Table of Contents:
About this resource x
Acknowledgements xii
Topic 1 Numeracy 1 1
1.1 Overview 1
1.2 Set A 2
1.3 Set B 6
Answers 9
Topic 2 Positive integers 10
2.1 Overview 10
2.2 Place value 11
2.3 Adding and subtracting positive integers 14
2.4 Multiplying and dividing positive integers 20
2.5 Long division 29
2.6 Order of operations 32
2.7 Factors and multiples 35
2.8 Lowest common multiple and highest common factor 39
2.9 Estimation 45
2.10 Review 48
Answers 54
Topic 3 Indices and primes 63
3.1 Overview 63
3.2 Index notation 64
3.3 Prime numbers and composite numbers 67
3.4 Squares and square roots 73
3.5 Cubes and cube roots 76
3.6 Review 79
Answers 84
Project: We are not alone! 89
Topic 4 Rational numbers 91
4.1 Overview 91
4.2 What are rational numbers? 92
4.3 Simplifying rational numbers 100
4.4 Mixed numbers and improper fractions 103
4.5 Adding and subtracting rational numbers 107
4.6 Multiplying rational numbers 112
4.7 Dividing rational numbers 116
4.8 Fractions as ratios 119
4.9 Working with mixed numbers 126
4.10 Review 132
Answers 137
Topic 5 Geometry 145
5.1 Overview 145
5.2 Measuring angles 146
5.3 Constructing angles with a protractor 153
5.4 Types of angles and naming angles 157
5.5 Triangles 163
5.6 Quadrilaterals and their properties 174
5.7 Parallel and perpendicular lines 181
5.8 Review 188
Answers 195
Topic 6 Decimals 204
6.1 Overview 204
6.2 Place value and comparing decimals 205
6.3 Converting decimals to fractions and fractions to decimals 211
6.4 Rounding and repeating decimals 215
6.5 Adding and subtracting decimals 220
6.6 Multiplying decimals (including by multiples of 10) 226
6.7 Dividing decimals (including by multiples of 10) 232
6.8 Review 237
Answers 243
Topic 7 Percentages 249
7.1 Overview 249
7.2 Percentages as fractions 250
7.3 Percentages as decimals 254
7.4 Fractions and decimals to percentages 256
7.5 Finding percentages of an amount 262
7.6 One amount as a percentage of another 268
7.7 Common percentages and short cuts 273
7.8 Review 277
Answers 282
Topic 8 Algebra 288
8.1 Overview 288
8.2 Using rules 289
8.3 Finding a formula 294
8.4 Substitution 300
8.5 Terms, expressions and equations 306
8.6 Simplifying and the distributive law 312
8.7 The associative law 317
8.8 Review 319
Answers 328
Topic 9 Measurement 335
9.1 Overview 335
9.2 Units of measurement and converting units of measurement 336
9.3 Reading scales and measuring length 342
9.4 Perimeter 349
9.5 Area 356
9.6 Area of composite shapes, using addition and subtraction 370
9.7 Volume 375
9.8 Capacity 385
9.9 Review 388
Answers 400
Project: Sustainable by design 406
Topic 10 Probability 409
10.1 Overview 409
10.2 The language of chance 410
10.3 The sample space 414
10.4 Simple probability 416
10.5 Using a table to show sample spaces 421
10.6 Experimenting with chance 426
10.7 Review 435
Answers 441
Topic 11 Numeracy 2 449
11.1 Overview 449
11.2 Set C 450
11.3 Set D 452
Answers 457
Topic 12 Positive and negative integers 458
12.1 Overview 458
12.2 Integers on the number line 459
12.3 Integers on the number plane 463
12.4 Addition and subtraction of integers 466
12.5 Multiplication and division of integers 472
12.6 Combined operations 477
12.7 Review 480
Answers 487
Topic 13 Linear equations 494
13.1 Overview 494
13.2 Solving equations using trial and error 495
13.3 Using inverse operations 499
13.4 Building up expressions 503
13.5 Solving equations using backtracking 507
13.6 Checking solutions 514
13.7 Keeping equations balanced 518
13.8 Review 524
Answers 529
Topic 14 Representing and interpreting data 536
14.1 Overview 536
14.2 Classifying data 537
14.3 Displaying data in tables 540
14.4 Measures of centre and spread 546
14.5 Representing data graphically 553
14.6 Comparing data 565
14.7 Review 570
Answers 578
Topic 15 Coordinates and the Cartesian plane 588
15.1 Overview 588
15.2 Alphanumeric grid references on a map 589
15.3 The Cartesian plane 597
15.4 Plotting simple linear relationships 603
15.5 Interpreting graphs 607
15.6 Review 613
Answers 621
Topic 16 Transformations 630
16.1 Overview 630
16.2 Axes of symmetry 631
16.3 Translations 637
16.4 Reflections 643
16.5 Rotations and combined transformations 649
16.6 Review 659
Answers 664
Topic 17 Views of 3-D shapes 670
17.1 Overview 670
17.2 Scales and house plans 671
17.3 Plans and views 678
17.4 Isometric drawing 684
17.5 Review 688
Answers 692
Topic 18 Money 697
18.1 Overview 697
18.2 Money 698
18.3 Money and percentages 702
18.4 Unitary method 706
18.5 Review 709
Answers 713
Topic 19 Numeracy 3 716
19.1 Overview 716
19.2 Set E 717
19.3 Set F 720
Answers 725
Topic 20 Programming
20.1 Overview
20.2 Variables
20.3 Expressions
20.4 Sequences
20.5 Algorithms
20.6 Review
Answers
Glossary 726
Index 732
