.4 A&A
FT9 8.5 SA
FT9 8.5 MC
FT9 8.5 A&A
They recognise and describe boundaries, surfaces and interiors of
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
Exterior angle sum of a polygon MZ9 p 390 (Investigation)
Tessellations and
constructions
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Page 68 of 84
VELS standards Course Heinemann references Assessment
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Tessellations of shapes MZ9 p 392 (8.6) FT9 8.6 SA
FT9 8.6 MC
FT9 8.6 A&A
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Use in designs and Escher-type
drawings
MZ9 p 394 (Investigation)
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
Compass constructions MZ9 p 395 (8.7) FT9 8.7 SA
FT9 8.7 MC
FT9 8.7 A&A
Enlargement (or reduction)
They apply isometric and similarity transformations of geometric
shapes in the plane.
Using scale factors and scale
diagrams to solve problems
MZ9 p 397 (8.8)
p 400 (Maths@Work)
FT9 8.8 SA
FT9 8.8 MC
FT9 8.8 A&A
Students represent two- and three-dimensional shapes using lines,
curves, polygons and circles.
They apply isometric and similarity transformations of geometric
shapes in the plane.
Enlarging or reducing shapes MZ9 p 402 (8.9) FT9 8.9 SA
FT9 8.9 MC
FT9 8.9 A&A
Congruent and similar
triangles
Students use the conditions for shapes to be congruent or similar. Congruent triangles MZ9 p 404 (8.10) FT9 8.10 SA
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VELS standards Course Heinemann references Assessment
FT9 8.10 MC
FT9 8.10 A&A
Students use the conditions for shapes to be congruent or similar. Similar triangles MZ9 p 407 (8.11)
p 412 (Computer
investigation)
FT9 8.11 SA
FT9 8.11 MC
FT9 8.11 A&A
Investigating shapes
Students use the conditions for shapes to be congruent or similar. They
apply isometric and similarity transformations of geometric shapes in
the plane
Design, creativity and technology/ Investigating and designing They
seek information to help their design thinking and identify the needs of
a variety of client groups. When designing, they generate a range of
alternative possibilities and justify their preferred option, explaining
how it provides a solution to the problem, need or opportunity
Design, creativity and technology/Producing They make
products/systems that meet the quality, aesthetic, functionality and
performance requirements outlined in the design brief.
Design, creativity and technology/Analysing and evaluating They use
a range of suitable testing methods to analyse and evaluate their
products/systems
Investigation of shapes MZ9 p 412 (VELS Design
Task)
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Page 70 of 84
Unit 9: Quadratic functions Level: A Dimensions: Structure Time: 4 weeks
VELS standards Course Heinemann references Assessment
Basic introduction to
parabolas and quadratics
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Quadratic relationships MZ9 p 423 (9.1 Q1–5) FT9 9.1 SA
FT9 9.1 MC
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Plotting parabolas MZ9 p 428 (9.2 Q1–6) FT9 9.2 SA
FT9 9.2 MC
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Using a parabolic nomogram MZ9 p 433 (Investigation)
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (e.g., exact and
approximate measurement formulas for the volumes of various three
dimensional objects such as truncated pyramids). They generalise from
one situation to another, and investigate it further by changing the
initial constraints or other boundary conditions.
Thinking/Reflection, evaluation and metacognition When reviewing
information and refining ideas and beliefs, students explain conscious
Parabolas by locus means (e.g.
folding)
MZ9 p 455 (Investigation)
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Page 71 of 84
VELS standards Course Heinemann references Assessment
changes in their own and others’ thinking and analyse alternative
perspectives and perceptions. They use explicit terms to discuss their
thinking, select and use thinking processes and tools appropriate to
particular tasks, and evaluate their effectiveness
They identify points that are invariant under a given transformation
(e.g., the point (2, 0) is invariant under reflection in the x-axis, so the x
axis intercept of the graph of y = 2x − 4 is also invariant under this
transformation).
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Parabolas and transformations MZ9 p 434 (9.3 Q1–6) FT9 9.3 SA
FT9 9.3 MC
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Page 72 of 84
Unit 9: Quadratic functions Level: B Dimensions: Structure Time: 4 weeks
VELS standards Course Heinemann references Assessment
Basic introduction to
parabolas and quadratics
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Quadratic relationships MZ9 p 423 (9.1 Q1–7) FT9 9.1 SA
FT9 9.1 MC
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Plotting parabolas MZ9 p 428 (9.2) FT9 9.2 SA
FT9 9.2 MC
FT9 9.2 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Using a parabolic nomogram MZ9 p 433 (Investigation)
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (e.g., exact and
approximate measurement formulas for the volumes of various three
dimensional objects such as truncated pyramids). They generalise from
one situation to another, and investigate it further by changing the
initial constraints or other boundary conditions.
