About the Book
Year Published: 2014
Page Count: 496
ISBN: 978-1-921972-47-8 (9781921972478)
Online ISBN: 978-1-921972-48-5 (9781921972485)
Discontinued Edition
Year Published: 2014
Page Count: 496
ISBN: 978-1-921972-47-8 (9781921972478)
Online ISBN: 978-1-921972-48-5 (9781921972485)
| 1 | NUMBER | 11 | |
| A | Natural numbers | 12 | |
| B | Integers | 13 | |
| C | Index notation | 15 | |
| D | Order of operations | 16 | |
| E | Absolute value | 20 | |
| F | Square numbers and square roots | 21 | |
| G | Primes and composites | 23 | |
| H | Highest common factor | 25 | |
| I | Lowest common multiple | 27 | |
| Review set 1A | 28 | ||
| Review set 1B | 29 | ||
| 2 | SETS AND VENN DIAGRAMS | 31 | |
| A | Sets | 32 | |
| B | Complement of a set | 34 | |
| C | Intersection and union | 36 | |
| D | Venn diagrams | 38 | |
| E | Problem solving with Venn diagrams | 44 | |
| Review set 2A | 46 | ||
| Review set 2B | 48 | ||
| 3 | REAL NUMBERS AND RATIO | 49 | |
| A | Fractions | 50 | |
| B | Operations with fractions | 53 | |
| C | Decimal numbers | 57 | |
| D | Operations with decimal numbers | 60 | |
| E | Rational numbers | 63 | |
| F | Irrational numbers | 66 | |
| G | Ratio | 68 | |
| Review set 3A | 73 | ||
| Review set 3B | 74 | ||
| 4 | ALGEBRAIC OPERATIONS | 75 | |
| A | Algebraic notation | 76 | |
| B | The language of mathematics | 78 | |
| C | Collecting like terms | 80 | |
| D | Generalising arithmetic | 81 | |
| E | Algebraic substitution | 83 | |
| F | Algebraic products | 86 | |
| G | Algebraic fractions | 87 | |
| Review set 4A | 89 | ||
| Review set 4B | 90 | ||
| 5 | PERCENTAGE | 91 | |
| A | Percentage | 92 | |
| B | Expressing one quantity as a percentage of another | 95 | |
| C | Finding a percentage of a quantity | 97 | |
| D | The unitary method in percentage | 98 | |
| E | Percentage increase and decrease | 100 | |
| F | Finding the original amount | 103 | |
| G | Simple interest | 104 | |
| Review set 5A | 106 | ||
| Review set 5B | 107 | ||
| 6 | INTERPRETING TABLES AND GRAPHS | 109 | |
| A | Interpreting tables | 110 | |
| B | Interpreting graphs | 115 | |
| C | Line graphs | 119 | |
| D | Travel graphs | 121 | |
| Review set 6A | 125 | ||
| Review set 6B | 127 | ||
| 7 | LAWS OF ALGEBRA | 129 | |
| A | Index laws | 130 | |
| B | Expansion laws | 133 | |
| C | The zero index law | 136 | |
| D | The negative index law | 137 | |
| E | The distributive law | 139 | |
| F | The product (a + b)(c + d) | 142 | |
| G | Perfect square expansion | 144 | |
| H | Difference of two squares | 145 | |
| Review set 7A | 146 | ||
| Review set 7B | 147 | ||
| 8 | EQUATIONS | 149 | |
| A | Solutions of an equation | 150 | |
| B | Linear equations | 151 | |
| C | Maintaining balance | 152 | |
| D | Inverse operations | 154 | |
| E | Algebraic flowcharts | 156 | |
| F | Solving equations | 157 | |
| G | Equations with a repeated unknown | 161 | |
| Review set 8A | 165 | ||
| Review set 8B | 166 | ||
| 9 | THE GEOMETRY OF POLYGONS | 167 | |
| A | Review of geometrical facts | 168 | |
| B | Triangles | 173 | |
| C | Isosceles triangles | 177 | |
| D | Quadrilaterals | 180 | |
| E | Angles of an n-sided polygon | 185 | |
| Review set 9A | 187 | ||
| Review set 9B | 189 | ||
| 10 | RADICALS AND PYTHAGORAS | 191 | |
| A | Square roots | 192 | |
| B | Solving x² = k | 195 | |
| C | Pythagoras' theorem | 197 | |
| D | The converse of Pythagoras' theorem | 202 | |
| E | Problem solving using Pythagoras | 204 | |
| F | 3-dimensional problems | 207 | |
| G | Cube roots | 209 | |
| Review set 10A | 211 | ||
| Review set 10B | 212 | ||
| 11 | LENGTH AND AREA | 213 | |
| A | Length | 214 | |
| B | Perimeter | 216 | |
| C | Circumference | 218 | |
| D | Area | 223 | |
| E | Area formulae | 224 | |
| F | Areas of circles and ellipses | 228 | |
| G | Areas of composite figures | 230 | |
| Review set 11A | 234 | ||
| Review set 11B | 235 | ||
| 12 | ALGEBRA: PATTERNS AND FORMULAE | 237 | |
| A | Geometric patterns | 238 | |
| B | Number crunching machines | 241 | |
