iii Contents About the authors ix Introduction xi Guide to the working programs xii Guide to this resource xiv Acknowledgements xviii Working with unfamiliar problems: Part 1 xix Working with unfamiliar problems: Part 2 xxi 1 Integers 2 1A Whole number addition and subtraction CONSOLIDATING 4 1B Whole number multiplication and division CONSOLIDATING 9 1C Number properties CONSOLIDATING 14 1D Divisibility and prime factorisation CONSOLIDATING 20 1E Negative integers CONSOLIDATING 26 Progress quiz 30 1F Addition and subtraction of negative integers CONSOLIDATING 31 Applications and problem-solving 36 1G Multiplication and division of integers 38 1H Order of operations and substitution 44 Modelling 49 Technology and computational thinking 51 Investigation 54 Problems and challenges 56 Chapter summary 57 Chapter checklist 58 Chapter review 59
Lines, shapes and solids 62 2A Angles at a point CONSOLIDATING 64 2B Parallel lines CONSOLIDATING 70 2C Triangles CONSOLIDATING 77 2D Quadrilaterals 85 Progr ess quiz 92 2E Polygons EXTENDING 94 Applications and problem-solving 100 2F Solids and Euler’s rule EXTENDING 102 2G Three-dimensional coordinate systems 108 Modelling 118 Technology and computational thinking 120 Strand: Number Strand: Space UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37290-9 • Ph 03 8671 1400
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iv Contents Investigation 122 Problems and challenges 124 Chapter summary 125 Chapter checklist 126 Chapter review 129 3 Fractions, decimals and percentages 134 3A Equivalent fractions CONSOLIDATING 136 3B Operations with fractions CONSOLIDATING 142 3C Operations with negative fractions 151 3D Understanding decimals CONSOLIDATING 157 3E Operations with decimals CONSOLIDATING 164 3F Terminating, recurring and rounding decimals 171 Progress quiz 177 3G Converting fractions, decimals and percentages CONSOLIDATING 178 3H Finding a percentage and expressing as a percentage 185 3I Decreasing and increasing by a percentage 191 Applications and problem-solving 196 3J Calculating percentage change 198 3K Percentages and the unitary method EXTENDING 204 Modelling 208 Technology and computational thinking 210 Investigation 212 Problems and challenges 214 Chapter summary 215 Chapter checklist 217 Chapter review 219
Measurement
Pythagoras’ theorem 222 4A Length and perimeter CONSOLIDATING 224 4B Circumference of a circle 232 4C Area of basic shapes 238 4D Area of kites, rhombuses and trapeziums 247 4E Area of a circle 253 4F Area of sectors EXTENDING 260 4G Surface area of a prism EXTENDING 267 Progress Quiz 273 4H Volume and capacity 275 4I Volume of prisms and cylinders 281 Applications and problem-solving 288 Strand: Number Strands: Numb er MeasurementUNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37290-9 • Ph 03 8671 1400
and introduction to
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v Contents 4J Time 290 4K Introduction to Pythagoras’ theorem 299 4L Using Pythagoras’ theorem 305 4M Finding the length of a shorter side 311 Modelling 317 Technology and computational thinking 318 Investigation 320 Problems and challenges 322 Chapter summary 323 Chapter checklist 324 Chapter review 328
Algebra 334 5A The language of algebra CONSOLIDATING 336 5B Substitution and equivalence CONSOLIDATING 342 5C Adding and subtracting terms 347 5D Multiplying and dividing terms 351 5E Adding and subtracting algebraic fractions EXTENDING 355 5F Multiplying and dividing algebraic fractions EXTENDING 360 Progress quiz 365 5G Expanding brackets 366 5H Factorising expressions 372 5I Applying algebra 377 Applications and problem-solving 381 5J Index laws: Multiplying and dividing powers 384 5K Index laws: The zero power and raising powers 389 Modelling 394 Technology and computational thinking 396 Investigation 398 Problems and challenges 400 Chapter summary 401 Chapter checklist 402 Chapter review 404 Semester review 1 408 6 Ratios and rates 418 6A Simplifying ratios 420 6B Solving ratio problems 427 6C Scale drawings 433 6D Introducing rates 440 Strands:
Strand: Measurement UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37290-9 • Ph 03 8671 1400
Number Al gebra
vi Contents Progress quiz 445 6E Solving rate problems 446 6F Speed 451 Applications and problem-solving 457 6G Ratios and rates and the unitary method EXTENDING 460 Modelling 466 Technology and computational thinking 467 Investigation 469 Problems and challenges 470 Chapter summary 471 Chapter checklist 472 Chapter review 474 7 Equations and inequalities 478 7A Equations review CONSOLIDATING 480 7B Equivalent equations CONSOLIDATING 486 7C Equations with fractions 493 7D Equations with pronumerals on both sides 498 7E Equations with brackets 503 Progress quiz 508 7F Formulas and relationships 509 Applications and problem-solving 514 7G Applications 516 7H Inequalities 521 7I Solving inequalities 526 Modelling 531 Technology and computational thinking 533 Investigation 535 Problems and challenges 536 Chapter summary 537 Chapter checklist 538 Chapter review 539
Probability and statistics 544 8A Interpreting graphs and tables CONSOLIDATING 546 8B Frequency tables and tallies CONSOLIDATING 554 8C Graphs of frequency tables 560 8D Measures of centre 569 8E Measures of spread EXTENDING 575 8F Surveying and sampling 581 Progress quiz 588 8G Probability 590 Strands: Statistics Pr obability Strand: Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37290-9 • Ph 03 8671 1400
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vii Contents 8H Two-step experiments 597 Applications and problem-solving 604 8I Tree diagrams 607 8J Venn diagrams and two-way tables 612 8K Experimental probability 620 Modelling 626 Technology and computational thinking 627 Investigation 629 Problems and challenges 630 Chapter summary 631 Chapter checklist 632 Chapter review 634 9 Straight line graphs 640 9A The number plane CONSOLIDATING 642 9B Rules, tables and graphs 646 9C Finding the rule using tables 652 9D Using graphs to solve linear equations 660 9E Using graphs to solve linear inequalities 670 9F The x - and y -intercepts 687 Progress quiz 692 9G Gradient EXTENDING 694 9H Gradient–intercept form EXTENDING 702 Applications and problem-solving 709 9I Applications of straight line graphs 711 9J Non-linear graphs EXTENDING 717 Modelling 723 Technology and computational thinking 725 Investigation 727 Problems and challenges 729 Chapter summary 730 Chapter checklist 731 Chapter review 734 10 Transformations and congruence 740 10A Reflection 742 10B Translation 750 10C Rotation 755 10D Congruent figures 762 10E Congruent triangles 768 Progress quiz 776 Strand: Space Strand: Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37290-9 • Ph 03 8671 1400
viii Contents 10F Tessellations EXTENDING 778 10G Congruence and quadrilaterals 786 Applications and problem-solving 791 10H Similar figures 793 10I Similar triangles 800 Modelling 808 Technology and computational thinking 809 Investigation 813 Problems and challenges 814 Chapter summary 815 Chapter checklist 816 Chapter review 819 Semester review 2 826 11 Algorithmic thinking 834 Introduction 836 Activity 1: Divisibility tests 837 Activity 2: Working with lists of data 839 Activity 3: Minimising and maximising in rectangles 844 Index 00 Answers 846 Curriculum strands and sub-strands © VCAA UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37290-9 • Ph 03 8671 1400
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