Table of Contents

About this resource vii Acknowledgements xiv Powering Up for Year 7 Week 1 Finding your place Week 2 Numbering up Week 3 Thinking quickly Week 4 Fishing for fractions Week 5 Getting to the point Week 6 Giving 100% NAPLAN Practice Set A Calculator allowed Set B Non-calculator Set C Calculator allowed Set D Non-calculator Set E Calculator allowed Set F Non-calculator 1 Positive Integers 1 1.1 Overview 2 1.2 Place value 4 1.3 Strategies for adding and subtracting positive integers 10 1.4 Algorithms for adding and subtracting positive integers 16 1.5 Multiplying positive integers 25 1.6 Dividing positive integers 34 1.7 Rounding and estimating 41 1.8 Order of operations 45 1.9 Review 52 Answers 61 2 Positive and Negative Integers 67 2.1 Overview 68 2.2 Integers on the number line 70 2.3 Integers on the number plane 75 2.4 Adding integers 80 2.5 Subtracting integers 85 2.6 Multiplying and dividing integers 91 2.7 Order of operations with integers 97 2.8 Review 102 Answers 109 3 Factors, Multiples, Indices and Primes 115 3.1 Overview 116 3.2 Factors and multiples 118 3.3 Lowest common multiple and highest common factor 123 3.4 Index notation 128 3.5 Prime and composite numbers 133 3.6 Squares and square roots 141 3.7 Divisibility tests 147 3.8 Cubes and cube roots 150 3.9 Review 155 Answers 162 4 Fractions and Percentages 167 4.1 Overview 168 4.2 What are fractions? 170 4.3 Simplifying fractions 182 4.4 Mixed numbers and improper fractions 186 4.5 Adding and subtracting fractions 192 4.6 Multiplying fractions 200 4.7 Dividing fractions 208 4.8 Working with mixed numbers 213 4.9 Percentages as fractions 220 4.10 Calculating percentages of an amount 225 4.11 One amount as a percentage of another 230 4.12 Common percentages and short cuts 236 4.13 Review 242 Answers 251 5 Ratios, Rates and Best Buys 261 5.1 Overview 262 5.2 Ratios 265 5.3 Rates 271 5.4 The unitary method and best buys 276 5.5 Review 281 Answers 286 6 Decimals 289 6.1 Overview 290 6.2 Decimals and place value 292 6.3 Converting decimals to fractions and fractions to decimals 300 6.4 Rounding and repeating decimals 305 6.5 Adding and subtracting decimals 311 6.6 Multiplying decimals 317 6.7 Dividing decimals 323 6.8 Decimals and percentages 330 6.9 Review 333 Answers 340 7 Algebra 347 7.1 Overview 348 7.2 Introduction to algebra 350 7.3 Substituting and evaluating 358 7.4 Simplifying expressions using like terms 362 7.5 Multiplying and dividing terms 367 7.6 Number laws 371 7.7 Expanding brackets 375 7.8 Review 379 Answers 385 Semester review 1 390 8 Equations 393 8.1 Overview 394 8.2 Introduction to equations 396 8.3 Building up expressions and backtracking 402 8.4 Solving equations using backtracking 408 8.5 Solving equations using inverse operations 415 8.6 Checking solutions 424 8.7 Review 429 Answers 435 9 Geometry 441 9.1 Overview 442 9.2 Measuring angles 445 9.3 Constructing angles with a protractor 453 9.4 Types of angles and naming angles 459 9.5 Triangles 465 9.6 Quadrilaterals and their properties 477 9.7 Parallel and perpendicular lines 487 9.8 Review 498 Answers 507 10 Measurement 517 10.1 Overview 518 10.2 Units of measurement 521 10.3 Reading scales and measuring length 528 10.4 Perimeter 536 10.5 Circles and circumference 544 10.6 Area 553 10.7 Area of composite shapes 566 10.8 Volume of rectangular prisms 571 10.9 Capacity 579 10.10 Drawing solids 583 10.11 Review 594 Answers 605 11 Coordinates and the Cartesian Plane 613 11.1 Overview 614 11.2 The Cartesian plane 617 11.3 Linear number patterns 625 11.4 Plotting simple linear relationships 632 11.5 Interpreting graphs 639 11.6 Review 651 Answers 659 12 Transformations 671 12.1 Overview 672 12.2 Line and rotational symmetry 674 12.3 Translations 680 12.4 Reflections 686 12.5 Rotations and combined transformations 693 12.6 Review 705 Answers 711 13 Introduction to Probability 723 13.1 Overview 724 13.2 The language of chance 726 13.3 The sample space 731 13.4 Simple probability 736 13.5 Experimental probability 742 13.6 Review 750 Answers 757 14 Representing and Interpreting Data 763 14.1 Overview 764 14.2 Collecting and classifying data 767 14.3 Displaying data in tables 774 14.4 Measures of centre and spread 780 14.5 Column graphs and dot plots 791 14.6 Stem-and-leaf plots 798 14.7 Pie charts and divided bar graphs 804 14.8 Comparing data 814 14.9 Review 820 Answers 829 Semester review 2 842 15 Algorithmic Thinking 15.1 Overview 15.2 Variables 15.3 Expressions 15.4 Sequences 15.5 Algorithms 15.6 Review Answers Glossary 844 Index 850

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