| C | Substituting into formulae | 244 | |
| D | Using patterns | 246 | |
| E | Practical problems | 249 | |
| F | Number sequences | 251 | |
| Review set 12A | 252 | ||
| Review set 12B | 253 | ||
| 13 | FURTHER MEASUREMENT | 255 | |
| A | Surface area | 256 | |
| B | Volume | 261 | |
| C | Capacity | 269 | |
| Review set 13A | 272 | ||
| Review set 13B | 273 | ||
| 14 | COORDINATE GEOMETRY | 275 | |
| A | The Cartesian plane | 277 | |
| B | Linear relationships | 279 | |
| C | Gradient | 282 | |
| D | Axes intercepts | 287 | |
| E | The equation of a line | 288 | |
| F | Graphing lines from equations | 290 | |
| G | Vertical and horizontal lines | 294 | |
| H | Finding equations from graphs | 295 | |
| Review set 14A | 296 | ||
| Review set 14B | 297 | ||
| 15 | SIMULTANEOUS EQUATIONS | 299 | |
| A | Trial and error solution | 301 | |
| B | Graphical solution | 302 | |
| C | Solution by equating values of y | 303 | |
| D | Solution by substitution | 304 | |
| E | Solution by elimination | 305 | |
| F | Problem solving with simultaneous equations | 308 | |
| Review set 15A | 311 | ||
| Review set 15B | 312 | ||
| 16 | PROBABILITY | 313 | |
| A | Probability | 314 | |
| B | Sample space | 316 | |
| C | Theoretical probability | 318 | |
| D | Using 2-dimensional grids | 321 | |
| E | Compound events | 322 | |
| F | Experimental probability | 326 | |
| G | Probabilities from tabled data | 331 | |
| H | Expectation | 334 | |
| Review set 16A | 335 | ||
| Review set 16B | 336 | ||
| 17 | PROBLEM SOLVING | 339 | |
| A | Writing problems as equations | 340 | |
| B | Problem solving with algebra | 341 | |
| C | Problem solving by search | 344 | |
| D | Problem solving by working backwards | 346 | |
| E | Miscellaneous problems | 348 | |
| Review set 17A | 353 | ||
| Review set 17B | 354 | ||
| 18 | SIMILARITY AND CONGRUENCE | 357 | |
| A | Enlargements and reductions | 358 | |
| B | Similar figures | 360 | |
| C | Similar triangles | 364 | |
| D | Problem solving | 367 | |
| E | Congruent figures | 371 | |
| F | Congruent triangles | 373 | |
| G | Proof using congruence | 378 | |
| Review set 18A | 379 | ||
| Review set 18B | 381 | ||
| 19 | ALGEBRAIC FACTORISATION | 383 | |
| A | Common factors | 384 | |
| B | Factorising with common factors | 386 | |
| C | Difference of two squares factorising | 389 | |
| D | Perfect square factorisation | 391 | |
| E | Factorising quadratic trinomials | 393 | |
| F | Miscellaneous factorisation | 395 | |
| Review set 19A | 396 | ||
| Review set 19B | 397 | ||
| 20 | STATISTICS | 399 | |
| A | Categorical data | 400 | |
| B | Numerical data | 403 | |
| C | Grouped data | 405 | |
| D | Measuring the centre and spread | 409 | |
| E | Comparing numerical data | 416 | |
| F | Data collection | 418 | |
| Review set 20A | 421 | ||
| Review set 20B | 423 | ||
| 21 | QUADRATIC EQUATIONS | 425 | |
| A | Quadratic equations | 426 | |
| B | The Null Factor law | 427 | |
| C | Solving quadratic equations | 428 | |
| D | Problem solving with quadratic equations | 432 | |
| Review set 21A | 436 | ||
| Review set 21B | 437 | ||
| 22 | TRIGONOMETRY | 439 | |
| A | Scale diagrams in geometry | 441 | |
| B | Labelling right angled triangles | 442 | |
| C | The trigonometric ratios | 443 | |
| D | Finding side lengths | 447 | |
| E | Finding angles | 449 | |
| F | Problem solving with trigonometry | 451 | |
| Review set 22A | 454 | ||
| Review set 22B | 455 | ||
| 23 | INTRODUCTION TO NETWORKS | 457 | |
| A | Network diagrams | ONLINE | |
| B | Constructing networks | ONLINE | |
| C | Topologically equivalent networks | ONLINE | |
| D | Precedence networks | ONLINE | |
| E | Counting pathways | ONLINE | |
| Review set 23A | ONLINE | ||
| Review set 23B | ONLINE | ||
| ANSWERS | 458 | ||
| INDEX | 495 | ||
Michael completed a Bachelor of Science at the University of Adelaide, majoring in Infection and Immunity, and Applied Mathematics. He studied laminar heat flow as part of his Honours in Applied Mathematics, and finished a PhD in high speed fluid flows in 2001. He has been the principal editor for Haese Mathematics since 2008.
