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ESSENTIAL MATHEMATICS FOR THE AUSTRALIAN CURRICULUM SECOND EDITION

DAVID GREENWOOD | BRYN HUMBERSTONE JUSTIN ROBINSON | JENNY GOODMAN JENNIFER VAUGHAN | STUART PALMER Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Introduction This second edition of Essential Mathematics for the Australian Curriculum has been developed into a complete resources pack comprising a revised and updated print textbook, a new interactive textbook with a host of cutting-edge features, and an online teaching suite. The successful elements of the first edition have been retained and improved upon. These include: t
logical sequencing of chapters and development of topics t
careful structuring of exercises according to the four Australian Curriculum proficiency strands (Understanding, Fluency, Problem-solving, Reasoning) plus Enrichment t
graduated difficulty of exercise questions within the overall exercise and within proficiency groups t
Let’s Start and Key Ideas to help introduce concepts and key skills. Additions and revisions to the text include: t
new topics reflecting updates to the Australian Curriculum and state syllabuses t
Revision and Extension topics marked as ‘Consolidating’ or ‘Extending’ to help customise the course to the needs of each classroom t
working programs embedded in each exercise to differentiate three student pathways: Foundation, Standard and Advanced t
‘Progress quiz’ placed approximately two-thirds of the way into each chapter, allowing students to check and consolidate their learning – in time to address misunderstandings or weaknesses prior to completing the chapter t
pre-tests revised and moved to the interactive textbook. Features of the all-new interactive textbook: t
seamlessly blended with Cambridge HOTmaths, allowing enhanced learning opportunities in blended classrooms, revision of previous years’ work, and access to Scorcher t
all worked examples linked to a high-quality video demonstration, supporting both in-class learning and the ‘flipped classroom’ t
searchable dictionary of mathematical terms and pop-up definitions in the text t
hundreds of interactive widgets, walkthroughs and games t
automatically-marked quizzes and assessment tests, with saved scores t
printable worksheets (HOTsheets) suitable for homework or class group work. Features of the online teaching suite, also powered by Cambridge HOTmaths: t
test generator, with ready-made tests t
printable worked solutions for all questions t
powerful learning management system with task-setting, progress-tracking and reporting functions. The information on the next pages shows how the components of this resource are integrated.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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UNDERSTANDING

The working programs that were previously available in separate supporting documents have been updated, refined and subtly embedded in the exercises for this second edition of Essential Mathematics for the Australian Curriculum. The suggested working programs provide three pathways through the course to allow differentiation for Foundation, Standard and Advanced students. As with the first edition, each exercise is structured in subsections that match the four Australian Curriculum proficiency strands (Understanding, Fluency, Problem-solving and Reasoning) as well as Enrichment (challenge). The questions* Foundation Standard Advanced suggested for each pathway are listed in 1–2 2 — three columns at the top of each subsection.

The working programs make use of the The working program for Exercise 3A in Year 7 gradients that have been carefully and (see pages 106-108) considerately written into the exercises. A gradient runs through the overall structure of each exercise – where there is an increasing level of mathematical sophistication required from Understanding through to Reasoning and Enrichment – but also within each proficiency strand; the first few questions in Fluency, for example, are easier than the last few, and the last Problem-solving question is more challenging than the first Problem-solving question.

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For question 9, try estimating by roundng the values in the question.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

For question 14, try using algebra as a tool: define the pronumerals, form an equation and then solve it.

For question 15, try using concrete, everyday materials to represent the problem.

For question 16, try applying one or more mathematical procedures, such as a rule for adding fractions.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

1

Whole numbers

Chapter

What you will learn

Australian curriculum

1A 1B 1C 1D

NUMBER AND ALGEBRA

Number systems (Extending) Place value (Consolidating) Addition and subtraction Addition and subtraction algorithms 1E Multiplication 1F Multiplying larger numbers 1G Division 1H Estimating and rounding (Consolidating) 1I Order of operations 

Essential Mathematics for the Australian Curriculum Year 7 2ed

Number and place value 16x16 Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

32x

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Whole numbers in the ancient world and now Whole numbers and number systems have been used for thousands of years to help count objects and record information. In ancient Egypt in about 3000 BCE if one hundred and twentyfour blocks of stone were needed to build a monument, this number would have been represented as Today we use whole numbers to help deal with all sorts of situations.

Essential Mathematics for the Australian Curriculum Year 7 2ed

Here are some examples: • Recording the number of points in a game • Calculating the number of pavers required for a terrace • Counting the number of items purchased at a shop • Tallying the number of votes in an election • Calculating the approximate distance between two towns.

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

3

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

2 × 100 + 7 × 10 + 3 × 1 is the expanded form of 273.

The place value of 3 in 1327 is 300.

Place value

Ancient number systems (Ext)

Addition and subtraction

Roman LXXVI is 76 XCIV is 94

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Mental strategies 172 + 216 = 300 + 80 + 8 = 388 98 − 19 = 98 − 20 + 1 = 79

Egyptian is 21 is 143

Order of operations Brackets first, then × and ÷, then + and − from left to right. 2 + 3 × 4 ÷ (9 ÷ 3) = 2 + 12 ÷ 3 =2+4 =6

Algorithms 2

29 ×____ 13 87 290 ____ 377

Estimation

955 to the nearest 10 is 960 950 to the nearest 100 is 1000

Essential Mathematics for the Australian Curriculum Year 7 2ed

Multiplication and division

Whole numbers

Leading digit approximation 39 × 326 ≈ 40 × 300 = 12 000

68 3 2025 with 1 remainder

Mental strategies 7 × 31 = 7 × 30 + 7 × 1 = 217 5 × 14 = 5 × 2 × 7 = 70 64 ÷ 8 = 32 ÷ 4 = 16 ÷ 2 = 8 156 ÷ 4 = 160 ÷ 4 − 4 ÷ 4 = 40 − 1 = 39

Multiplying by 10, 100, …… 38 × 100 = 3800 38 × 700 = 38 × 7 × 100 = 26 600

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2

Geometry

Chapter

What you will learn

Australian curriculum

2A Points, lines and angles (Consolidating) 2B Measuring angles (Consolidating) 2C Angles at a point 2D Transversal lines and parallel lines 2E Problems with parallel lines (Extending) 2F Circles and constructions 2G Dynamic geometry

MEASUREMENT AND GEOMETRY

Essential Mathematics for the Australian Curriculum Year 7 2ed

Geometric reasoning Identify corresponding, alternate and cointerior angles when two parallel straight lines are crossed by a transversal (ACMMG163) Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)

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Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Thales, pyramids and the solar eclipse From the Egyptian pyramids to modern architecture, points, lines and angles are everywhere. Geometry is a very visual element of mathematics where the designs of buildings and the orbits of planets can be studied using basic objects like points, lines and circles. Thales (624–546 BCE) is known to be the founder of Greek geometry. He was an astronomer and philosopher, and records show he was the first person to

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use mathematical geometry to calculate the height of an Egyptian pyramid using the sun’s rays and to accurately predict the timing of a solar eclipse.

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Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Chapter

3

Number properties and patterns

What you will learn

Australian curriculum

3A Factors and multiples (Consolidating) 3B Highest common factor and lowest common multiple (Consolidating) 3C Divisibility (Extending) 3D Prime numbers 3E Powers 3F Prime decomposition 3G Squares and square roots 3H Number patterns (Consolidating) 3I Spatial patterns 3J Tables and rules 3K The number plane and graphs

NUMBER AND ALGEBRA

Essential Mathematics for the Australian Curriculum Year 7 2ed

Number and place value Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149) Investigate and use square roots of perfect square numbers (ACMNA150) Linear and non-linear relationships Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178) 16x16 and analyse graphs from32x32 Investigate, interpret authentic data (ACMNA180)

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Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Number patterns around us: Architecture The Louvre Palace in Paris is the world’s largest museum and is visited by over 8 million people a year. Visitors enter the museum through a giant glass pyramid that has a square base of length 35.4 metres and is 21.6 metres in height. It is said that the pyramid contains 666 glass panels. To carefully count the number of glass panels, we can observe how the sides of the pyramid are constructed. Each triangular side of the pyramid has 17 rows of rhombus-shaped glass panels. The base row is joined to

Essential Mathematics for the Australian Curriculum Year 7 2ed

the ground by triangular-shaped glass panels. The trapezium-shaped entry has a height of one rhombus and a width of six triangles. The number of glass panels used in the Louvre Pyramid can be determined using these facts and the related properties and patterns. Each rhombus panel is supported by four segments of steel. Adjacent rhombuses share the ame steel segment for support. The number of steel segments per row can be calculated, as well as the total number of steel segments used.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

JOQVU     

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

 

   

 

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

x

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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&/3*$).&/5

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB

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Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Composite numbers 10: factors 1, 2, 5, 10 62: factors 1, 2, 31, 62 Composite numbers are not prime.

Multiples

Factor trees

Multiples are ³ number 20: 20, 40, 60, 80, ... 15: 15, 30, 45, 60, 75, ... Lowest common multiple LCM = 60

90 9 3

10 3

2

5

90 = 2 × 3 × 3 × 5 90 = 2 × 32 × 5

Factors are £ number 20: 1, 2, 4, 5 , 10, 20 15: 1, 3, 5 , 15 Highest common factor HCF = 5

base number

Powers

Factors

Number properties

243 = 3 × 3 × 3 × 3 × 3 = 35 basic numeral

index index number form

expanded form

First 10 square numbers

Square number 16 = 4 × 4 = 42 25 = 5 × 5 = 52 Prime numbers A prime number only has two factors: 1 and itself. 5: factors 1 and 5 17: factors 1 and 17

√16 = 4 √25 = 5

Divisibility tests (Ext)

dividend→ 52 1 divisor→ 3 = 173

remainder

quotient 52 = 3 × 17 + 1

Essential Mathematics for the Australian Curriculum Year 7 2ed

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Square root

Division 1 is not a prime number.



