iii Contents About the authors ix Introduction x Guide to the working programs xi Guide to this resource xiii Acknowledgements xvii Working with unfamiliar problems: Part 1 xix Working with unfamiliar problems: Part 2 xxi 1 Whole numbers 2 1A Ancient number systems 4 1B Place value 9 1C Adding and subtracting whole numbers 15 1D Algorithms for addition and subtraction 20 1E Multiplying small whole numbers 25 Progr ess quiz 30 1F Multiplying large whole numbers 31 1G Dividing whole numbers 35 Applications and problem-solving 40 1H Estimating and rounding whole numbers CONSOLIDATING 42 1I Order of operations with whole numbers 47 Modelling 52 Technology and algorithms 53 Investigation 55 Problems and challenges 56 Chapter summary 57 Chapter checklist 58 Chapter review 59 2 Number properties and patterns 62 2A Factors and multiples CONSOLIDATING 64 2B Highest common factor and lowest common multiple CONSOLIDATING 69 2C Divisibility EXTENDING 74 2D Prime numbers 79 2E Powers 82 2F Prime decomposition 88 Progr ess quiz 92 2G Squares and square roots 93
Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37279-4 • Ph 03 8671 1400
Strand: Number Strands: Number
iv Contents 2H Number patterns CONSOLIDATING 99 Applications and problem-solving 105 2I Spatial patterns 107 2J Tables and rules 115 2K The number plane and graphs 122 Modelling 129 Technology and algorithms 130 Investigation 132 Problems and challenges 133 Chapter summary 134 Chapter checklist 136 Chapter review 138 3 Fractions and percentages 142 3A Introduction to fractions CONSOLIDATING 144 3B Equivalent fractions and simplified fractions 150 3C Mixed numerals CONSOLIDATING 157 3D Ordering fractions 163 3E Adding fractions 169 3F Subtracting fractions 175 3G Multiplying fractions 180 Progr ess quiz 187 3H Dividing fractions 188 3I Fractions and percentages 194 3J Finding a percentage of a number 199 Applications and problem-solving 204 3K Introduction to ratios 206 3L Solving problems with ratios 213 Modelling 218 Technology and algorithms 219 Investigation 221 Problems and challenges 222 Chapter summary 223 Chapter checklist 224 Chapter review 226 4 Algebra 230 4A Introduction to algebra 232 4B Substituting and evaluating 238 4C Equivalent expressions 243 4D Like terms 248 Progr ess quiz 253 Strands: Number Strand: Algebra MeasurementUNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37279-4 • Ph 03 8671 1400
v Contents 4E Multiplying and dividing expressions 254 Applications and problem-solving 259 4F Expanding brackets EXTENDING 261 4G Algebraic modelling 267 Modelling 272 Technology and computational thinking 273 Investigation 275 Problems and challenges 276 Chapter summary 277 Chapter checklist 278 Chapter review 279 5 Decimals 282 5A Decimals and place value CONSOLIDATING 284 5B Rounding decimals 289 5C Addition and subtraction of decimals CONSOLIDATING 294 5D Multiplying and dividing by powers of 10 299 5E Multiplication of decimals 305 Progr ess quiz 310 5F Division of decimals 311 5G Decimals and fractions 317 Applications and problem-solving 322 5H Decimals and percentages 324 5I Expressing a quantity as a proportion 329 Modelling 335 Technology and algorithms 336 Investigation 338 Problems and challenges 339 Chapter summary 340 Chapter checklist 341 Chapter review 343 Semester review 1 346 6 Negative numbers 354 6A Integers CONSOLIDATING 356 6B Adding and subtracting positive integers 361 6C Adding and subtracting negative integers 366 6D Multiplication and division of integers EXTENDING 371 Progr ess quiz 376 Strand: Number Strands: Number Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37279-4 • Ph 03 8671 1400
vi Contents 6E Order of operations with integers EXTENDING 377 Applications and problem-solving 381 6F Substituting integers EXTENDING 383 6G Introducing the number plane 386 Modelling 391 Technology and algorithms 393 Investigation 395 Problems and challenges 396 Chapter summary 397 Chapter checklist 398 Chapter review 399
Geometry 402 7A Objects and angles CONSOLIDATING 404 7B Angles at a point 414 7C Parallel lines and transversals 421 7D Problems involving parallel lines EXTENDING 430 7E Classifying and constructing triangles 436 7F Classifying quadrilaterals and other polygons 443 Progr ess quiz 451 7G Angle sum of a triangle 454 7H Symmetry 462 7I Reflection and rotation 467 Applications and problem-solving 476 7J Translation 478 7K Drawing solids 484 7L Nets 489 Modelling 495 Technology and algorithms 496 Investigation 499 Problems and challenges 500 Chapter summary 501 Chapter checklist 503 Chapter review 507 8 Statistics and probability 514 8A Collecting and classifying data 516 8B Summarising data numerically 522 8C Column graphs and dot plots 528 8D Line graphs 537 Strands: Measurement Strands: Algebra Space Statistics Probability UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37279-4 • Ph 03 8671 1400
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vii Contents 8E Stem-and-leaf plots 544 8F Pie charts and divided bar graphs EXTENDING 552 Progr ess quiz 558 8G Describing chance CONSOLIDATING 560 Applications and problem-solving 566 8H Theoretical probability 568 8I Experimental probability EXTENDING 575 Modelling 580 Technology and algorithms 582 Investigation 584 Problems and challenges 585 Chapter summary 586 Chapter checklist 587 Chapter review 589
Equations 594 9A Introduction to equations 596 9B Solving equations by inspection CONSOLIDATING 602 9C Equivalent equations 607 9D Solving equations algebraically 612 Progr ess quiz 619 9E Equations with fractions EXTENDING 620 9F Equations with brackets EXTENDING 625 Applications and problem-solving 630 9G Using formulas 632 9H Applications of equations 637 Modelling 641 Technology and algorithms 643 Investigation 645 Problems and challenges 646 Chapter summary 647 Chapter checklist 648 Chapter review 649 10 Measurement 652 10A Metric units of length CONSOLIDATING 654 10B Perimeter CONSOLIDATING 661 10C Circles, π and circumference 667 10D Units of area and area of a rectangle 674 10E Area of a parallelogram 681 10F Area of a triangle 687 Progr ess quiz 692 Strand: Algebra Strands: Algebra Measurement UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37279-4 • Ph 03 8671 1400
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viii Contents 10G Area of composite shapes EXTENDING 694 10H Volume of rectangular prisms 701 Applications and problem-solving 707 10I Volume of triangular prisms 709 10J Capacity CONSOLIDATING 717 10K Mass and temperature CONSOLIDATING 722 Modelling 727 Technology and algorithms 728 Investigation 730 Problems and challenges 731 Chapter summary 732 Chapter checklist 733 Chapter review 735 Semester review 2 740 11 Appendix A: Algorithmic thinking E1 Introduction E3 Activity 1: Algorithms for working with data E4 Activity 2: Adding consecutive numbers E6 Activity 3: Turtle graphics E8 Index 000 Answers 000 Digital only UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37279-4 • Ph 03 8671 1400