Naplan Practice vii
About This Resource viii
Acknowledgements xiv
Powering up for Year 7 xvii
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 62
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 76
2.4 Adding integers 81
2.5 Subtracting integers 86
2.6 Multiplying and dividing integers (extending) 92
2.7 Order of operations with integers (extending) .. 98
2.8 Review 102
Answers 110
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 (extending) 150
3.9 Review 155
Answers 163
4 Fractions and percentages 169
4.1 Overview 170
4.2 What are fractions? 172
4.3 Simplifying fractions 184
4.4 Mixed numbers and improper fractions 188
4.5 Adding and subtracting fractions 194
4.6 Multiplying fractions 202
4.7 Dividing fractions 210
4.8 Working with mixed numbers 215
4.9 Percentages as fractions 222
4.10 Calculating percentages of an amount 227
4.11 One amount as a percentage of another 232
4.12 Common percentages and short cuts 238
4.13 Review 244
Answers 254
5 Ratios, rates and best buys 263
5.1 Overview 264
5.2 Ratios 267
5.3 Rates 273
5.4 The unitary method and best buys 278
5.5 Review 283
Answers 289
6 Decimals 291
6.1 Overview 292
6.2 Decimals and place value 294
6.3 Converting decimals to fractions and fractions to decimals 302
6.4 Rounding and repeating decimals (extending) 307
6.5 Adding and subtracting decimals 313
6.6 Multiplying decimals 319
6.7 Dividing decimals 325
6.8 Decimals and percentages 332
6.9 Review 335
Answers 343
7 Algebra 349
7.1 Overview 350
7.2 Introduction to algebra 352
7.3 Substituting and evaluating 360
7.4 Simplifying expressions using like terms 364
7.5 Multiplying and dividing terms 369
7.6 Number laws 373
7.7 Expanding brackets (extending) 377
7.8 Review 381
Answers 388
Semester review 1 392
8 Equations 395
8.1 Overview 396
8.2 Introduction to equations 398
8.3 Building up expressions and backtracking 404
8.4 Solving equations using backtracking 410
8.5 Solving equations using inverse operations 417
8.6 Checking solutions 426
8.7 Review 431
Answers 438
9 Geometry 443
9.1 Overview 444
9.2 Measuring angles 447
9.3 Constructing angles with a protractor 455
9.4 Types of angles and naming angles 461
9.5 Triangles 467
9.6 Quadrilaterals and their properties 479
9.7 Parallel and perpendicular lines 489
9.8 Review 500
Answers 510
10 Measurement 519
10.1 Overview 520
10.2 Units of measurement 523
10.3 Reading scales and measuring length 530
10.4 Perimeter 538
10.5 Area 546
10.6 Area of composite shapes (extending) 559
10.7 Volume of rectangular prisms 564
10.8 Capacity 572
10.9 Drawing solids 576
10.10 Review 587
Answers 599
11 Coordinates and the Cartesian plane 607
11.1 Overview 608
11.2 The Cartesian plane 611
11.3 Linear number patterns 619
11.4 Plotting simple linear relationships 626
11.5 Interpreting graphs 633
11.6 Review 645
Answers 654
12 Transformations 665
12.1 Overview 666
12.2 Line and rotational symmetry 668
12.3 Translations 674
12.4 Reflections 680
12.5 Rotations and combined transformations 687
12.6 Review 698
Answers 704
13 Introduction to probability 715
13.1 Overview 716
13.2 The language of chance 718
13.3 The sample space 723
13.4 Simple probability 728
13.5 Experimental probability (extending) 734
13.6 Review 742
Answers 750
14 Representing and interpreting data 755
14.1 Overview 756
14.2 Collecting and classifying data 759
14.3 Displaying data in tables 766
14.4 Measures of centre and spread 772
14.5 Column graphs and dot plots 783
14.6 Stem-and-leaf plots 789
14.7 Pie charts and divided bar graphs (extending) 795
14.8 Comparing data 806
14.9 Review 812
Answers 822
Semester review 2 834
15 Algorithmic thinking
15.1 Overview
15.2 Variables
15.3 Expressions
15.4 Sequences
15.5 Algorithms
15.6 Review
Answers
Glossary 836
Index 842