Thinking/Reflection, evaluation and metacognition When reviewing
information and refining ideas and beliefs, students explain conscious
Parabolas by locus means (e.g.
folding)
MZ9 p 455 (Investigation)
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Page 73 of 84
VELS standards Course Heinemann references Assessment
changes in their own and others’ thinking and analyse alternative
perspectives and perceptions. They use explicit terms to discuss their
thinking, select and use thinking processes and tools appropriate to
particular tasks, and evaluate their effectiveness
Solving quadratic equations
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Null factor law MZ9 p 442 (9.4 Q1–8) FT9 9.4 SA
FT9 9.4 MC
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Finding the solution to quadratic
equations
MZ9 p 446 (9.5 Q1–6) FT9 9.5 SA
FT9 9.5 MC
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (e.g., exact and
approximate measurement formulas for the volumes of various three
dimensional objects such as truncated pyramids). They generalise from
one situation to another, and investigate it further by changing the
initial constraints or other boundary conditions. They judge the
reasonableness of their results based on the context under
consideration.
Solving problems involving
quadratics
MZ9 p 457 (9.7Q1–8) FT9 9.7 SA
FT9 9.7 MC
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Page 74 of 84
VELS standards Course Heinemann references Assessment
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Graphing quadratics
They identify points that are invariant under a given transformation
(e.g., the point (2, 0) is invariant under reflection in the x-axis, so the x
axis intercept of the graph of y = 2x − 4 is also invariant under this
transformation).
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Parabolas and transformations MZ9 p 434 (9.3)
p 441 (Problem solving)
FT9 9.3 SA
FT9 9.3 MC
FT9 9.3 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Sketching parabolas MZ9 p 449 (9.6 Q1–7)
p 454 (Graphics calculator
investigation)
p 460 (VELS Design
Task) p 461
(Maths@Work)
FT9 9.6 SA
FT9 9.6 MC
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Page 75 of 84
Unit 9: Quadratic functions Level: C Dimensions: Structure Time: 4 weeks
VELS standards Course Heinemann references Assessment
Basic introduction to
parabolas and quadratics
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Quadratic relationships MZ9 p 423 (9.1 ) FT9 9.1 SA
FT9 9.1 MC
FT9 9.1 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Plotting parabolas MZ9 p 428 (9.2) FT9 9.2 SA
FT9 9.2 MC
FT9 9.2 A&A
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Using a parabolic nomogram MZ9 p 433 (Investigation)
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Page 76 of 84
VELS standards Course Heinemann references Assessment
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (e.g., exact and
approximate measurement formulas for the volumes of various three
dimensional objects such as truncated pyramids). They generalise from
one situation to another, and investigate it further by changing the
initial constraints or other boundary conditions.
Thinking/Reflection, evaluation and metacognition When reviewing
information and refining ideas and beliefs, students explain conscious
changes in their own and others’ thinking and analyse alternative
perspectives and perceptions. They use explicit terms to discuss their
thinking, select and use thinking processes and tools appropriate to
particular tasks, and evaluate their effectiveness
Parabolas by locus means (e.g.
folding)
MZ9 p 455 (Investigation)
Solving quadratic equations
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Null factor law MZ9 p 442 (9.4) FT9 9.4 SA
FT9 9.4 MC
FT9 9.4 A&A
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Finding the solution to quadratic
equations
MZ9 p 446 (9.5) FT9 9.5 SA
FT9 9.5 MC
FT9 9.5 A&A
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Page 77 of 84
VELS standards Course Heinemann references Assessment
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (e.g., exact and
approximate measurement formulas for the volumes of various three
dimensional objects such as truncated pyramids). They generalise from
one situation to another, and investigate it further by changing the
initial constraints or other boundary conditions. They judge the
reasonableness of their results based on the context under
consideration.
They solve equations of the form f(x) = k, where k is a real constant
(e.g., x(x + 5) = 100) and simultaneous linear equations in two
variables (e.g., {2x − 3y = −4 and 5x + 6y = 27} using algebraic,
numerical (systematic guess, check and refine or bisection) and
graphical methods.
Solving problems involving
quadratics
MZ9 p 457 (9.7) FT9 9.7 SA
FT9 9.7 MC
FT9 9.7 A&A
Graphing quadratics
They identify points that are invariant under a given transformation
(e.g., the point (2, 0) is invariant under reflection in the x-axis, so the x
axis intercept of the graph of y = 2x − 4 is also invariant under this
transformation).
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Parabolas and transformations MZ9 p 434 (9.3)
p 441 (Problem solving)
FT9 9.3 SA
FT9 9.3 MC
FT9 9.3 A&A
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
Sketching parabolas MZ9 p 449 (9.6)
p 454 (Graphics calculator
p 460 (VELS Design
Task)
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Page 78 of 84
VELS standards Course Heinemann references Assessment
coordinate system) with consideration of independent and dependent
variables, domain and range.
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
investigation) p 461
(Maths@Work)
FT9 9.6 SA
FT9 9.6 MC
FT9 9.6 A&A
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Page 79 of 84
Unit 10: Probability Level: A Dimensions: Measurement, chance and data Time: 4 weeks
VELS standards Course Heinemann references Assessment
Probability
Students estimate probabilities based on data (experiments, surveys,
samples, simulations) and assign and justify subjective probabilities in
familiar situations.
