The CD has our new ‘self-tutoring’ software. For every worked
example in this book, a student can listen to a teacher’s voice explain
each step in the worked example – ‘click’ anywhere in the
worked example where you see the
icon.
1. Whole numbers
2. Plane figure geometry
NB: Sample chapters do not have working links.
This is a thorough revision of our established course for students in Year 8. The content is presented in 24 short chapters, in full colour.
The book caters for a range of student abilities. It contains many problems, graded from basic to advanced. Some exercises are designed to build skills, others contextualise the problem so that students can see the practical, everyday applications of the mathematics they are studying.
Most chapters begin with an Opening Problem to show the application of the
mathematics that will be studied in the chapter. Definitions and rules are
highlighted and worked examples (with
) give
step-by-step, easy-to-follow instructions. Investigations are included to help
students develop problem-solving skills and discover mathematical concepts for
themselves.
| 1 | WHOLE NUMBERS | 9 | |
| A | The number system | 12 | |
| B | Rounding and estimation | 14 | |
| C | Operating with numbers | 17 | |
| D | Square numbers and square roots | 22 | |
| E | Order of operations | 24 | |
| Review set 1A | 30 | ||
| Review set 1B | 31 | ||
| 2 | PLANE FIGURE GEOMETRY | 33 | |
| A | Turning | 35 | |
| B | Measuring angles | 36 | |
| C | Classifying and naming angles | 38 | |
| D | Complementary and supplementary angles | 40 | |
| E | Angles in a revolution | 42 | |
| F | Bisecting angles | 43 | |
| G | Constructing 90° angles to a line | 44 | |
| H | Plane shapes | 45 | |
| I | Points and lines | 48 | |
| Review set 2A | 51 | ||
| Review set 2B | 52 | ||
| 3 | DIRECTED NUMBERS | 53 | |
| A | Opposites | 54 | |
| B | Directed numbers and the number line | 59 | |
| C | Using a number line to add and subtract | 63 | |
| D | Rules for adding and subtracting | 67 | |
| E | Multiplying directed numbers | 71 | |
| F | Dividing directed numbers | 73 | |
| G | Combined operations | 74 | |
| H | Using your calculator | 76 | |
| Review set 3A | 77 | ||
| Review set 3B | 78 | ||
| 4 | PROPERTIES OF WHOLE NUMBERS | 79 | |
| A | Divisibility rules | 80 | |
| B | Factors of natural numbers | 83 | |
| C | Index notation | 87 | |
| D | Multiples of natural numbers | 89 | |
| E | Number patterns | 92 | |
| Review set 4A | 95 | ||
| Review set 4B | 95 | ||
| 5 | ALGEBRA: PATTERNS AND MODELS | 97 | |
| A | Geometric patterns | 98 | |
| B | Symbols in algebra | 103 | |
| C | Number crunching machines | 107 | |
| D | Substituting into formulae | 113 | |
| E | Using patterns | 115 | |
| Review set 5A | 118 | ||
| Review set 5B | 119 | ||
| 6 | FRACTIONS | 121 | |
| A | Representing fractions | 123 | |
| B | Improper fractions and mixed numbers | 126 | |
| C | Placing fractions on a number line | 128 | |
| D | Equal fractions | 129 | |
| E | Comparing fraction sizes | 132 | |
| Review set 6A | 135 | ||
| Review set 6B | 136 | ||
| 7 | DECIMAL NUMBERS | 137 | |
| A | Place value | 138 | |
| B | Ordering decimal numbers | 141 | |
| C | Adding and subtracting decimal numbers | 143 | |
| D | Multiplying and dividing by powers of 10 | 145 | |
| E | Multiplying decimal numbers | 147 | |
| F | Dividing decimal numbers | 149 | |
| G | Terminating and recurring decimals | 151 | |
| H | Decimal approximations | 154 | |
| Review set 7A | 155 | ||
| Review set 7B | 156 | ||
| 8 | THE GEOMETRY OF SOLIDS | 157 | |
| A | Solids | 158 | |
| B | Nets of solids | 162 | |
| C | Drawing solids | 166 | |
| D | Plans | 167 | |
| E | Paper modelling | 168 | |
| Review set 8A | 170 | ||
| Review set 8B | 171 | ||
| 9 | ALGEBRA: EXPRESSIONS AND RULES | 173 | |
| A | Building expressions | 174 | |
| B | Expressions with two pronumerals | 177 | |
| C | Simplifying expressions with like terms | 180 | |
| D | Algebraic products | 182 | |
| E | Evaluation of algebraic expressions | 183 | |
| F | The distributive law | 185 | |
| G | Factorisation (Extension) | 189 | |
