This book presents an alternative course for Year 9 students. The particular aim of the book is to show the everyday applications of mathematics in the context of the world around us.
There are 16 ‘core’ chapters. These chapters cover the basic skills of mathematics appropriate for Year 9 students who may study a more formal mathematics course, or a Mathematical Applications or Foundation Mathematics course in the future.
In addition, there are three ‘option’ chapters which are entirely focused on particular themes. Throughout these chapters, the emphasis is on relating the theory and application of mathematics to real-life:
The authors hope that by presenting a course of mathematics in this way, students may understand the relevance and importance of mathematics in everyday life
By clicking on the CD-link icon, students can access a range of interactive features, including:
The CD is ideal for independent study. Students can revisit concepts taught in class and also discover new ideas for themselves. It is fantastic for demonstrations and simulations. The CD also contains the text of the book – students can leave the textbook at school and keep the CD at home to save carrying a heavy textbook to and from school each day.
| 1 | INTEGERS AND FRACTIONS | 9 | |
| A | Integers | 10 | |
| B | Order of operations | 13 | |
| C | Using your calculator with integers | 15 | |
| D | Operations with fractions | 16 | |
| Review of Chapter 1 | 23 | ||
| 2 | GEOMETRY (POLYGONS AND CONSTRUCTIONS) | 25 | |
| A | Review of geometrical facts | 27 | |
| B | Triangles | 32 | |
| C | Quadrilaterals and other polygons | 34 | |
| D | Constructing a triangle given its sides | 36 | |
| E | Bisecting angles | 38 | |
| F | Constructing perpendiculars | 39 | |
| G | Angle construction | 42 | |
| Review of Chapter 2 | 43 | ||
| 3 | ALGEBRA | 45 | |
| A | The language of mathematics | 47 | |
| B | Changing words to symbols | 48 | |
| C | Evaluation | 51 | |
| D | Collecting like terms | 52 | |
| E | Algebraic simplification and index form | 53 | |
| F | Index laws | 56 | |
| G | Zero and negative indices | 57 | |
| H | Number patterns and rules | 58 | |
| I | Equations | 59 | |
| Review of Chapter 3 | 65 | ||
| 4 | DECIMALS AND PERCENTAGES | 67 | |
| A | Decimals | 68 | |
| B | Fraction and decimal conversions | 71 | |
| C | Percentage | 72 | |
| D | Working with percentages | 74 | |
| E | Unitary method in percentage | 76 | |
| F | Percentage increase and decrease | 78 | |
| G | Standard form (scientific notation) | 79 | |
| Review of Chapter 4 | 82 | ||
| 5 | ROUNDING, ESTIMATION AND ERRORS | 85 | |
| A | Rounding numbers | 86 | |
| B | Rounding money | 88 | |
| C | One figure approximations | 91 | |
| D | Estimation of numbers of objects | 93 | |
| E | Rounding decimal numbers | 94 | |
| F | Rounding with a calculator | 96 | |
| G | Significant figure rounding | 98 | |
| H | Error in measurement | 100 | |
| Review of Chapter 5 | 101 | ||
| 6 | MEASUREMENT | 103 | |
| A | Length | 105 | |
| B | Perimeter | 107 | |
| C | Circumference | 111 | |
| D | Areas of polygons | 114 | |
| E | Areas of circles | 120 | |
| F | Volume | 123 | |
| G | Capacity | 127 | |
| H | Mass | 130 | |
| I | Time | 133 | |
| J | 24-hour time | 135 | |
| Review of Chapter 6 | 136 | ||
| 7 | RATIO AND RATES | 137 | |
| A | Ratio | 138 | |
| B | Simplifying ratios | 139 | |
| C | Equal ratios | 141 | |
| D | The unitary method for ratios | 143 | |
| E | Using ratios to divide quantities | 144 | |
| F | Rates | 145 | |
| G | Rate graphs | 148 | |
| H | Travel Graphs | 150 | |
| Review of Chapter 7 | 151 | ||
| 8 | INTERPRETING GRAPHS AND CHARTS | 153 | |
| A | Interpreting graphs | 154 | |
| B | Interpreting tables | 159 | |
| C | Life expectancy and insurance | 162 | |
| D | General information | 164 | |
| Review of Chapter 8 | 166 | ||
| 9 | EARNING AN INCOME | 169 | |
| A | Wages and salaries | 170 | |
| B | Overtime, holiday leave loading and bonuses | 174 | |