Use of long-run relative
frequency to estimate
proportion and probability,
expressed as fraction, decimal
or percentage
MZ9 p 371 (10.1 Q1–7) FT9 10.1 SA
FT9 10.1 MC
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables).
One-step experiments and
equally likely outcomes:
listing outcomes
MZ9 p 474 (10.2) FT9 10.2 SA
FT9 10.2 MC
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Theoretical probability MZ9 p 478 (10.3) FT9 10.3 SA
FT9 10.3 MC
FT9 10.3 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Complementary events MZ9 p 478 (10.3) FT9 10.3 SA
FT9 10.3 MC
FT9 10.3 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Multiple events MZ9 p 485 (10.4 Q1–4), FT9 10.14 SA
FT9 10.4 MC
They list event spaces (for combinations of up to three events) by lists, Mutually exclusive events MZ9 p 491 (10.5 Q1–8) MZ9 p 496 (VELS
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 80 of 84
VELS standards Course Heinemann references Assessment
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Design Task)
FT9 10.5 SA
FT9 10.5 MC
They generate data using surveys, experiments and sampling
procedures.
Simulation MZ9 p 500 (10.6 Q1–3) FT9 10.6 SA
FT9 10.6 MC
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 81 of 84
Unit 10: Probability Level: B Dimensions: Measurement, chance and data Time: 4 weeks
Course Heinemann references Assessment
Students estimate probabilities based on data (experiments, surveys,
samples, simulations) and assign and justify subjective probabilities in
familiar situations.
Use of long-run relative
frequency to estimate
proportion and probability,
expressed as fraction, decimal
or percentage
MZ9 p 371 (10.1 Q1–11) FT9 10.1 SA
FT9 10.1 MC
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables).
One-step experiments and
equally likely outcomes:
listing outcomes
MZ9 p 474 (10.2) FT9 10.2 SA
FT9 10.2 MC
FT9 10.2 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Theoretical probability MZ9 p 478 (10.3)
p 483 (Computer
investigation)
FT9 10.3 SA
FT9 10.3 MC
FT9 10.3 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Complementary events MZ9 p 478 (10.3) FT9 10.3 SA
FT9 10.3 MC
FT9 10.3 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Multiple events MZ9 p 485 (10.4 Q1–8)
p 489 (Graphics calculator
investigation)
FT9 10.4 SA
FT9 10.4 MC
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
Mutually exclusive events MZ9 p 491 (10.5 Q1–9)
p 497 (Maths in Action)
MZ9 p 496 (VELS
Design Task)
FT9 10.5 SA
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Page 82 of 84
Course Heinemann references Assessment
exclusive, and compound events (defined using and, or and not). FT9 10.5 MC
They generate data using surveys, experiments and sampling
procedures.
Simulation MZ9 p 500 (10.6 ) FT9 10.6 SA
FT9 10.6 MC
FT9 10.6 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 83 of 84
Unit 10: Probability Level: C Dimensions: Measurement, chance and data Time: 4 weeks
VELS standards Course Heinemann references Assessment
Students estimate probabilities based on data (experiments, surveys,
samples, simulations) and assign and justify subjective probabilities in
familiar situations.
Use of long-run relative
frequency to estimate
proportion and probability,
expressed as fraction, decimal
or percentage
MZ9 p 371 (10.1) FT9 10.1 SA
FT9 10.1 MC
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables).
One-step experiments and
equally likely outcomes:
listing outcomes
MZ9 p 474 (10.2) FT9 10.2 SA
FT9 10.2 MC
FT9 10.2 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Theoretical probability MZ9 p 478 (10.3)
p 483 (Computer
investigation)
FT9 10.3 SA
FT9 10.3 MC
FT9 10.3 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Complementary events MZ9 p 478 (10.3) FT9 10.3 SA
FT9 10.3 MC
FT9 10.3 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
Multiple events MZ9 p 485 (10.4)
p 489 (Graphics calculator
investigation)
FT9 10.4 SA
FT9 10.4 MC
FT9 10.4 A&A
They list event spaces (for combinations of up to three events) by lists,
grids, tree diagrams, Venn diagrams and Karnaugh maps (two-way
Mutually exclusive events MZ9 p 491 (10.5)
p 497 (Maths in Action)
MZ9 p 496 (VELS
Design Task)
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)
Page 84 of 84
VELS standards Course Heinemann references Assessment
tables). They calculate probabilities for complementary, mutually
exclusive, and compound events (defined using and, or and not).
p 503 (Problem solving) FT9 10.5 SA
FT9 10.5 MC
FT9 10.5 A&A
They generate data using surveys, experiments and sampling
procedures.
Simulation MZ9 p 500 (10.6 ) FT9 10.6 SA
FT9 10.6 MC
FT9 10.6 A&A
Heinemann Maths Zone 9 VELS Edition Copyright © Pearson Australia (a division of Pearson Australia Pty Ltd)