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2: last digit even (0, 2, 4, 6, 8) 3: sum digits ÷ 3 4: number from last two digits ÷ 4 5: last digit 0 or 5 6: ÷ by 2 and 3 8: number from last 3 digits ÷ 8 9: sum digits ÷ 9 10: last digit 0

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Sequence 2, 4, 6, 8, ... ↑↑↑ ↑ terms

Common difference of minus 3 100, 97, 94, ... Common ratio of times 2 3, 6, 12, 24, ... Pair differences increase by 3 6, 7, 11, 18, 28, ...

Number patterns

Rules, graphs and tables show a relation between two quantities that can vary.

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Rule: Number of sticks = 4 times the number of diamonds input output

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Sam = Mikaela + 5

Sam is 5 years older than his sister Mikaela Mikaela’s Mikael ’s age Sam’s age

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Essential Mathematics for the Australian Curriculum Year 7 2ed

This dot is represented by the coordinates (2, 4) 1 2 3 4 5

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the horizontal, x-axis

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Chapter

4

What you will learn

4A What are fractions? (Consolidating) 4B Equivalent fractions and simplified fractions 4C Mixed numbers (Consolidating) 4D Ordering fractions 4E Adding fractions 4F Subtracting fractions 4G Multiplying fractions 4H Dividing fractions 4I Fractions and percentages 4J Percentage of a number 4K Expressing a quantity as a proportion

Essential Mathematics for the Australian Curriculum Year 7 2ed

Fractions and percentages Australian curriculum NUMBER AND ALGEBRA

Real numbers Compare fractions using equivalence. Locate and represent fractions and mixed numerals on a number line (ACMNA152) Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153) Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154) Express one quantity as a fraction of another with and without the use of digital technologies (ACMNA155) Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157) Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158) Recognise and solve problems involving simple ratios. (ACMNA173) Money and financial mathematics Investigate and calculate ‘best buys’, with and without digital 32x32 16x16 technologies (ACMNA174)

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Ancient Egyptian fractions The ancient Egyptians used fractions over 4000 years ago. The Egyptian sky god Horus was a falcon-headed man whose eyes were believed to have magical healing powers. Egyptian jewellery, ornaments or clothing decorated with the Eye of Horus design were regarded as good luck charms for health and magical protection from evil. The six parts in the Eye of Horus design represent the six ways that information enters the brain. These six different parts or symbols represented the six fractions used by ancient Egyptian mathematics. For example,

1 , Egyptians would write 2 1 instead of writing they would write 8

instead of writing

, and .

Eye of Horus fraction symbols are found in ancient Egyptian medical prescriptions for mixing ‘magical’ medicine. Amazingly, modern doctors still use the eye of Horus ( ) symbolism when they write (Rx) at the start of a prescription. ISBN 978-1-107-56882-2 Essential Mathematics for the Australian Curriculum Year 7 2ed

1 thought (eyebrow closest to brain) 8

1 hearing (pointing to ear) 16 1 smell (pointing to nose) 2 1 sight (pupil of the eye) 4 1 touch (leg touching the ground) 64 1 taste (curled top of wheat plant) 32

A proportion or fraction can be written using a combination of these symbols. For example:

3 = 4 3 = 16

and .

Which symbols would represent

1 7 ? Can be 3 8

written using the Eye of Horus symbols?

© Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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First, you cut two loaves in half and give half a loaf to each of your four customers.

You have one loaf remaining and you can cut that into quarters (i.e. half and then half again).

3 So each of your four customers now receives half a loaf and one-quarter of a loaf, which is ( 4 of a loaf.

Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

2 parts selected

Equivalent fractions

numerator denominator

2 5

50 100

30 60

=

21 42

=

=

8 16

1 2

=

simplest form 5 parts in the whole 1 100

1% = 3 4

proper fraction

10 7

improper fraction

3 4

mixed numeral 5

Fractions mixed 10 5

=

3 5

+

=

13 5

improper

=

1 10

75% =

75 100

=

3 4

20% =

20 100

=

1 5

80% =

80 100

=

4 5

25% =

25 100

=

1 4

100% =

= 2 10 = 2 23 15

40 15

=

=7÷7=1

or

5×8 5×3

8 3

=

HCF of 42 and 63 is 21.

= 2 23

42 63

=

7×6 7×9

42 63

=

21 × 2 21 × 3

4 5

+

2 3

=

12 15

+

10 15

=

22 15

7 = 1 15

Multiplying fractions 5 10

= =

Subtracting fractions Or

2 1 34 − 13

1 23

= (2 − 1) + ( =1+(

=1

−

5 4

− 23 )

8 ) 12

7 = 1 12

Essential Mathematics for the Australian Curriculum Year 7 2ed

of

20 50

5 1 20 2 × 10 50 5 1 2 5

3 15

×

2 14

=

16 4 9 × 1 4 5

=

36 5

=

−

5 3

=

39 12

−

20 12

=

39 − 20 12

=

19 12

Percentage of a quantity 25% of $40 120% of 50 minutes = 1 × 40 = $10 7

= 1 12

=

120 × 100 2

=

=

3×2 3×3

=

2 3

2 3

50

?

3 4

5 8

<

6 8

1 1 46 ÷ 19

= =

1

5 8

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=

4

6 9

8 is the lowest common denominator (LCD) which is the lowest common multiple (LCM) of 4 and 8.

= 7 15

2 1 34 − 13 13 4

=

Comparing fractions

Adding fractions

15 12

100 100

Simplify

mixed

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−

1 2

10 100

Operation with fractions

=

=

10% =

Recall 7 7

2 54

50 100

improper

2 35

or

50% =



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=

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÷

10 9

25 5 9 3 × 6 2 10 2 15 4 3 34

Reciprocal of

10 9

is

9 10

= 60 minutes = 1 hour

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Chapter

5

Algebra

What you will learn

Australian curriculum

5A 5B 5C 5D 5E

NUMBER AND ALGEBRA

Introduction to algebra Substituting and evaluating Equivalent expressions Like terms Multiplying and dividing expressions 5F Expanding brackets (Extending) 5G Algebraic modelling (Extending)

Essential Mathematics for the Australian Curriculum Year 7 2ed

Patterns and algebra Introduce the concept of variables as a way of representing numbers using letters (ACMNA175) Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176) 16x16 to Extend and apply the laws and properties of arithmetic algebraic terms and expressions (ACMNA177)

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

32x

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Designing robots Algebra provides a way to describe everyday activities using mathematics alone. By allowing letters like x or y to stand for unknown numbers, different concepts and relationships can be described easily. Engineers apply their knowledge of algebra and geometry to design buildings, roads, bridges, robots, cars, satellites, planes, ships and hundreds of other structures and devices that we take for granted in our world today. To design a robot, engineers use algebraic rules to express the relationship between the position of the robot’s ‘elbow’ and the possible positions of a robot’s ‘hand’. Although they cannot think for themselves, electronically

Essential Mathematics for the Australian Curriculum Year 7 2ed

programmed robots can perform tasks cheaply, accurately and consistently, without ever getting tired or sick or injured, or the need for sleep or food! Robots can have multiple arms, reach much farther than a human arm and can safely lift heavy, awkward objects. Robots are used extensively in car manufacturing. At one plant that uses robots and humans, a finished car comes off the assembly line every 76 seconds. Understanding and applying mathematics has made car manufacturing safer and also extremely efficient.

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3



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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/VNCFS BOE "MHFCSB

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Pronumerals are letters used to represent numbers g: number of grapes in a bunch d: distance travelled (in metres)

Creating expressions 6 more than k: k + 6 Product of 4 and x : 4x 10 less than b: b − 10 q Half of q: 2 The sum of a and b is tripled: 3(a + b)

Terms are pronumerals and numbers combined with ×, ÷ e.g. 4x, 10y, 3a , 12 3a means 3 × a b means b ÷ 10 10

Algebraic expressions

Like terms have exactly the same pronumerals. 5a and 3a 2ab and 12ba 7ab and 2a

Combination of numbers, pronumerals and operations, e.g. 2xy + 3yz, 12 −3 x

Equivalent expressions

Algebra

Always equal when pronumerals are substituted. e.g. 2x + 3 and 3 + 2x are equivalent. 4(3x) and 12x are equivalent.

To simplify an expression, find a simpler expression that is equivalent. Applications (Ext)

Expanding brackets (Ext) 3(a + 4) = 3a + 12 5k(10 − 2j ) = 50k − 10kj Using the distributive law gives an equivalent expression.

Essential Mathematics for the Australian Curriculum Year 7 2ed

Substitution Replacing pronumerals with values. e.g. 5x + 2y when x =10 & y = 3 becomes 5(10) + 2(3) = 50 + 6 = 56 e.g. q2 when q = 7 becomes 72 = 49

Combining like terms gives a way to simplify. e.g. 4a + 2 + 3a = 7a + 2 3b + 5c + 2b − c = 5b + 4c 12xy + 3x − 5yx = 7xy + 3x

Commonly used expressions A= l×w P = 2l + 2w w l Cost is 50 + 90x call-out fee

hourly rate

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Chapter

6

Decimals

What you will learn

Australian curriculum

6A Decimals and place value (Consolidating) 6B Rounding decimals 6C Addition and subtraction of decimals (Consolidating) 6D Multiplying and dividing by powers of 10 6E Multiplication of decimals 6F Division of decimals 6G Decimals and fractions 6H Decimals and percentages

NUMBER AND ALGEBRA

Real numbers Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154) Round decimals to a specified number of decimal places (ACMNA156) Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157) Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158) Money and financial mathematics 32x32 16x16 Investigate and calculate ‘best buys’, with and without digital technologies (ACMNA174)

Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Swimming records and decimal places Swimming times are electronically measured and recorded with the seconds given to 2 decimal places. Accuracy is very important so that the right decision is made for placegetters and records. Sometimes winners are separated by as little as one-hundredth of a second. Ian Thorpe, who set 13 world records, had his 400 m freestyle record (3:40.06) broken in 2009 by German swimmer Paul Biedermann, who swam only 0.01 of a second faster than Thorpe. The decimal system allows us to express quantities with great accuracy.

