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.
INFINITY Test and Homework Generator is available for this publication. For more information, click here.
1. Number systems
6. Fractions
9. Decimals
10. Problem solving
14. Percentage
15. Time and temperature
22. Transformations
NB: Sample chapters do not have working links.
This is the first book in our new Middle Years series for international schools (for use with MYP 1, approx. Grade/Year 6).
This book may also be used as a general textbook at about Grade 6 level in schools where students are expected to complete a rigorous course in mathematics.
A URL may be made available so that teachers can preview the contents - email ray@haeseandharris.com.au.
The complete series comprises:
A feature of the accompanying CD is our new ‘self-tutoring’ software where
a teacher’s voice explains each step in every worked example in the book. Click anywhere on
any worked example where you see the
icon to activate the self-tutoring software.
Other features include:
For a complete list of all the active links on the MYP 1 CD, click here.
The CD is ideal for independent study and revision. It also contains the full text of the book so that if students load it onto a home computer, they can keep the textbook at school and access the CD at home.
| 1 | Number systems | 9 | |
| A | Different number systems | 10 | |
| B | The Hindu-Arabic system | 17 | |
| C | Big numbers | 20 | |
| Review set 1A | 23 | ||
| Review set 1B | 24 | ||
| 2 | Operations with whole numbers | 25 | |
| A | Adding and subtracting whole numbers | 26 | |
| B | Multiplying and dividing whole numbers | 28 | |
| C | Two step problem solving | 32 | |
| D | Number lines | 34 | |
| E | Rounding numbers | 35 | |
| F | Estimation and approximation | 40 | |
| Review set 2A | 44 | ||
| Review set 2B | 45 | ||
| 3 | Points, lines and angles | 47 | |
| A | Points and lines | 48 | |
| B | Angles | 52 | |
| C | Angles at a point or on a line | 57 | |
| D | Angles of a triangle | 59 | |
| E | Angles of a quadrilateral | 61 | |
| F | Bisecting angles | 62 | |
| Review set 3A | 64 | ||
| Review set 3B | 65 | ||
| 4 | Location | 67 | |
| A | Map references | 69 | |
| B | Number grids | 71 | |
| C | Interpreting points on a grid | 75 | |
| D | Bearings and directions | 77 | |
| Review set 4A | 82 | ||
| Review set 4B | 83 | ||
| 5 | Number properties | 85 | |
| A | Addition and subtraction | 86 | |
| B | Multiplication and division | 88 | |
| C | Zero and one | 90 | |
| D | Index or exponent notation | 91 | |
| E | Order of operations | 92 | |
| F | Powers with base 10 | 95 | |
| G | Squares and cubes | 96 | |
| H | Factors of natural numbers | 98 | |
| I | Divisibility tests | 99 | |
| J | Prime and composite numbers | 100 | |
| K | Multiples and LCM | 102 | |
| Review set 5A | 104 | ||
| Review set 5B | 105 | ||
| 6 | Fractions | 107 | |
| A | Representing fractions | 110 | |
| B | Fractions of regular shapes | 112 | |
| C | Equal fractions | 113 | |
| D | Simplifying fractions | 115 | |
| E | Fractions of quantities | 117 | |
| F | Comparing fraction sizes | 120 | |
| G | Improper fractions and mixed numbers | 122 | |
| Review set 6A | 124 | ||
| Review set 6B | 125 | ||
| 7 | Polygons | 127 | |
| A | Polygons | 128 | |
| B | Triangles | 130 | |
| C | Quadrilaterals | 134 | |
| D | Euler's rule for plane figures | 140 | |
| Review set 7A | 142 | ||
| Review set 7B | 143 | ||
| 8 | Fraction operations | 145 | |
| A | Adding fractions | 146 | |
| B | Subtracting fractions | 150 | |
| C | Multiplying fractions | 154 | |
| D | Reciprocals | 157 | |
| E | Dividing fractions | 158 | |
| F | Problem solving | 159 | |
| Review set 8A | 161 | ||
| Review set 8B | 162 | ||
| 9 | Decimals | 165 | |
| A | Constructing decimal numbers | 166 | |
| B | Representing decimal numbers | 170 | |
| C | Decimal currency | 172 | |
| D | Using a number line | 174 | |
| E | Ordering decimals | 176 | |
| F | Rounding decimal numbers | 178 | |
| G | Converting decimals to fractions | 179 | |
| H | Converting fractions to decimals | 180 | |
| Review set 9A | 182 | ||
| Review set 9B | 183 | ||
| 10 | Problem solving | 185 | |
| A | Trial and error | 186 | |
| B | Making a list | 188 | |
