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Mathematics for Year 8: (Middle Years: Standard)

Mathematics for Year 8: (Middle Years: Standard)


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About the Book

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. 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 self tutor 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. Casio calculators graphics calculators are also given on the CD and can be printed.

Table of Contents:
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 90degree 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 60degree 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


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Product Details
  • ISBN-13: 9781876543402
  • Publisher: Haese & Harris Publications
  • Publisher Imprint: Haese & Harris Publications
  • Edition: Revised edition
  • No of Pages: 528
  • ISBN-10: 187654340X
  • Publisher Date: 30 Apr 2007
  • Binding: SA
  • Height: 250 mm
  • Series Title: Middle Years: Standard


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Mathematics for Year 8: (Middle Years: Standard)
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