Essential Mathematics for the Australian Curriculum Year 7 2ed

There are many instances in our everyday lives in which accuracy of measurement is highly important. For example, bicycle, car and aeroplane parts must be manufactured to precise measurements; medicine production requires measurement of chemicals in precise quantities; and investment rates, stock market prices and values are measured to many decimal places (8% per year equals 0.153 846% per week). Can you think of any other quantities that require decimal measurement?

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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534 × 12 1068 5340 6408

decimal points ignored here 5.34 × 1.2 = 6.408

3 decimal places in the answer

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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∴ 0.192 × 100 = 19.2 Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB

Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.

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Changing decimals to fractions 16 4 = 25 100 8 1 2 1000 = 2 125

0.16 = 2.008 =

Comparing decimals 12.3 > 12.1 6.72 < 6.78 0.15 ≠ 0.105 284.7 ≤ 284.7

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= =

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2.34 | 2 2.34 2.34 | 5 2.35 2.34 | 6 2.35 5.89 | 9 5.90 5.99 | 7 6.00 If critical digit is ≥ 5 round up. If critical digit is < 5 round down.

Decimals

Subtraction 1

1

216.94 − 31.53 185.41 Align decimal points.

Addition 1

9.807 + 26.350 36.157 1

Multiplication 278 × 34 1112 8340 9452 2.78 × 34 = 94.52 2.78 × 3.4 = 9.452 0.278 × 3.4 = 0.9452 0.278 × 0.34 = 0.094 52

Align decimal points.

Division by powers of 10 2.76 ÷ 10 000 = 0.000276 Decimal point moves left.

Division 8.547 ÷ 0.03 = 854.7 ÷ 3 284.9 2 1 2

3 854.7

Number of decimal places in the question equals number of decimal places in the answer.

Multiplication by powers of 10 2.76 × 10 000 = 27 600.0 Decimal point moves right.

Fractions to decimals 13 100

Decimals and percentage 0.63 = 63 ÷ 100 = 63% 8% = 8 ÷ 100 = 0.08 240% = 240 ÷ 100 = 2.4

Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Chapter

7

Negative numbers

What you will learn

Australian curriculum

7A Integers (Consolidating) 7B Adding and subtracting positive integers 7C Adding and subtracting negative integers 7D Multiplication and division of integers (Extending) 7E Order of operations (Extending) 7F Substituting integers (Extending) 7G The number plane

NUMBER AND ALGEBRA

Essential Mathematics for the Australian Curriculum Year 7 2ed

Number and place value Compare, order, add and subtract integers (ACMNA280) Linear and non-linear relationships 16x16 Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)

32x32

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

The coldest place on Earth The coldest place on Earth is Antarctica, where maximum daily temperatures below 0° Celsius are commonplace. The coldest temperature ever recorded on Earth was about –89°C in 1983 at the Russian Vostok Station in Antarctica. Temperatures on the coast of Antarctica can reach 15°C in summer but average temperatures are generally below 0°C. A layer of ice surrounds and covers almost all of the continent.

Essential Mathematics for the Australian Curriculum Year 7 2ed

The surrounding ice sits both above and below sea level, making it very difficult for ships to reach their destinations. Like the temperature scale, heights above and below sea level can be recorded using both positive and negative numbers.

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



 

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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/VNCFS BOE "MHFCSB



 

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Adding and subtracting positive integers −3 + 5 = 2 −4 + 3 = −1 5 − 7 = −2 −1 −10 = −11

Number line negative

positive

−3 −2 −1 0 −2 < 3

1

2 + (−3) = 2 − 3 = −1 −5 + (−4) = −5 − 4 = −9 4 − (−3) = 4 + 3 = 7 −10 − (−6) = −10 + 6 = −4

2 3 1 > −1

Cartesian plane y

Multiplication (Ext)

3 2 (0, 2) (3, 1) 1

(−3, 0)

−3 −2 −1−1O (−2, −2) −2 −3

1 2 3

Adding and subtracting negative integers

x

Integers …, −3, −2, −1, 0, 1, 2, 3, …

2×3=6 2 × (−3) = −6 −2 × 3 = −6 −2 × (−3) = 6

(1, −2)

Substitution (Ext)

Division (Ext)

If a = −2 and b = 4, then: b − a = 4 − (−2) = 6 ab + 2a = −2 × 4 + 2 × (−2) = −8 + (−4) = −12

10 ÷ 5 = 2 10 ÷ (−5) = −2 −10 ÷ 5 = −2 −10 ÷ (−5) = 2 Order of operations (Ext) First brackets, then × or ÷ then + or −, from left to right. 3 × (5 − (−2)) + 8 ÷ (−4) = 3 × 7 + (−2) = 21 + (−2) = 19

Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Chapter

8

Statistics and probability

What you will learn

Australian curriculum

8A Collecting and classifying data 8B Summarising data numerically 8C Dot plots and column graphs 8D Line graphs 8E Stem-and-leaf plots 8F Pie charts and divided bar graphs (Extending) 8G Describing chance (Consolidating) 8H Theoretical probability 8I Experimental probability (Extending)

S TAT I S T I C S A N D P R O B A B I L I T Y

Chance Construct sample spaces for single-step experiments with equally likely outcomes (ACMSPA167) Assign probabilities to the outcomes of events and determine probabilities for events (ACMSPA168) Data representation and interpretation Identify and investigate issues involving continuous or large count data collected from primary and secondary sources (ACMSPA169) Construct and compare a range of data displays including stem-and-leaf plots and dot plots (ACMSPA170) Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSPA171) Describe and interpret data displays and the relationship between the median and mean (ACMSPA172) NUMBER AND ALGEBRA

Linear and non-linear relationships 32x32data 16x16and analyse graphs from authentic Investigate, interpret (ACMNA180) Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Codes and ciphers Cracking codes and deciphering secret messages involves a lot of maths, from simple addition and subtraction to data handling and logical thinking. One style of code replaces letters with symbols or pictures. This type of code was used in the sixteenth century by Mary Queen of Scots, when she was plotting against Queen Elizabeth I and sending coded messages about her plans to her co-conspirators. Unfortunately for Mary, there was a simple mathematical way of cracking the code. The letter ‘E’ is the most commonly used letter Essential Mathematics for the Australian Curriculum Year 7 2ed

in the English language. ‘T’ is the second most common letter and ‘A’ is the third most commonly used letter. All that Elizabeth’s spymaster had to do to crack the code was to look through the coded message and count the number of times each symbol came up. The symbol that came up the most would probably stand for the letter ‘E’. The next letter that occurred most often was probably ‘T’, and so forth. This method, called ‘frequency analysis’, gave the spymaster enough information to decode Mary’s messages and foil her plans.

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

4UBUJTUJDT BOE 1SPCBCJMJUZ



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

Distance (km)

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed





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Essential Mathematics for the Australian Curriculum Year 7 2ed

30 25 20 15 10 5 0

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Data types • Numerical e.g. number of people (discrete), height of trees (continuous) • Categorical e.g. colours, gender

Data collection • Primary source (firsthand) or secondary source (collected by someone else) • Census (whole population) or sample (selection)

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basketball

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angle = 360° ´ proportion

Statistics and probability

Summarising data numerically range = 10 - 1 = 9 1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10

Experimental probability (Ext) Use an experiment or survey or simulation to estimate probability. e.g. Spinner lands on blue 47 times out of 120 47 Experimental probability = 120

median = 5 mode = 4 (most common value) (middle value) sum of values mean = number of values 78 = = 5.2 15 Probability: how likely an event is unlikely 1 likely 0 1 2

Outcome: possible result of an experiment Event: either a single outcome or a collection of outcomes

impossible even chance more likely

Experiment/trial: e.g. roll a fair die Sample space: {1, 2, 3, 4, 5, 6} Pr(roll a 5) = 16 Pr(roll odd number) = 36 = 12

certain

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blue

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e.g. Roll die 36 times, expected number of 5s = Essential Mathematics for the Australian Curriculum Year 7 2ed

1 6

´ 36 = 6

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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9

Chapter

Polygons, solids and transformations

What you will learn

Australian curriculum

9A Polygons 9B Triangles 9C Constructing triangles (Extending) 9D Triangle angle sum 9E Quadrilaterals 9F Quadrilateral angle sum 9G Symmetry 9H Reflection and rotation 9I Translation 9J Drawing solids 9K Nets and the Platonic solids (Extending)

MEASUREMENT AND GEOMETRY

Essential Mathematics for the Australian Curriculum Year 7 2ed

Location and transformation Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (ACMMG181) Geometric reasoning Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165) Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166) Shape 32x32 16x16 Draw different views of prisms and solids formed from combinations of solids (ACMMG161)

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Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Crystals and viruses The geometry of shapes and solids occurs naturally in many forms. The way in which atoms and molecules are arranged in crystalline solids gives rise to three-dimensional (3D) shapes with flat surfaces and straight edges. These types of solids are called polyhedra. Some common crystal solids are based on the tetrahedron, cube and octahedron. These are examples of a special group of solids that are regular polyhedra, and are called the Platonic solids named

Essential Mathematics for the Australian Curriculum Year 7 2ed

after the Greek philosopher and mathematician Plato. They have faces that are identical, regular polygons. Early in the twentieth century, it was discovered that many viruses take the shape of regular polyhedra. A more modern example is the human immunodeficiency virus (HIV), which is enclosed by a layer of protein cells arranged in the shape of a regular icosahedron (i.e. a 20-sided regular polyhedron and Platonic solid).