| C | Modelling or drawing a picture | 189 | |
| D | Making a table and looking for a pattern | 191 | |
| E | Working backwards | 194 | |
| Review set 10A | 196 | ||
| Review set 10B | 196 | ||
| 11 | Operations with decimals | 197 | |
| A | Adding and subtracting decimals | 198 | |
| B | Multiplying and dividing by powers of 10 | 200 | |
| C | Large decimal numbers | 203 | |
| D | Multiplying decimal numbers | 205 | |
| E | Dividing decimals by whole numbers | 208 | |
| F | Terminating and recurring decimals | 210 | |
| G | Using a calculator | 212 | |
| Review set 11A | 213 | ||
| Review set 11B | 214 | ||
| 12 | Measurement | 215 | |
| A | Units of measurement | 217 | |
| B | Reading scales | 219 | |
| C | Length conversions | 221 | |
| D | Perimeter | 223 | |
| E | Scale diagrams | 226 | |
| F | Mass | 228 | |
| G | Problem solving | 230 | |
| Review set 12A | 232 | ||
| Review set 12B | 233 | ||
| 13 | Directed numbers | 235 | |
| A | Opposites | 236 | |
| B | Directed numbers and the number line | 241 | |
| C | Using a number line to add and subtract | 245 | |
| D | Adding and subtracting negatives | 248 | |
| E | Multiplying directed numbers | 250 | |
| F | Dividing directed numbers | 253 | |
| G | Combined operations | 254 | |
| H | Using your calculator | 256 | |
| Review set 13A | 257 | ||
| Review set 13B | 257 | ||
| 14 | Percentage | 259 | |
| A | Percentages | 260 | |
| B | Converting fractions to percentages | 263 | |
| C | Converting percentages to fractions | 266 | |
| D | Converting decimals to percentages | 267 | |
| E | Converting percentages to decimals | 268 | |
| F | Plotting numbers on a number line | 270 | |
| G | Shaded regions of figures | 271 | |
| Review set 14A | 273 | ||
| Review set 14B | 274 | ||
| 15 | Time and temperature | 275 | |
| A | Time lines | 277 | |
| B | Units of time | 279 | |
| C | Differences in time | 281 | |
| D | Reading clocks and watches | 283 | |
| E | Timetables | 286 | |
| F | Time zones | 288 | |
| G | Average speed | 290 | |
| H | Temperature conversions | 292 | |
| Review set 15A | 293 | ||
| Review set 15B | 294 | ||
| 16 | Using percentages | 297 | |
| A | Comparing quantities | 298 | |
| B | Finding percentages of quantities | 301 | |
| C | Percentages and money | 302 | |
| D | Profit and loss | 303 | |
| E | Discount | 305 | |
| F | Goods tax | 306 | |
| G | Simple interest | 308 | |
| Review set 16A | 309 | ||
| Review set 16B | 310 | ||
| 17 | Data collection and representation | 311 | |
| A | Samples and populations | 313 | |
| B | Categorical data | 315 | |
| C | Graphs of categorical data | 318 | |
| D | Numerical data | 322 | |
| E | Mean or average | 326 | |
| Review set 17A | 329 | ||
| Review set 17B | 330 | ||
| 18 | Algebra and patterns | 331 | |
| A | Patterns | 332 | |
| B | Variables and notation | 335 | |
| C | Algebraic form | 336 | |
| D | The value of an expression | 338 | |
| E | Substituting into formulae | 339 | |
| F | Practical problems using formulae | 342 | |
| G | Linear graphs | 344 | |
| Review set 18A | 346 | ||
| Review set 18B | 346 | ||
| 19 | Area, volume and capacity | 349 | |
| A | Area | 350 | |
| B | Conversion of area units | 353 | |
| C | The area of a rectangle | 355 | |
| D | The area of a triangle | 358 | |
| E | Volume | 361 | |
| F | Capacity | 366 | |
| G | Problem solving | 368 | |
| Review set 19A | 370 | ||
| Review set 19B | 371 | ||
| 20 | Equations | 373 | |
| A | What are equations? | 374 | |
| B | Solving simple equations | 375 | |
| C | Maintaining balance | 377 | |
| D | Inverse operations | 380 | |
| E | Solving equations | 382 | |
| F | Problem solving with equations | 386 | |
| Review set 20A | 388 | ||
| Review set 20B | 389 | ||
| 21 | Coordinates and lines | 391 | |
| A | The number plane | 392 | |
| B | Points on a straight line | 394 | |
| C | Graphing straight lines | 395 | |
| D | Special lines | 396 | |
| E | The x and y-intercepts | 398 | |
| Review set 21A | 400 | ||
| Review set 21B | 401 | ||
| 22 | Transformations | 403 | |
| A | Reflections and line symmetry | 406 | |
| B | Rotations and rotational symmetry | 409 | |
| C | Translations | 414 | |
| D | Enlargements and reductions | 415 | |
| E | Tessellations | 417 | |