| Review set 9A | 192 | ||
| Review set 9B | 193 | ||
| 10 | OPERATIONS WITH FRACTIONS | 195 | |
| A | Adding fractions | 196 | |
| B | Subtracting fractions | 200 | |
| C | Multiplying fractions | 204 | |
| D | Reciprocals | 207 | |
| E | Dividing fractions | 207 | |
| F | Problem solving | 209 | |
| G | Operations with rational numbers | 211 | |
| Review set 10A | 214 | ||
| Review set 10B | 215 | ||
| 11 | PERCENTAGES | 217 | |
| A | Understanding percentages | 218 | |
| B | Interchanging number forms | 220 | |
| C | One quantity as a percentage of another | 223 | |
| D | Finding percentages of quantities | 226 | |
| E | The unitary method in percentage | 227 | |
| F | Percentage increase or decrease | 228 | |
| G | Finding the percentage change | 229 | |
| H | Business applications of percentage | 231 | |
| I | Simple interest | 237 | |
| Review set 11A | 239 | ||
| Review set 11B | 240 | ||
| 12 | COORDINATES | 241 | |
| A | Map references | 243 | |
| B | Grid lines and coordinates on a map | 245 | |
| C | Number grids | 247 | |
| D | Interpreting points on a grid | 250 | |
| E | The number plane | 254 | |
| F | Qualitative data | 255 | |
| Review set 12A | 257 | ||
| Review set 12B | 258 | ||
| 13 | LENGTH AND AREA | 261 | |
| A | Length | 264 | |
| B | Perimeter | 267 | |
| C | Circumference | 271 | |
| D | Areas of polygons | 275 | |
| E | Areas of circles | 284 | |
| Review set 13A | 287 | ||
| Review set 13B | 288 | ||
| 14 | RATIO AND PROPORTION | 289 | |
| A | Ratio | 290 | |
| B | Equal ratios | 293 | |
| C | Equal ratios and proportion | 297 | |
| D | Using ratios to divide quantities | 301 | |
| E | Scale diagrams | 303 | |
| F | Gradient (or slope) | 309 | |
| Review set 14A | 311 | ||
| Review set 14B | 312 | ||
| 15 | EQUATIONS | 313 | |
| A | Equations | 314 | |
| B | Algebraic expressions and equations | 315 | |
| C | Maintaining balance | 318 | |
| D | Inverse operations | 323 | |
| E | Building and undoing expressions | 325 | |
| F | Equations with two or more operations | 330 | |
| G | Equations where the unknown occurs more than once | 332 | |
| H | Equations where the unknown occurs on both sides | 333 | |
| Review set 15A | 335 | ||
| Review set 15B | 336 | ||
| 16 | GEOMETRY (PART 1) | 337 | |
| A | Plane figures | 338 | |
| B | Line pairs | 341 | |
| C | Constructing perpendiculars | 347 | |
| D | Classifying triangles | 350 | |
| E | Constructing and drawing triangles | 352 | |
| Review set 16A | 354 | ||
| Review set 16B | 355 | ||
| 17 | STATISTICS | 357 | |
| A | Statistical enquiries (investigations) | 360 | |
| B | Populations and samples | 364 | |
| C | Categorical data | 367 | |
| D | Discussion and report writing | 371 | |
| Review set 17A | 373 | ||
| Review set 17B | 374 | ||
| 18 | LINE GRAPHS | 375 | |
| A | Estimating from line graphs | 376 | |
| B | Conversion graphs | 380 | |
| C | Travel graphs | 382 | |
| D | Continuous and discrete graphs | 384 | |
| E | Graphing linear relationships | 386 | |
| Review set 18A | 390 | ||
| Review set 18B | 391 | ||
| 19 | FURTHER MEASUREMENT | 393 | |
| A | Volume | 394 | |
| B | Capacity | 399 | |
| C | Mass | 403 | |
| D | Time | 406 | |
| Review set 19A | 412 | ||
| Review set 19B | 413 | ||
| 20 | RATES | 415 | |
| A | Rates | 416 | |
| B | Average speed | 420 | |
| C | Density | 422 | |
| D | Converting rates | 424 | |
| Review set 20A | 426 | ||
| Review set 20B | 426 | ||
| 21 | GEOMETRY (PART 2) | 429 | |
| A | Angles of a triangle | 430 | |
| B | Constructing a 60° angle | 432 | |
| C | Exterior angles of triangles | 435 | |
| D | Quadrilaterals | 436 | |
| E | Angles of a quadrilateral | 440 | |
| F | Interior angles of polygons | 442 | |
| Review set 21A | 444 | ||
| Review set 21B | 445 | ||
| 22 | PROBLEM SOLVING | 447 | |
| A | Writing equations using symbols | 448 | |
| B | Solving simple problems with algebra | 450 | |
| C | Solving problems involving measurement | 452 | |
| D | Solving money problems | 453 | |
| E | Miscellaneous problem solving | 454 | |
| F | Other problem solving techniques (Extension) | 456 | |
| Review set 22A | 461 | ||