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Type

Polygons irregular regular convex non-convex pentagon octogon

scalene

isosceles

Constructing triangles equilateral 60°

acute

right

Symmetry

• SSS • SAS • AAS • RHS

obtuse

Angle sum a°

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Polygons and transformations

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Transformations

Quadrilaterals

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Special quadrilaterals

A (-2, 3)

y

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• parallelogram - rectangle - rhombus - square • trapezium • kite Angle sum Translation

Rotation y

A

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

10

Chapter

Equations

What you will learn

Australian curriculum

10A Introduction to equations 10B Solving equations by inspection (Consolidating) 10C Equivalent equations 10D Solving equations algebraically 10E Equations with fractions (Extending) 10F Equations with brackets (Extending) 10G Formulas 10H Applications

NUMBER AND ALGEBRA

Essential Mathematics for the Australian Curriculum Year 7 2ed

16x16 Linear and non-linear relationships Solve simple linear equations (ACMNA179)

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32x32

Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Theme park equations Equations are used widely in mathematics and in many other fields. Whenever two things are equal, or should be equal, there is the potential to use the study of equations to help deal with such a situation. Knowledge of mathematics and physics is vitally important when designing theme park rides. Engineers use equations to ‘build’ model rides on a computer so that safety limits can be determined in a virtual reality in which nobody gets injured. Algebraic equations are solved to determine the dimensions and strengths of structures required Essential Mathematics for the Australian Curriculum Year 7 2ed

to deal safely with the combined forces of weight, speed and varying movement. Passengers might scream with a mixture of terror and excitement but they must return unharmed to earth! At Dreamworld on the Gold Coast, Queensland, ‘The Claw’ swings 32 people upwards at 75 km/h to a maximum height of 27.1 m (9 storeys), simultaneously spinning 360° at 5 r.p.m. (revolutions per minute). ‘The Claw’ is the most powerful pendulum ride on the planet. It is built to scare!

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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x + 2 = 11

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

/VNCFS BOE "MHFCSB



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.

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/VNCFS BOE "MHFCSB





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Essential Mathematics for the Australian Curriculum Year 7 2ed

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Solving an equation Finding pronumeral values to make equation true e.g. 15 + x = 20 solution: x = 5 Equivalent equations are obtained by performing the same operation to both sides e.g. 12 + 3x = 5 +8 +8 20 + 3x = 13

Formulas or rules are types of equations. e.g. F = ma, A = l × w, P = 4x

e.g.

e.g. e.g.

Equations

−5 3x + 5 = 38 −5 3x = 33 ÷3 x = 11 ÷3 ×4

To solve algebraically, use equivalent equations and opposite operations.

x 4

=7 ×4 x = 28

+ 2 5x − 2 = 33 +2 ÷ 5 5x = 35 ÷5 x=7

Main expression

First step

3x + 5 12x 5x − 2

−5 ÷12 +2 ×4

x 4

Brackets should be expanded and like items collected. Use the distributive law to expand. (Ext)

Equations with fractions are solved by multiplying by the denominator when fraction is by itself. (Ext)

e.g. e.g.

−2

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×7

e.g.

x 7

x 7

=4

=2

x = 14 3x + 9 4

−2 5(x + 3) + 2x = 29 5x + 15 + 2x = 29 −15 7x + 15 = 29 −15 7x = 14 ÷7 x = 2 ÷ 7

e.g.

×7

=6

×4 3x + 9 = 24 −9 −9 3x = 15 ÷3 x = 5 ÷3

×4

4(x + 2) = 4x + 8

Applications 1 2 3 4

Use a pronumeral for the unknown. Write an equation. Solve the equation. Answer the original question.

e.g. John’s age in 3 years will be 15. How old is he now? Let j = John’s current age in years j + 3 = 15 j + 3 = 15 −3 −3 j = 12 4 John is currently 12 years old. 1 2 3

Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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11

Measurement

Chapter

What you will learn

Australian curriculum

11A Measurement systems (Extending) 11B Using and converting metric lengths (Consolidating) 11C Perimeter (Consolidating) 11D Areas and rectangles 11E Area of a triangle 11F Area of a parallelogram 11G Area of composite shapes (Extending) 11H Volume of rectangular prisms 11I Capacity (Consolidating) 11J Mass and temperature (Consolidating)

MEASUREMENT AND GEOMETRY

Essential Mathematics for the Australian Curriculum Year 7 2ed

Using units of measurement Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159) Calculate volumes of rectangular prisms (ACMMG160) Shape 16x16 Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)

32x32

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Online resources • Chapter pre-test • Videos of all worked examples • Interactive widgets • Interactive walkthroughs • Downloadable HOTsheets • Access to HOTmaths Australian Curriculum courses

Measurement everywhere Imagine trying to describe facts about the world around us without using any form of measurement. We use units of length to describe distance and degrees Celsius (°C) to describe temperature. Other units are used for area, volume, time, capacity and mass. Here are some examples of facts that use different units of measurement. • The Eiffel Tower in France is painted with 50 tonnes of paint every 7 years. • The Great Wall of China is more than 6000 km long. • The Great Pyramid of Giza was built

Essential Mathematics for the Australian Curriculum Year 7 2ed

•

• •

•

around 2500 BCE and includes about 2 300 000 blocks of stone, each weighing about 2500 kg. The world’s smallest country is Vatican City in Rome, with an area of 0.44 km2. The maximum temperature during the day on Mars is about 20°C. The distance between the orbits of Mars and the Earth around the Sun is about 78 000 000 km. The volume of water in Sydney Harbour is about 500 gigalitres or five hundred thousand million litres or 0.5 km3.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Up for a challenge? If you get stuck on a question, check out the 'Working with unfamiliar problems' poster at the end of the book to help you.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

A = 6h =5×2 = 10 cm2

2 cm 5 cm

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Metric mm2 cm2 m2 ha km2 1 ha = 10 000 m2

Parallelogram

A=l2 = 92 = 81 m2

9m

Triangle 2m 3m A = 12 bh

Rectangle 2 cm 16 digits = 12 inches = 1 foot 5 feet = 1 pace 1000 paces = 1 mile

= 12 × 3 × 2 = 3 m2

4 cm

Roman (Ext)

A = lw =4×2 = 8 cm2

Composite shapes (Ext) 18 m 10 m 19 m 8m

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A = l × w + 12 bh

12 inches = 1 foot 3 feet = 1 yard 1760 yards = 1 mile

= 18 × 10 + = 225

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1 2

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m2

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Metric 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km

Capacity 1 L = 1000 mL 1 kL = 1000 L 1 ML = 1000 kL and 1 mL = 1 cm3 1 m3 = 1000 L

Length

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2 cm 4 cm

2.1 cm 1.5 cm



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Essential Mathematics for the Australian Curriculum Year 7 2ed

Mass 1 g = 1000 mg 1 kg = 1000 g 1 t = 1000 kg

Metric mm3 cm3 m3 km3

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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D

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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Essential Mathematics for the Australian Curriculum Year 7 2ed

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E :FT DPSSFTQPOEJOH BOHMFT BSF FRVBM F /P BMUFSOBUF BOHMFT TIPVME CF FRVBM G

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JJ B =  C = 

BOHMF CZ DPOTUSVDUJOH UIF BOHMF CJTFDUPS UP GPSN UXP ¡ BOHMFT TFF 2VFTUJPO   C $POTUSVDU BO BOHMF CJTFDUPS PG POF PG UIF ¡BOHMFT GSPN QBSU B  B 'JSTU DPOTUSVDU B ¡ BOHMF CZ DPOTUSVDUJOH B QFSQFOEJDVMBS MJOF BOE UIFO DPOTUSVDU UIF BOHMF CJTFDUPS

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PG UIF ¡ BOHMF C $POTUSVDU UIF BOHMF CJTFDUPS PG POF PG UIF ¡ BOHMFT GSPN

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JJ ∠#&% BMUFSOBUF

C BEE UP ¡ D 5ISFF JOTJEF BOHMFT PG B USJBOHMF BEE UP ¡ XIJDI JT BMXBZT USVF  &BDI USJBOHMF BEET UP ¡ TP UIF UPUBM JT ¡

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



B J ¡ JW ¡

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

 B 

C 

D 

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⎪ , , , ,  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ , , , ,  ⎪ ⎪ ⎪ ⎪ ⎪ , , , ,  ⎪ ⎪ ⎪ ⎪ ⎭ , , , , 

 

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

C 

  +  =  BOE  +  =  "MM QSJNFT PUIFS UIBO  BSF PEE BOE UXP PEET TVN UP HJWF BO FWFO OVNCFS UIBU JT OPU B QSJNF 4P BOZ QBJS UIBU TVNT UP B QSJNF NVTU DPOUBJO BO FWFO

     

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&

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BT XFMM BT PUIFS HSPVQT   =  +   =  +   =  +   =  +   =  +   =  +   =  +   =  +   =  + 

I  ¨  ¨  C ¨¨¨¨¨¨ D ¨¨¨¨ E ¨¨¨¨¨¨¨¨ F ¨¨¨¨ G ¨¨¨¨¨ H  ¨  ¨  ¨  ¨  ¨  ¨  I  ¨  ¨  ¨  ¨   B  F 

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

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Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

4 2

18 2 9

4 2

3

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2

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8 4

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B      

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C 

D B =  C = 

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D ZFT TVN PG  ÷  BOE FWFO ÷  E ZFT TVN PG  ÷ 

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

 B SBUJP PG 

C EJGGFSFODF TVCUSBDUJOH 

D EJGGFSFODF BEEJOH   F SBUJP PG  H OFJUIFS  B   

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C 

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C D

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

 B BOE

G BOE  B J

C

JJ      JJJ  TUJDLT BSF SFRVJSFE UP TUBSU UIFO  BSF BEEFE

/P PG DSPTTFT











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D /VNCFS PG TUJDLT =  ¨ OVNCFS PG DSPTTFT E  TUJDLT

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F

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D /VNCFS PG QMBOLT =  ¨ OVNCFS PG GFODF TFDUJPOT +  E  QMBOLT 

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C /VNCFS PG TUVEFOUT =  ¨ OVNCFS PG UBCMFT +  D  TUVEFOUT E  UBCMFT

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C /VNCFS PG UJMFT =  ¨ TQB MFOHUI +  D  UJMFT E  VOJUT  "  "

JJ      JJJ  TUJDLT BSF SFRVJSFE UP TUBSU UIFO  BSF BEEFE F J

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D

JJ      JJJ  TUJDLT BSF SFRVJSFE UP TUBSU UIFO  BSF BEEFE G J

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

E

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G

JOQVU PVUQVU

 

 



B PVUQVU = JOQVU +  D PVUQVU = JOQVU +   PVUQVU =  ¨ JOQVU

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C 

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C PVUQVU =  ¨ JOQVU E PVUQVU = JOQVU Ÿ 