| Review set 22A | 421 | ||
| Review set 22B | 422 | ||
| 23 | Sets | 423 | |
| A | Sets and their members | 424 | |
| B | The intersection of sets | 428 | |
| C | The union of sets | 429 | |
| D | Venn diagrams | 430 | |
| Review set 23A | 434 | ||
| Review set 23B | 435 | ||
| 24 | Solids and polyhedra | 437 | |
| A | Types of solids | 439 | |
| B | Freehand drawings of solids | 442 | |
| C | Isometric projections | 445 | |
| D | Constructing block solids | 446 | |
| E | Nets of solids | 447 | |
| Review set 24A | 449 | ||
| Review set 24B | 450 | ||
| Answers | 451 | ||
| Index | 488 | ||
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:
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.
The International Baccalaureate Middle Years Programme focuses teaching and learning through five areas of interaction:
The Areas of Interaction are intended as a focus for developing connections between different subject areas in the curriculum and to promote an understanding of the interrelatedness of different branches of knowledge and the coherence of knowledge as a whole.
In an effort to assist busy teachers, we offer the following printable pages of ideas for projects and investigations:
| Chapter 2: Operations with whole numbers (p. 44) |
Tennis rankings
Human ingenuity/Approaches to learning
|
| Chapter 3: Points, lines and angles (p. 64) |
Making a protractor
Human ingenuity
|
| Chapter 5: Number properties (p. 104) |
Cicadas
Environments/Approaches to learning
|
| Chapter 7: Polygons (p. 142) |
Protecting yourself, the old fashioned way
Human ingenuity
|
| Chapter 11: Operations with decimals (p. 213) |
Body mass index
Health and social education
|
| Chapter 12: Measurement (p. 232) |
Calculating your carbon footprint
Environments/Community and service
|
| Chapter 15: Time and temperature (p. 293) |
How many steps do you take each day?
Environments/Health and social education
|
| Chapter 19: Area, volume and capacity (p. 370) |
How many bricks are needed to build a house?
Approaches to learning
|
| Chapter 20: Equations (p. 388) |
How are diving scores calculated?
Community and service/Health and social education
|
| Chapter 24: Solids and polyhedra (p. 449) |
Platonic solids
Human ingenuity/Approaches to learning
|
This book may be used as a general textbook at about 6th Grade (or Year 6) level in classes where students are expected to complete a rigorous course in Mathematics. It is the first book in our Middle Years series ‘Mathematics for the International Student’.
In terms of the IB Middle Years Programme (MYP), our series does not pretend to be a definitive course. In response to requests from teachers who use ‘Mathematics for the International Student’ at Diploma level, we have endeavoured to interpret their requirements, as expressed to us, for a series that would prepare students for the Mathematics courses at Diploma level. We have developed the series independently of the International Baccalaureate Organization (IBO) in consultation with experienced teachers of IB Mathematics. Neither the series nor this text is not endorsed by the IBO.
In regard to this book, it is not our intention that each chapter be worked through in full. Time constraints will not allow for this. Teachers must select exercises carefully, according to the abilities and prior knowledge of their students, to make the most efficient use of time and give as thorough coverage of content as possible.
We understand the emphasis that the IB MYP places on the five Areas of Interaction and in response there are links on the CD to printable pages which offer ideas for projects and investigations to help busy teachers (see p. 5).
Frequent use of the interactive features on the CD should nurture a much deeper understanding and
appreciation of mathematical concepts. The inclusion of our new
software (see p. 4) is intended to help students
who have been absent from classes or who experience difficulty understanding the material.
The book contains many problems to cater for a range of student abilities and interests, and efforts have been made to contextualise problems so that students can see the practical applications of the mathematics they are studying.
We welcome your feedback.