What motivates you to write mathematics books?
My passion is for education as a whole, rather than just mathematics. In Australia I think it is too easy to take education for granted, because it is seen as a right but with too little appreciation for the responsibility that goes with it. But the more I travel to places where access to education is limited, the more I see children who treat it as a privilege, and the greater the difference it makes in their lives. But as far as mathematics goes, I grew up with mathematics textbooks in pieces on the kitchen table, and so I guess it continues a tradition.
What do you aim to achieve in writing?
I think a few things:
What interests you outside mathematics?
Lots of things! Horses, show jumping and course design, alpacas, badminton, running, art, history, faith, reading, hiking, photography ....
Sandra completed a Bachelor of Science at the University of Adelaide, majoring in Pure Mathematics and Statistics. She taught at Underdale High School and Westminster School before founding Haese and Harris Publications (now Haese Mathematics), together with husband Robert (Bob) and colleague Kim Harris.
What drew you to the field of mathematics?
I always found mathematics the easiest subject at school. I’m not sure why. I intended to study Chemistry at university, but found I didn’t enjoy it as much as I thought I would – so I came back to mathematics, and have been involved with it ever since.
What motivated you to switch from teaching to writing mathematics books?
Bob used to write notes for his class. Other teachers at the school used the notes, then teachers at other schools started asking for them. Eventually Bob said, “Well, I might as well start writing textbooks!”
Initially, I was proofreading. As the workload increased, I began editing as well as proofreading. It just gradually became a full-time job, between writing material, editing and proofreading it, and then distributing the books. These days, Michael does the editing and I do proofreading and audio.
How has the field of textbook publishing changed in the years since you started?
When we started, text was typed and worked solutions were handwritten. Bob would draw any graphics by hand.
We moved to typesetting, but writing a mathematics textbook with the printing tools available presented its own difficulties. For example, symbols had to be copied, cut and pasted by hand onto the original pages, which was very tedious and time-consuming! Fractions were also problematic: we would type a line containing all the numerators, and then a line underneath for all the denominators.
Now it’s all done by computers, which is very much easier, and quicker!
What interests you outside mathematics?
I own a few alpacas. I enjoy my garden - I don’t do much in it, but I enjoy it! I like listening to music; mainly classical, but I enjoy other genres as well.
I really love to travel. The scenery, the history of a place, its architecture, its art – all of those things fascinate me. As a result I also enjoy photography; I like taking pictures of the things I’ve seen and places I’ve experienced.
Mark has a Bachelor of Science (Honours), majoring in Pure Mathematics, and a Bachelor of Economics, both of which were completed at the University of Adelaide. He studied public key cryptography for his Honours in Pure Mathematics. He started with the company in 2006, and is currently the writing manager for Haese Mathematics.
What got you interested in mathematics? How did that lead to working at Haese Mathematics?
I have always enjoyed the structure and style of mathematics. It has a precision that I enjoy. I spend an inordinate amount of my leisure time reading about mathematics, in fact! To be fair, I tend to do more reading about the history of mathematics and how various mathematical and logic puzzles work, so it is somewhat different from what I do at work.