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JOQVU      PVUQVU     

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D  E 

 JOQVU C E F H NO Y D   PVUQVU CD DE FD H D DNO YD D  D PVQVU = D ¨ JOQVU  B PVUQVU =  ¨ JOQVU +  PVUQVU =  ¨ JOQVU o  C JOýOJUF  B J PVUQVU =  ¨ JOQVU o  JJ PVUQVU =  ¨ JOQVU + 

&YFSDJTF + 

B USVF

C GBMTF

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JJJ PVUQVU =  ¨ JOQVU o  JW PVUQVU = JOQVU Ÿ  +  W PVUQVU =  ¨ JOQVU +  WJ PVUQVU =  ¨ JOQVU o 

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y 6 5 4 3 2 1 O



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y 4 3 2 1 O

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x

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

C

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C ZBYJT

y 5 4 3 2 1



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Output

D PSJHJO F ZDPPSEJOBUF 

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Output  B

C

Output

O

x

1 2 3 4 5 y

x

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1 2 3 4 5 6 7 8

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y 10 9 8 7 6 5 4 3 2 1

PVUQVU Z

   

y 5 4 3 2 1 O

5 4 3 2 1

8 7 6 5 4 3 2 1

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x 1 2 3 4 5 Input

y



y

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F C D

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x 1 2 3 4 5 6 7 8 9 10 C  

 

 

 

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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C  UIPVTBOEUIT =

 

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D USVF

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST



B GBMTF



F USVF G  ¨  + 

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

 "

 

 

 

D 

  

    B USVF

C USVF





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B J Y =  JJ Z =  C Y + Z + [ = 

E 

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

C 

F     B B

G

E N 

D 

E 

−10 −9 −8 −7 −6

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F  + B

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Essential Mathematics for the Australian Curriculum Year 7 2ed

K − O − G K

− −

C 

 

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D + + − + G − + − −



ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

&YFSDJTF $ 

C  − G  −

 B  E TVCUSBDUJOH  B GBMTF F GBMTF  B  F −

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H GBMTF

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D 

E 

G

−

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L − P −

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E 

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Q 

 − N  − 

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C



  −

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−

− − −



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−

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C 

 B

−

E 

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¨

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 B

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C USVF

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−

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−

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M

−

L −

M

D 

E 



H −

I −

C −

 B  F 

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G

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D OFHBUJWF G OFHBUJWF

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−

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− 

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− 

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− 

− 

− 

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D ¨ ¨

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− 

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JJJ −

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

 B −BC

C −BC

D BC

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

 

   −  

C −

D −

F −

G

H

J

K

−

 

C *G UIFSF JT BO FWFO OVNCFS PG OFHBUJWF GBDUPST UIF SFTVMU XJMM

E 

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I  M



1SPHSFTT RVJ[

CF QPTJUJWF JG PEE UIFO OFHBUJWF  B  C  D −

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E 

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D 

E −

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E 

J

D 

E −

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C NVMUJQMJDBUJPO F BEEJUJPO

D NVMUJQMJDBUJPO G TVCUSBDUJPO

H NVMUJQMJDBUJPO

I NVMUJQMJDBUJPO

J

C GBMTF F GBMTF

D USVF G USVF

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B 

N

B EJWJTJPO E EJWJTJPO

D 

E 

G K

H  L −

I − M − E 

 −

N −

O 

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P 

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C −

D −

N   

O −

P −

 −

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H  L 

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C − ÷ ( + ) = −

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E  I 

D 

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H 

I 

C  G −

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D −

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G

−

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C  NFUSFT QFS TFDPOE D  NFUSFT QFS TFDPOE

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C  G  K



F −



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JJ −

C " OFHBUJWF XJEUI JT OPU QPTTJCMF  "OTXFS NBZ WBSZ  "OTXFST NBZ WBSZ  B B − B =  BOE −C + C =  B C = B D B−B= BC E DBODFMT UP TJNQMZ HJWF B. C JJ −◦ $  B J ◦ $ $ C '= +  

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B %

C #

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F &

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H '

I (

D  H 

E 

)

F ( − ) ÷  +  =  G  × ( − ) × (−) = 

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J

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H − × ( − (−)) −  = − I (− + ) ÷ (− + ) = −

( − (−)) ÷ (− + ) = 

 UISFF BOTXFST − − −

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C  G 

D ZFT

F OP

G

 B USVF E USVF

C USVF F GBMTF

D USVF G GBMTF

 B J OFHBUJWF JW QPTJUJWF

JJ OFHBUJWF W OFHBUJWF

ZFT

JJJ OFHBUJWF WJ OFHBUJWF

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

 B C

C

y

y 4 3 2 1

4 3 2 1 −4 −3 −2 −1−1O −2 −3 −4

1 2 3 4

x

−4 −3 −2 −1−1O −2 −3 −4

 B "(, ), #(, −), $(−, ), %(, ), &(, ), '(, )  B

C D

y

y

5 4 3 2 1

4 3 2 1 1 2 3 4

x

−4 −3 −2 −1−1O −2 −3 −4 −5 −6 −7

C 5IFZ MJF JO B TUSBJHIU MJOF  B y

5 4 3 2 1

1 2 3 4

x

E 5IFZ BSF JO B TUSBJHIU MJOF

1SPCMFNT BOE DIBMMFOHFT 

−4 −3 −2 −1−1O −2 −3 −4 −5 −6 −7

1 2 3 4

x

C  − 

E − − −

 B  D 

C −

 B − × ( + (−)) = − PS − ×  ÷ (−) = − C − ×  × (−) +  =  PS −  ×  ÷ (−) +  =  D  ×  ÷ (−) − (−) = −

 B  TRVBSF VOJUT

C  TRVBSF VOJUT

D  TRVBSF VOJUT   LN

E  TRVBSF VOJUT

 B  BOE −

D # " $ JJJ  BOE 

C  BOE −

  QBJST  B = , C = −, D = −, E = −, F =    −   B Q + U > R + U C U − Q < U − R D QU < RU  BMM OVNCFST MFTT UIBO  FYDFQU 

 Z =   Z =  C $ JJ 

B −  − D − − −

C 5IFZ MJF JO B TUSBJHIU MJOF  B USJBOHMF C SFDUBOHMF D USBQF[JVN E LJUF

 B #  B J  BOE 

x

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((, −), )(−, )

−4 −3 −2 −1−1O −2 −3 −4

1 2 3 4

.VMUJQMFDIPJDF RVFTUJPOT JW 

 $  "

 &  &

 #  $

 %  #

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

F

TBNQMF



G H

TBNQMF VTJOH TFDPOEBSZ TPVSDF EBUB DFOTVT UIJT RVFTUJPO BQQFBST PO UIF QPQVMBUJPO DFOTVT

I J

DFOTVT PG UIF DMBTT TBNQMF

K L

SFTVMUT GSPN UIF QPQVMBUJPO DFOTVT PCTFSWBUJPO

M N

PCTFSWBUJPO TBNQMF

B 

C 

D 

E 

 B −

C −

D −

E 

 B −

C −

D −

E 

 B −

C −

D 

E −

 B −

C −

F − J −

G K

F −

G

F −

G

 B − F 

−  − 

C  G 

H  L −

I − M 

H −

I 

H 

I −

D −

E −

D −

E 

 B  C − D − E −  "(, ), #(, ), $(−, ), %(−, −), &(, −), '(, −)

O  B

TBNQMF TFDPOEBSZ o B NBSLFU SFTFBSDI DPNQBOZ

C D

TFDPOEBSZ o EFQBSUNFOU PG FEVDBUJPO EBUB QSJNBSZ EBUB DPMMFDUJPO WJB B TBNQMF

E F

TFDPOEBSZ TPVSDF VTJOH SFTVMUT GSPN UIF DFOTVT TFDPOEBSZ TPVSDF VTJOH /"1-"/ SFTVMUT PS TJNJMBS

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1SPYJNJUZ UP UIF *OEJBO 0DFBO NBLFT ýSTU IBOE DPMMFDUJPO PG UIF EBUB EJGýDVMU

C

5PP NBOZ QFPQMF UP BTL BOE B TFOTJUJWF UPQJD NFBOT UIBU VTJOH UIF DFOTVT SFTVMUT BT ZPVS TPVSDF XPVME CF CFUUFS

D

&YUSFNFMZ MBSHF QPQVMBUJPO NBLFT QSJNBSZ EBUB EJGýDVMU UP DPMMFDU

$IBQUFS 

E

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F

$VMUVSBM JTTVFT BOE UIF EJGGFSFOU DVMUVSBM HSPVQT UIBU FYJTU JO UIF DPNNVOJUZ NBLFT DPMMFDUJPO EJGýDVMU

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B ◦ $

 SPDLFU



C −◦ $ D ◦ $

B JJJ E W

 B DBUFHPSJDBM

E ◦ $

F ◦ $

C JW F WJ

D J G JJ

C OVNFSJDBM

D OVNFSJDBM

E DBUFHPSJDBM F OVNFSJDBM  "OTXFST XJMM WBSZ  B EJTDSFUF OVNFSJDBM C D

DPOUJOVPVT OVNFSJDBM DPOUJOVPVT OVNFSJDBM

E F

DBUFHPSJDBM DBUFHPSJDBM

G H

DBUFHPSJDBM EJTDSFUF OVNFSJDBM

I J

EJTDSFUF OVNFSJDBM DPOUJOVPVT OVNFSJDBM

G

OVNFSJDBM

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1PQVMBUJPO JT UIF FOUJSF HSPVQ PG QFPQMF CVU B TBNQMF JT B TFMFDUJPO GSPN XJUIJO JU

C

*G UIF QPQVMBUJPO JT TNBMM FOPVHI FH B DMBTT PS UIFSF JT FOPVHI UJNFNPOFZ UP TVSWFZ UIF FOUJSF QPQVMBUJPO FH OBUJPOBM DFOTVT  8IFO JU JT UPP FYQFOTJWF PS EJGýDVMU UP TVSWFZ UIF XIPMF