| C | Deductions from earnings | 177 | |
| D | Income tax | 178 | |
| Review of Chapter 9 | 181 | ||
| 10 | CATEGORICAL DATA AND TIME SERIES | 183 | |
| A | Statistics | 185 | |
| B | Graphing categorical data | 187 | |
| C | Data collection and misleading graphs | 191 | |
| D | Time series data | 194 | |
| Review of Chapter 10 | 196 | ||
| 11 | BUSINESS MATHEMATICS | 199 | |
| A | Profit and loss | 200 | |
| B | Percentage profit, percentage loss | 202 | |
| C | Discount | 204 | |
| D | Goods and services tax (GST) | 207 | |
| Review of chapter 11 | 211 | ||
| 12 | COORDINATES, LINE GRAPHS AND MAPS | 213 | |
| A | The number plane | 214 | |
| B | Linear relationships | 217 | |
| C | Plotting linear graphs | 221 | |
| D | Non-linear graphs | 223 | |
| E | Bearings and directions | 224 | |
| Review of Chapter 12 | 232 | ||
| 13 | NUMERICAL DATA | 235 | |
| A | Numerical data | 236 | |
| B | Grouped discrete data | 240 | |
| C | Continuous data | 243 | |
| D | Measuring the centre | 244 | |
| E | Measuring the spread of discrete data | 247 | |
| F | Using technology | 250 | |
| G | Comparing and reporting discrete data | 251 | |
| Review of Chapter 13 | 253 | ||
| 14 | INTEREST AND DEPRECIATION CALCULATIONS | 255 | |
| A | Simple interest | 257 | |
| B | Compound interest | 261 | |
| C | Depreciation | 263 | |
| Review of Chapter 14 | 265 | ||
| 15 | PROBABILITY | 267 | |
| A | Probability by experiment | 269 | |
| B | Probability by symmetry | 271 | |
| C | Probabilities from a grid | 274 | |
| D | Simulating random events | 276 | |
| E | Expectation | 279 | |
| F | Odds | 280 | |
| Review of Chapter 15 | 282 | ||
| 16 | TRANSFORMATIONS AND SIMILARITY | 283 | |
| A | Reflection | 285 | |
| B | Rotation | 287 | |
| C | Translation | 289 | |
| D | Enlargement | 290 | |
| E | Properties of transformations | 292 | |
| F | Similarity | 293 | |
| Review of Chapter 16 | 297 | ||
| 17 | OVERSEAS TRAVEL | 299 | |
| A | Foreign exchange | 300 | |
| B | Air fares | 303 | |
| C | Accommodation and food costs | 304 | |
| D | Travel insurance and other costs | 305 | |
| E | A holiday in Fiji | 306 | |
| 18 | PARK IMPROVEMENT | 311 | |
| A | Order of tasks | 313 | |
| B | Draw the plan | 314 | |
| C | The fountain | 314 | |
| D | The watering system | 315 | |
| E | Brick paving | 316 | |
| F | Rotary hoeing the lawn and garden areas | 317 | |
| G | The total cost | 317 | |
| 19 | MATHS IN FITNESS AND HEALTH | 319 | |
| A | Heart rate | 320 | |
| B | Body-mass index | 322 | |
| C | Respiration | 323 | |
| D | Stopping distance | 325 | |
| 20 | MATHEMATICS IN DESIGN AND ART | 331 | |
| A | Making stellated solids | 332 | |
| B | Making boxes and containers | 333 | |
| C | Tiling patterns | 337 | |
| ANSWERS | 340 | ||
| INDEX | 367 | ||
We have written this book to provide an alternative course for Year 9 students. Our particular aim was to show the everyday applications of mathematics in the context of the real world.
We have deliberately presented the content in short chapters and because mastery of the basic skills is so important, sixteen chapters cover the core skills that we feel are appropriate for Year 9 students who may go on to complete a Mathematical Applications or a Foundation Mathematics course in the future.
In addition, there are four ‘option’ chapters which are entirely focused on particular themes:
In these chapters, the emphasis is on relating the theory and application of mathematics to real life.
Throughout the book, there are worked examples, exercises and activities, and with the support of the interactive Student CD, students are given the structure and content for independent practice and revision.
We hope that by presenting a course of mathematics in this way, students may understand the relevance and importance of mathematics in everyday life, but we also caution that no single book should be the sole resource for any classroom teacher.
We welcome your feedback.
Email: info@haeseandharris.com.au
