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