D

QPQVMBUJPO FH UFMFWJTJPO WJFXJOH IBCJUT PG BMM PG /48  B 5IF BOTXFST TUBOE GPS EJGGFSFOU DBUFHPSJFT BOE BSF OPU USFBUFE BT OVNCFST 5IFZ DPVME IBWF CFFO "o& SBUIFS UIBO o

K

DPOUJOVPVT OVNFSJDBM

C J

L M

DPOUJOVPVT OVNFSJDBM EJTDSFUF OVNFSJDBM

JJ

N O

DPOUJOVPVT OVNFSJDBM EJTDSFUF OVNFSJDBM

 = QPPS  = TBUJTGBDUPSZ  = TUSPOH  = FYDFMMFOU

JJJ

P Q

DBUFHPSJDBM EJTDSFUF OVNFSJDBM

 = OFWFS  = SBSFMZ  = TPNFUJNFT  = VTVBMMZ  = BMXBZT

JW

R S

EJTDSFUF OVNFSJDBM DBUFHPSJDBM

 = TUSPOHMZ EJTBHSFF  = EJTBHSFF  = OFVUSBM  = BHSFF  = TUSPOHMZ BHSFF

 B C

PCTFSWBUJPO TBNQMF PG EBZT VTJOH PCTFSWBUJPO PS TFDPOEBSZ TPVSDF

D

SFDPSET XJUIJO FBDI EBZ DFOTVT PG UIF DMBTT

E

TBNQMF

Essential Mathematics for the Australian Curriculum Year 7 2ed

"OTXFST

4IPSUBOTXFS RVFTUJPOT

 B

C

 = TUSPOHMZ EJTBHSFF  = TPNFXIBU EJTBHSFF  = TPNFXIBU BHSFF  = TUSPOHMZ BHSFF

&YDMVEFT QFPQMF XIP IBWF POMZ NPCJMF OVNCFST PS XIP BSF PVU XIFO QIPOF JT SVOH DPVME CJBT UPXBSET QFPQMF XIP IBWF NPSF GSFF UJNF &YDMVEFT QFPQMF XIP EP OPU SFTQPOE UP UIFTF UZQFT PG NBJM PVUT CJBT UPXBSET QFPQMF XIP IBWF NPSF GSFF UJNF

 ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

D

&YDMVEFT XPSLJOH QBSFOUT CJBT UPXBSET TIJGU XPSLFST PS

E

VOFNQMPZFE &YDMVEFT BOZPOF XIP EPFT OPU SFBE UIJT NBHB[JOF CJBT

F

UPXBSET HJSMT &YDMVEFT QFPQMF XIP EP OPU VTF 'BDFCPPL CJBT UPXBSET

 B C

JJ 

JJJ 

JW 

G J



JJ 

JJJ 

JW 



JJ 

JJJ 

JW 

I J



JJ 

JJJ 

JW 

ZPVOHFS QFPQMF PS QFPQMF XJUI BDDFTT UP UFDIOPMPHZ 'PS FYBNQMF OVNCFS PG CBCJFT BU B MPDBM QMBZHSPVOE

 B 

C 

D 

 B #SFOU

C #SFOU

D "MJ

0UIFS BOTXFST QPTTJCMF $PVOU B TBNQMF FH KVTU POF þPPS PG POF DBS QBSL

   B 

QSPDFTT BOE OFFE GPS IPOFTUZ JO UIF DPMMFDUJPO BOE VTF PG BOZ EBUB  B

5PP FYQFOTJWF BOE EJGýDVMU UP NFBTVSF UFMFWJTJPO WJFXJOH JO NJMMJPOT PG IPVTFIPMET

C D

/PU FOPVHI QFPQMF o SFTVMUT DBO CF NJTMFBEJOH 1SPHSBNT UBSHFUFE BU ZPVUI BSF NPSF MJLFMZ UP CF XBUDIFE

E

CZ UIF TUVEFOUT 3FTFBSDI SFRVJSFE

 B

5PP FYQFOTJWF BOE QFPQMF NJHIU SFGVTF UP SFTQPOE JG JU DBNF UPP PGUFO

C

&OHMJTI BT B TFDPOE MBOHVBHF DBO JNQBDU UIF DPMMFDUJPO PG EBUB TJNQMF VOBNCJHVPVT &OHMJTI JT SFRVJSFE  4PNF

E   B 

D

4PNF QFPQMF DBOOPU BDDFTT EJHJUBM UFDIOPMPHJFT BOE UIFZ

E

XPVME CF FYDMVEFE GSPN UIF SFTVMUT -BSHFS QPQVMBUJPOT BOE B HSFBUFS QSPQPSUJPO PG QFPQMF JO

QPWFSUZ DBO NBLF DFOTVT EBUB IBSEFS UP PCUBJO  %JGGFSFOU QFPQMF BSF DIPTFO JO UIF TBNQMFT -BSHFS SBOEPNMZ TFMFDUFE TBNQMFT HJWF NPSF BDDVSBUF HVJEFT  B J BOE JJ "OTXFST XJMM WBSZ JJJ

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Number of births

Number of students pink blue yellow green red

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

C  DN

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Distance (km)

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Distance (km)

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

-FBG

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

C $

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

D 

D /P UFDIOJRVF GPS ýOEJOH UIFPSFUJDBM QSPCBCJMJUZ IBT CFFO

E /P CFDBVTF JU JT BMXBZT  −

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blue

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Essential Mathematics for the Australian Curriculum Year 7 2ed









/P PG TUVEFOUT









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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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B

Age (years)



30 25 20 15 10 5 0

Ja n Fe b M ar A pr M ay Ju n Ju l A ug Se p O ct N ov D ec

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Sven Dane Kelly Hugo Frankie Name C  D  IPVST

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

TJEF  B ZFT

C /P UIF UISFF TJEFT XJMM OPU KPJO

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C 

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∴ B + C + D =  C B + C + D = 

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B + C =  − D

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D + ∠#$% = ◦ ∠#$% = ( − D)◦ 

'SPN  BOE  XF IBWF ∠#"$ = B◦ + C◦ 

 B 5SJBOHMFT XJUI UIF TBNF BOHMFT DPVME CF PG EJGGFSFOU TJ[F

CF VTFE UP DSFBUF UIF UIJSE TJEF D 5IF JOGPSNBUJPO EPFT OPU HJWF B VOJRVF USJBOHMF

("MUFSOBUF UP ∠"#$ BOE %& JT QBSBMMFM UP "#.)

E 4UBSU XJUI UIF  DN TFHNFOU DPOTUSVDU B SJHIU BOHMF TFF 2

UIFO UIF IZQPUFOVTF

C 5IF BOHMF CFUXFFO UIF UXP TJEFT DPVME WBSZ  C  USJBOHMFT UIFSF BSF UXP QPJOUT PO UIF SBZ "& UIBU DPVME

"OTXFST

 B ZFT C JTPTDFMFT  5IF UXP TIPSUFS TJEFT UPHFUIFS NVTU CF MPOHFS UIBO UIF MPOHFTU

&YFSDJTF & 

B

 B $IFDL UIBU UIF EBTIFE MJOFT GPSN BO FRVJMBUFSBM USJBOHMF C 6TF UIF EJBHSBN UP BTTJTU D

a°

a°

a°

a°

b° a°

a° b°

C

E

a°

a°

a°

a° a°

b° a°

b°

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

F

G

 B 

a°

C 

 B QPTTJCMF D JNQPTTJCMF

a°

D  C JNQPTTJCMF E QPTTJCMF

F JNQPTTJCMF  B + C + G =  (TVN PG BOHMFT JO B USJBOHMF)

 B

D + E + F = 

(TVN PG BOHMFT JO B USJBOHMF)

5PUBM TVN = B + C + G + D + E + F =  +  = 

C   B DPOWFY

C OPODPOWFY

D OPODPOWFY

 B TRVBSF E SIPNCVT

C USBQF[JVN F SFDUBOHMF

D LJUF G QBSBMMFMPHSBN

 B SFDUBOHMFT LJUF QBSBMMFMPHSBN C SIPNCVT QBSBMMFMPHSBN

 B  E 

C  F 

D  G 

1SPHSFTT RVJ[ 

B DPODBWF JSSFHVMBS QFOUBHPO C DPOWFY SFHVMBS IFYBHPO D DPOWFY JSSFHVMBS SFDUBOHMF

D TRVBSF SFDUBOHMF SIPNCVT QBSBMMFMPHSBN E USBQF[JVN

E OPODPOWFY JSSFHVMBS EFDBHPO  B JTPTDFMFT USJBOHMF

F LJUF  B B =  C = 

C SJHIUBOHMFE USJBOHMF

C B =  C =  D B =  C = 



 B  C  D   'PSNJOH B TRVBSF JT QPTTJCMF

E 

6 cm

 B TRVBSF SFDUBOHMF C TRVBSF SIPNCVT LJUF  B " TRVBSF JT B UZQF PG SFDUBOHMF CFDBVTF B SFDUBOHMF DBO CF DPOTUSBJOFE UP GPSN B TRVBSF C :FT B QBSBMMFMPHSBN DBO CF DPOTUSBJOFE UP CF B SIPNCVT D OP  B 6TF HJWFO EJBHSBN BOE DIFDL UIBU BMM TJEFT BSF UIF TBNF MFOHUI C 6TF HJWFO EJBHSBN BOE DIFDL UIBU UIF EJTUBODF CFUXFFO UIF MJOFT BSF BMXBZT FRVBM

6 cm

6 cm   B 

C 

 B 

C 



C USBQF[JVN E QBSBMMFMPHSBN

◦

B TRVBSF D SIPNCVT

 B 

C 

D 

&YFSDJTF '