| Review set 22B | 462 | ||
| 23 | CHANCE | 463 | |
| A | Describing chance | 464 | |
| B | Assigning numbers to chance | 466 | |
| C | The statistics-probability connection | 467 | |
| D | Listing possible outcomes | 472 | |
| E | Calculating probabilities | 474 | |
| F | Making probability generators | 477 | |
| Review set 23A | 478 | ||
| Review set 23B | 479 | ||
| 24 | ALGEBRAIC FRACTIONS | 481 | |
| A | Multiplying algebraic fractions | 482 | |
| B | Dividing algebraic fractions | 483 | |
| C | Adding and subtracting algebraic fractions | 485 | |
| Review set 24A | 488 | ||
| Review set 24B | 489 | ||
| ANSWERS | 491 | ||
| INDEX | 528 | ||
This 6th edition is a thorough revision of our established course in mathematics for Year 8 students. The content of this new edition is presented in 24 short chapters, in full colour.
A feature of the 6th edition is our new
software on the accompanying CD: click anywhere in any worked example to
activate a teacher’s voice which will explain each step in the worked
example. The
is intended as a help for students who have been
absent from classes or for those who need extra revision and practice.
The CD offers exciting possibilities for students and teachers. In addition
to the
, it contains links to spreadsheets, graphing and
geometry software, calculator instructions, computer demonstrations and
simulations. Teachers will be able to demonstrate concepts quickly, clearly and
simply, and students have the opportunity to revisit the demonstrations and
experiment for themselves. (See the note ‘Using the interactive CD’
on the page immediately after this Foreword.)
The book contains many problems from the basic to the advanced, to cater for a range of student abilities and interests. While some of the exercises are designed simply to build skills, every effort has been made to contextualise problems so that students can see everyday uses and practical applications of the mathematics they are studying. Extension problems are marked with red numbers.
An Opening Problem appears at the start of most chapters to offer an insight into the application of the mathematics that will be studied in the chapter. Definitions and rules are highlighted and worked examples provide step-by-step, easy-to-follow instructions. Exercises within each chapter are carefully graded and Investigations are included to assist students to develop their problem solving skills, discover mathematical concepts for themselves and appreciate the applications of mathematics.
We hope the combination of textbook and interactive CD will foster the mathematical education of students in a stimulating way. In this changing world of mathematics education, we believe that the contextual approach adopted in this book, with the associated use of technology, will enhance students’ understanding, knowledge and appreciation of mathematics, and its universal application.
The interactive CD is ideal for independent study.
Students can revisit concepts taught in class and undertake their own revision and practice. The CD also has the text of the book, allowing students to leave the textbook at school and keep the CD at home.
By clicking on the relevant icon, a range of new interactive features can be accessed:
Graphics calculators: instructions for using Texas Instruments and Casio calculators graphics calculators are also given on the CD and can be printed. Click on the relevant icon (TI or C) to access printable instructions.
Examples in the textbook are not always given for both types of calculator. Where that occurs, click on the relevant icon to access the instructions for the other type of calculator.
SELF TUTOR is a new exciting feature of this book. The
icon on each worked example denotes an active link on the CD.
Simply ‘click’ on the
(or
anywhere in the example box) to access the worked example, with a
teacher’s voice explaining each step necessary to reach the answer.
Play any line as often as you like. See how the basic processes come alive using movement and colour on the screen.
Ideal for students who have missed lessons or need extra help.