How did I end up at Haese Mathematics?
I was undertaking a PhD, and I realised that what I really wanted to do was put my knowledge to use. I wanted to pass on to others all this interesting stuff about mathematics. I emailed Haese Mathematics (Haese and Harris Publications as they were known back then), stating that I was interested in working for them. As it happened, their success with the first series of International Baccalaureate books meant that they were looking to hire more people at the time. I consider myself quite lucky!
What are some interesting things that you get to do at work?
On an everyday basis, it’s a challenge (but a fun one!) to devise interesting questions for the books. I want students to have questions that pique their curiosity and get them thinking about mathematics in a different way. I prefer to write questions that require students to demonstrate that they understand a concept, rather than relying on rote memorisation.
When a new or revised syllabus is released for a curriculum that we write for, a lot of work goes into devising a structure for the book that addresses the syllabus. The process of identifying what concepts need to be taught, organising those concepts into an order that makes sense from a teaching standpoint, and finally sourcing and writing the material that addresses those concepts is very involved – but so rewarding when you hold the finished product in your hands, straight from the printer.
What interests you outside mathematics?
Apart from the aforementioned recreational mathematics activities, I play a little guitar, and I enjoy playing badminton and basketball on a social level.
Pamela completed a Bachelor of Science with Honours at the University of East Anglia in the UK. She has also completed a Postgraduate Certificate of Education at the Cambridge Institute of Education.
When did you start teaching, and where have you taught?
I started teaching in 1973 at the Hewett School in Norwich, and taught all levels up to and including A level Pure, A Level Applied and S level Mathematics. I was also Pastoral Tutor to Year 11. I was then recruited by the British Council to be Head of Mathematics and Science at the English High School for Girls in Istanbul, where I stayed for 6 years. In 1985, I came to Frankfurt International School. I became Head of the Mathematics Department and have taught IB Mathematics at all levels. I was also elected by the faculty to the Board of Trustees of the school where I served for more than 6 years.
How did you come to collaborate with Haese Mathematics?
When Haese Mathematics brought out their first edition of Mathematics for the International Student MYP5, we bought some copies to have a look at. Shortly after, I received an email from their marketing department asking whether I would be willing to give them my evaluation of the book, which I did. Ray O'Farrell, responsible for marketing, got in touch, and I mentioned to him the problems that schools like ours were having in finding a set of suitable maths textbooks for grade 6-10 which would be rigorous enough to prepare students for IB. I also told him that we had even joked about contacting a publisher to produce such a series. Famous last words! This was the point where Ray asked whether I would be willing, in principle, to work with Haese Mathematics to produce such a series. I agreed....... and the rest is history!
What interests you outside mathematics?
Outside school, when I'm not looking after my family, I enjoy going to the theatre, both watching and acting. I love entertaining friends (and being entertained!), walking, and I read far too many crime/espionage novels. I also love travelling and (trying to speak) foreign languages; at the moment I am learning Japanese.
A complete electronic copy of the textbook, with interactive, animated, and/or printable extras.
Animated worked examples with step-by-step, voiced explanations.
Projects to guide Global Context work.
Graphics Calculator Instructions
For Casio fx-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire
This book is available on electronic devices through our Snowflake learning platform. This book includes 15 months of Snowflake access, featuring a complete electronic copy of the textbook.
Where relevant, Snowflake features include interactive geometry, graphing, and statistics software, demonstrations, games, spreadsheets, and a range of printable worksheets, tables, and diagrams. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.
This book offers SELF TUTOR for every worked example. On the electronic copy of the textbook, access SELF TUTOR by clicking anywhere on a worked example to hear a step-by-step explanation by a teacher. This is ideal for catch-up and revision, or for motivated students who want to do some independent study outside school hours.
The International Baccalaureate Middle Years Programme focuses teaching and learning through six Global Contexts:
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There are 6 projects included in this book, one for each of the Global Contexts. Each project is divided into factual, conceptual, and debatable questions to help guide the unit of work.
Projects are accompanied by a general descriptor and a task-specific descriptor for each of the relevant assessment criteria, to help teachers assess the unit of work.
The Global Contexts 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.
Graphics calculator instructions for Casio fx-9860G Plus, Casio fx-CG20, TI-84 Plus, and TI-nspire are included with this textbook. The textbook will either have comprehensive instructions at the start of the book, specific instructions available from icons located throughout, or both. The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology.
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