 B 

C 

D 



 B 

"OTXFS NBZ WBSZ CVU UIF TVN PG BOHMFT TIPVME CF WFSZ DMPTF

UP ◦   "OTXFS NBZ WBSZ CVU UIF TVN PG BOHMFT TIPVME CF WFSZ DMPTF UP ◦   B B +  =  TP B = 

 B B =  C = 

C B =  C = 

D B =  C =  F B =  C =   B B =  D B =  

B 

 B 

E B =  C =  G B =  C =  C B =  C = 

C 

D 

C 

D 

D 

E 

&YFSDJTF ( 

C C +  +  +  =  TP C =   B  C  D 

C 

B  XBZT

C  XBZT

D  XBZT

E  XBZ

F  XBZT

G

C  F 

D  G 

 B  E 

 XBZT

 B  BOE 

C  BOE 

D  BOE 

E  BOE 

F  BOE 

G

 B FRVJMBUFSBM C JTPTDFMFT  B J LJUF JJJ OPOF

 BOE 

D TDBMFOF

JJ SFDUBOHMF SIPNCVT JW TRVBSF

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

F

G

JJ SFDUBOHMF SIPNCVT QBSBMMFMPHSBN JJJ OPOF JW TRVBSF  B MJOF BOE SPUBUJPOBM TZNNFUSZ PG PSEFS  C MJOF BOE SPUBUJPOBM TZNNFUSZ PG PSEFS  D MJOF BOE SPUBUJPOBM TZNNFUSZ PG PSEFS  E MJOF BOE SPUBUJPOBM TZNNFUSZ PG PSEFS 

 B (−, )

 B " # $ % & , . 5 6 7 8 : C ) * 0 9 D ) * / 0 4 9 ;  B C

C (−, )

D (, −)

E  

 B OP C OP  B "′  

#′  

$′  

%′  

"OTXFST

C J USBQF[JVN LJUF

C "′ (−, ) #′ (−, ) $′ (−, ) %′ (−, ) D "′ (−, −) #′ (−, −) $′ (−, −) %′ (−, −)

D

E "′ (, −) #′ (, −) $′ (, −) %′ (, −) F "′ (−, ) #′ (−, ) $′ (−, ) %′ (−, )  B

G "′ (−, −) #′ (−, −) $′ (−, −) %′ (−, −)  B (−, −) C (, −) D (−, )

C

E (−, ) F  

 B "′ (, −) #′  

%′ (, −)

D

G

(−, −)

C "′  

#′  

%′  

D "′  

#′ (−, ) %′  

E

 B "′ (−, ) #′ (−, ) %′ (−, ) C "′ (, −) #′ (, −) %′ (−, −)

D "′  

#′  

%′ (, −)  B C F

 B  BOE 

C  BOE 

 B

 B J OP

E

F

G

D 

F JOýOJUF

G

&YFSDJTF ) 

D

JJ OP

C JTPTDFMFT USBQF[JVN  B  C  E 

D  BOE 

C

B

D

JOýOJUF

C

E

 (, −)  B (, −)

 B

◦

 B ◦  B (, −)

D UIF TBNF QPJOU

C  

D (−, )

C

D ◦

◦

C ◦

D ◦ C (, −)

E   GPS CPUI

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

 5IF USJBOHMF IBT CFFO TIJGUFE OPU SPUBUFE

&YFSDJTF +

 $IFDL XJUI ZPVS UFBDIFS  $IFDL XJUI ZPVS UFBDIFS



B

C

&YFSDJTF * 

B  

C  

D  

E  

F  

G

H  

I  

 

 B VQ

C MFGU

D EPXO

E VQ

F MFGU  B  VOJUT

G

H SJHIU

I SJHIU

MFGU

 B 

C  VOJUT JD  VOJUT

JJ  VOJUT

 B

C 

D 

 B

C

D

E

F

G

C

D

E

 B  

F (−, ) J (, −)

C (−, )

D (−, )

G K

H  

L (−, )

 

(−, )

 B  VOJUT VQ

E (−, −)

I  

M (−, −)

 4FF HJWFO EJBHSBNT  4FF HJWFO EJBHSBNT JO 2VFTUJPO  C  B

C  VOJUT EPXO

D  VOJUT EPXO F  VOJUT MFGU

E  VOJUT VQ G  VOJUT SJHIU

H  VOJU MFGU BOE  VOJUT VQ I  VOJUT SJHIU BOE  VOJUT VQ J K

D

 B

 VOJUT SJHIU BOE  VOJUT EPXO  VOJUT MFGU BOE  VOJUT VQ

D

D  VOJU SJHIU BOE  VOJUT EPXO E  VOJUT SJHIU BOE  VOJUT EPXO

E

 B  C    QPJOUT  *U JT OFJUIFS SPUBUFE OPS FOMBSHFE

F

E (−, −)

F (, −)

(circle, isosceles triangle)

, (square, isosceles triangle) ,

C  SJHIU BOE  VQ E  SJHIU BOE  VQ

C (−, −)

(square and rectangle with the same top side length)

,

 B  VOJUT MFGU BOE  VOJUT VQ C  VOJUT MFGU BOE  VOJUT VQ

 B (−, −)

,

C

L  VOJUT SJHIU BOE  VOJUT EPXO M  VOJUT MFGU BOE  VOJUT EPXO

 B  SJHIU BOE  EPXO D  MFGU BOE  EPXO

(two squares)

D (−, )

(square, diamond) ,

G

(2 circles) ,

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

(square, triangle on square)

 "OTXFST NBZ WBSZ

,

I

B

C

D

E

F

G

"OTXFST

H

(circle in square, semicircle on rectangle) ,

J

(circle, triangle on semicircle) ,

     B

C

(4-sided pyramid) (8-sided double pyramid) D

 B UFUSBIFESPO PDUBIFESPO JDPTBIFESPO

(pyramid with 5-sided base)  :FT POF DBO CF SPUBUFE UP NBUDI UIF PUIFS  B $ C " D #  B J front left

C JDPTBIFESPO D PDUBIFESPO

E %

E UFUSBIFESPO F IFYBIFESPO PDUBIFESPO

top



G IFYBIFESPO PDUBIFESPO B PDUBIFESPO D EPEFDBIFESPO F UFUSBIFESPO

JJ

front

left

C J

top

JJ

C IFYBIFESPO E JDPTBIFESPO

 B 

C 

E 

F 

D 

 B

C

 B 

C 

 B 

C :FT

D 5IFSF JT OPU UIF TBNF OVNCFS PG GBDFT NFFUJOH BU FBDI WFSUFY  B J  JJ  C

&YFSDJTF ,  B FRVBM  " BOE $

C SFHVMBS

 B FRVJMBUFSBM USJBOHMF D FRVJMBUFSBM USJBOHMF

D QMBUPOJD

O

 

OVNCFS PG

C TRVBSF E SFHVMBS QFOUBHPO C DZMJOEFS







    

 DN DVCFT

F FRVJMBUFSBM USJBOHMF  B DVCF D USJBOHVMBS QZSBNJE

O TJEF MFOHUI

/VNCFS PG JOTJEF DVCFT





/VNCFS PG PVUTJEF DVCFT    



D J O

 

JJ (O − )



JJJ O − (O − )

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

1SPCMFNT BOE DIBMMFOHFT

&YUFOEFESFTQPOTF RVFTUJPOT





UFUSBIFESPO

B ◦ C ◦ E *U TUBZT UIF TBNF



y

  C 

   

−4 −3 −2 −1−1O −2 a −3 −4

.VMUJQMFDIPJDF RVFTUJPOT  &

 #

 $

 %

 $

 "

 &

 $

 &

 $

B 

C 

D 

 B  C   $IFDL MFOHUIT BOE BOHMFT XJUI B SVMFS BOE QBJS PG DPNQBTTFT  $IFDL MFOHUIT BOE BOHMFT XJUI B SVMFS BOE QBJS PG DPNQBTTFT  B ZFT ""4

C OP

D ZFT 3)4

 B  E 

C  F 

D  G 

H 

I 

J

B USBQF[JVN

C SIPNCVT

D LJUF



 B  E 

x

1 2 3 4 b

$IBQUFS 

4IPSUBOTXFS RVFTUJPOT 

4 3 2 1

c

   B 

D 



C 

D 

F 

G

 B "′ (, −) #′ (−, ) %′ (−, −) C "′  

#′ (, −) %′ (, −) D "′ (−, ) #′  

%′ (−, )  B "′ (, −) #′ (, −) $′  

C "′ (−, ) #′ (−, ) $′ (−, )

 B



B & G /

C / H &

D & I &

E & J /

F &

 B USVF  USVF

C GBMTF

D GBMTF

 B 

C 

D USVF

 B USVF F GBMTF

C GBMTF G GBMTF

D USVF H USVF

E USVF I GBMTF

J USVF N GBMTF

K USVF O GBMTF

L GBMTF P USVF

M

 B GBMTF

C USVF

D GBMTF

E USVF



B USVF

C USVF

D GBMTF

E USVF

 B USVF F USVF

C GBMTF G GBMTF

D USVF H GBMTF

E USVF I USVF



 B   C   D    B "′ (−, −) #′ (−, −) $′ (−, −) C "′  

#′  

$′  

&YFSDJTF "

J

USVF

USVF

 B  + Y = 

C L = 

D B + C = 

E E =  U H =    B D = 

F Y = 

G

Q = 

I R+Q=R×Q C Y = .

E G +  =   N =   L =  L = 

D B + C = 

F K +  + N +  = 

 Y =  BOE Z =  Y =  BOE Z =  Y =  BOE Z =  Y =  BOE Z =  Y =  BOE Z =   B 4 C 4 D " E " F / G / H " I 4

C

J

"

K

4

L /

M

/

 B  =  ×  PUIFS TPMVUJPOT QPTTJCMF C  −  =  PUIFS TPMVUJPOT QPTTJCMF

D  ÷  =  −  PUIFS TPMVUJPOT QPTTJCMF E  −  =  ÷  PUIFS TPMVUJPOT QPTTJCMF

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

 B (Y + ) = 

C  D :FT JG  JT DIBOHFE UP  UIFO  +  =  JT B USVF FRVBUJPO E :FT JG + JT DIBOHFE UP − UIFO  −  =  JT B USVF FRVBUJPO

 B & (+) F $ (×) 

B USVF

B × UIFO +

D USVF

E GBMTF

 B 

C 

D 

E 

 B  F 

C  G 

D  H 

E  I 

 B Y

C D

D C

E E

 B Z= F M = 

C M= G B=

D M= H T = 

E E= I Y=

× 10

K

L T=

M

+1

C Q= G V=

D R= H H=

E W= I F=

K

L N=

M

F=

 B Q= F C= J 

E=

S = 

E=

B Y= E Y=

 B  E 

C  F 

D  G 

 B Y = 

C Y = 

 B

−2

C X =  C Y=

 B Z +  = Z

C Z=

 B Y = 

C Y +  =  TP Y = 

 B Y =  TP   BOE  BSF UIF OVNCFST C -)4 JT Y +  PS (Y + ) XIJDI XJMM BMXBZT CF B NVMUJQMF PG   B Y =  BOE Z =  PUIFS TPMVUJPOT QPTTJCMF C Y =  BOE Z =  PUIFS TPMVUJPOT QPTTJCMF

D

 B

E

&YFSDJTF $

 B  + Y =  E  + B = 

C F +  =  E Y +  = 

H =+B  B TVCUSBDUJOH 

C Y =  F  + C = 

F "

D  = R G  = C + 

I Y +  = 

J

C BEEJOH 

D EJWJEJOH CZ 

E NVMUJQMZJOH CZ  F EJWJEJOH CZ  H EJWJEJOH CZ  I BEEJOH 

G

÷5

× 10

+2

x=7

÷5

x+2=9

+2

+1

−4

(x ÷ 2) + 4 = 9

−4

x÷2=5 x = 10 x + 8 = 18

×2 +8

Q =  BEEJOH 

+2 +8 +8 7x + 2 = 23 8 + 2x = 14 5SVF ZPV DBO + UP CPUI TJEFT BOE UIFO − UP HFU UIF PSJHJOBM FRVBUJPO BHBJO 5SVF TJNQMZ QFSGPSN UIF PQQPTJUF PQFSBUJPOT JO UIF SFWFSTF PSEFS TP + CFDPNFT − 5SVF VTF UIF PQFSBUJPOT UIBU UBLF FRVBUJPO  UP FRVBUJPO  BOE UIFO UIF PQFSBUJPOT UIBU UBLF FRVBUJPO  UP FRVBUJPO  GBMTF FH FRVBUJPO  Y =  FRVBUJPO  Y =  FRVBUJPO  Y =  +2

D

E #

÷3

+3

5x = 35

÷2 (x + 8) ÷ 2 = 9  B J  =  JJ  =  JJJ  =  C 3FHBSEMFTT PG PSJHJOBM FRVBUJPO XJMM BMXBZT SFTVMU JO  =   B C x=3 x=3 ×7 ×2 ×7 ×2 7x = 21 2x = 6

F Y =  BOE Z =  PUIFS TPMVUJPOT QPTTJCMF G Y =  BOE Z =  PUIFS TPMVUJPOT QPTTJCMF

D &

10x = 40

×2

C

C %

x=4

5x − 3 = 32

10x + 1 = 41

D Y =  BOE Z =  PUIFS TPMVUJPOT QPTTJCMF E Y =  BOE Z = . PUIFS TPMVUJPOT QPTTJCMF

 B $

+3

−2

÷2

 B X = 

B E +  =  D B +  = 

D ÷ UIFO −

E Y =  C

3x = 12

+8

 B .Y = .



E # (−)

C Y = 

3x + 2 = 14

÷3

P=

D Y= G Y=

C × UIFO −

D  + Y = 

[=

C Y= F Y=

D % (÷)

 B R = 

C GBMTF

J

E ( + B) =  G (Y + ) = 

C " (+)

E − UIFO ÷

&YFSDJTF # 

C  = (B + )

D E =  F (Z + ) = 

"OTXFST

 B 

&YFSDJTF % 

B USVF

C GBMTF

E GBMTF

F GBMTF

 B   H=  B −

 B N= F U=

D USVF C Y=

C ÷

C H =  G R=

D ×

D T= H Z = 

E + E J =  I T = 

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

J

K

K=

N L= R C =   B

−3

M=

L W=

M

O Z= S Q = 

P [= T B=

Q U =  U O=

C

7a + 3 = 38

−3

÷7

÷2

q + 6 = 10 −6

q=4

5= −3 ×10

C Y=

D M=

E U=

G

H K=

I E=

C = 

&YFSDJTF &

x +3 10

x 2= 10

F T=



−3

B USVF

C GBMTF

D USVF

E GBMTF

F USVF

G

C 

D GBMTF

 B 

×10

GBMTF

 B C = 

C E = 

D I = 

E Q = 

D EJWJEF CZ  E EJWJEF CZ 

 B #

C $

D "

E %

C L= G B=

D Y= H O = 

E B= I O=

 B N =  F V = 

C D =  G Z = 

D T =  H Y=

E S =  I B = 

J H= N E=

K R =  O U=

L [ =  P V=

M Q= Q D=

K

L W=

M

R R = 

S Z = 

T R=

U

C Z= G U=

D K= H X=

E C= I S=

J R= N W = 

K T= O G=

L M= P Y=

M [= Q E=

R O=

S N = 

T Q=

U

B Z = −

C B = − D Y = − E Y = −

20 = x 

 B Y = 

÷4

b=6 E

2(q + 6) = 20

−6

÷4

÷7

a= 5 ÷2

+ 10

4b = 24

7a = 35

D

C 4FDPOE TUFQ -)4 EJWJEFE CZ  3)4 IBT  TVCUSBDUFE D 'JSTU TUFQ 3)4 IBT  BEEFE OPU TVCUSBDUFE E 'JSTU TUFQ -)4 IBT B TVCUSBDUFE OPU 

4b − 10 = 14

+ 10

 B 'JSTU TUFQ Y+  JT OPU DPNQMFUFMZ EJWJEFE CZ 

Z = 

B TVCUSBDU  C BEE 

 B G =  F L=

   E Y=   B S = −  B Y=

J

 B I= F V=

V = 

  D X=     F Y= G Y=   C Y = − D U = − E Z = − C L=

F Y = − G L = − − J Y=   B Y +  =  → Y =  D C +  =  → C =  C F +  =  → C =    B O +  = 

H Y = −

I Y = −

C Z =  → Z =  E (L − ) =  → L =  L G −  =  → L =   C O =  I

 B  + Y C  + Y = . D Y = . TP QFOT DPTU  DFOUT  B X =  → X =  C Y =  → Y =  D ( + Y) =  → Y = 

÷2 ×5

2x = 8 x=4 5x = 20

÷2

÷2

−3

×5

×2 D ZFT

E ZFT

x−3=2 2(x − 3) = 4

R=

B=

F V = − G Z = − H V = − I E = − U R  B =  → U =  C =  → R =    S R− D =  → S =  E =  → R =    Y+ Z F =→Y= G +=→Z=   C  B = . C C =  D   Y +  B  Y C +  =  → Y = $  D  NVMUJQMJFE CZ  C NVMUJQMZ CZ 

D TVCUSBDU  E /P UIF EJGGFSFODF CFUXFFO UIFN JT BMXBZT  GPS BOZ

−10

2x = 10 x=5



K = 

 B 5IF EJGGFSFOU PSEFS JO XIJDI  JT BEEFE BOE UIF SFTVMU JT

E X =  → X = 

 B Y =  C Y= D Y=  &YBNQMFT JODMVEF Y +  = , Y = ,  − Y = ,  Y = Y, =  Y  C  B 10 + 2x = 20 2x + 5 = 13 −10 −5 −5

I = 

÷2 −3 ×2

WBMVF PG Y  B Y =  PUIFS TPMVUJPOT QPTTJCMF

C Y =  D ZFT FH Y +  =   B J NVMUJQMZ CZ  JJ EJWJEF CZ C Y =  GPS CPUI PG UIFN

 

D .BLFT UIF ýSTU TUFQ B EJWJTJPO CZ B GSBDUJPO SBUIFS UIBO NVMUJQMJDBUJPO      B Y = C Y= D Y= E Y=    

 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.



 B K = 

B &

C /

D &

E /

 B 5

C '

D 5

E '

 B  + N = 

C E = 

D Y =   B B=

E D + C =  C Y=

 B Y =  B B = 

E B=

C Ÿ C X = 

D ¨ D L = 

E N=

 B Y = 

C B=

D N=

E Z=

 B D = 

C B=

D I = 

E N = 

 B

N +  = ; N =  

C

+Y = ; Y =  

F 3

D 

E 

C GBMTF

D USVF

E USVF

F GBMTF

G

GBMTF

 B Y +  C C +  D B −  E B +  F Y +  G  − Z H B +  I V −   B B +  F Y + 

C  + Y G L+

D C −  H C + 

E B +  I L + 

 B T=

C M=

D Q=

E Z=

F R= J Q=

G K

H N= L Z=

I C= M S=

B E= F B=

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D Y= H V=

E F= I R = 

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D D=

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G

H Z=

I G=

D Q = −

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F L= J U=  B V = −

Q =  Q=

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F V = − G Y = − J Y = −  B J ( + Y) = 

H Q = −

C J (R − ) =  D J (Y + ) = 

I S = −

D 

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D N=

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C Y=

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C R=

D U=

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D Z= JJ TRVBSF

C I=

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D  VOJUT TRVBSFE D

E ◦ $

◦ $

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D $IFDL CZ TVCTUJUVUJOH WBMVFT CBDL JOUP FRVBUJPO %U E 'PS FYBNQMF $ = U − , $ = + ; PUIFS  TPMVUJPOT QPTTJCMF  B "CCPUTGPSE "QFT C  HPBMT D 4 = R+ H + C E  HPBMT BOE  CFIJOET  HPBMT BOE  CFIJOET  HPBMT BOE  CFIJOET  HPBMT BOE  CFIJOET

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B "

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D  N

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST



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C 4PMVUJPO JT Y =



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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

  DN

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

C  NN

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Essential Mathematics for the Australian Curriculum Year 7 2ed

N

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

"OTXFST

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Essential Mathematics for the Australian Curriculum Year 7 2ed

 "

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ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

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 Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.

Essential Mathematics for the Australian Curriculum Year 7 2ed

ISBN 978-1-107-56882-2 © Greenwood et al. 2016 Cambridge University Press Photocopying is restricted under law and this material must not be transferred to another party.