In line with the SACSA Framework for Middle Years Mathematics and the R-7 SACSA Mathematics Teaching Resource.
This second edition is a general revision and updating of the original text, with some reorganisation of chapters. Changes include:
In the table of contents, page numbers for corresponding sections in the first edition are given in brackets. This is intended as a guide for teachers who may wish to use the first and second editions within the same classroom. A glance at the contents pages will show how both books correlate (the absence of a page number in brackets denotes the introduction of a new section).
An interactive CD is included with this book. The CD contains the text of the book, so that students can keep the CD at home and the book at school, to avoid carrying the book to and from school each day.
The CD also contains many ‘active icons’. Click on the ‘CD LINK’ icons to access:
The CD is an excellent resource for classroom demonstrations or individual study and revision. 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 | ADDING AND SUBTRACTING | 9 | (41) | |
| A | Number systems | 10 | (42) | |
| B | Place value | 11 | (44) | |
| C | Numbers in words | 13 | (46) | |
| D | Rounding off numbers | 14 | (47) | |
| E | Estimating | 17 | (50) | |
| F | Adding whole numbers | 18 | (52) | |
| G | Subtraction | 23 | (57) | |
| H | Using symbols | 28 | ||
| I | Using a calculator | 28 | (62) | |
| J | Mixed problem solving | 29 | (63) | |
| Mental set 1A | 31 | |||
| Mental set 1B | 31 | |||
| Mental set 1C | 31 | |||
| Skill tester: Whole numbers | 33 | |||
| Review exercise 1 | 34 | |||
| 2 | 2-DIMENSIONAL SHAPES | 35 | ||
| A | Angles | 36 | (10) | |
| B | Measuring and drawing angles | 39 | ||
| C | Polygons | 42 | (12) | |
| D | Parallel lines | 44 | (15) | |
| E | Symmetrical figures | 46 | (17) | |
| F | Triangles and quadrilaterals | 47 | (19) | |
| G | Circles | 51 | (23) | |
| Skill tester: Plane geometry | 55 | |||
| Activity: Circumference | 56 | |||
| Mental set 2A | 57 | |||
| Mental set 2B | 57 | |||
| Review exercise 2 | 58 | |||
| 3 | MULTIPLYING AND DIVIDING WHOLE NUMBERS | 59 | (91) | |
| A | Factors | 60 | (92) | |
| B | Multiples | 62 | ||
| C | Multiplying by 10, 100, 1000 | 63 | (94) | |
| D | Estimating multiplications | 65 | ||
| E | Multiplication | 66 | (96) | |
| F | Division | 70 | (99) | |
| G | Estimating divisions | 73 | ||
| H | Using a calculator | 74 | (102) | |
| I | Problem solving using multiplication and division | 75 | (103) | |
| J | Further problem solving | 76 | ||
| K | Order of operations | 77 | (106) | |
| Skill tester: Mary’s mixed up multiplication machine | 81 | |||
| Mental set 3A | 82 | |||
| Mental set 3B | 82 | |||
| Mental set 3C | 82 | |||
| Mental set 3D | 82 | |||
| Review exercise 3 | 83 | |||
| Have fun with these using a calculator | 84 | |||
| 4 | LOCATION | 85 | (69) | |
| A | The language of position | 86 | (70) | |
| B | Finding points | 89 | (72) | |
| C | Direction | 91 | (74) | |
| D | Scales | 94 | (76) | |
| E | Degrees | 97 | (79) | |
| F | Finding treasures | 98 | (81) | |
| G | Coordinates | 100 | (83) | |
| Skill tester: Location | 103 | |||
| Mental set 4A | 104 | |||
| Mental set 4B | 104 | |||
| Review exercise 4 | 105 | |||
| 5 | FRACTIONS | 107 | (113) | |
| A | Representing fractions | 108 | (115) | |
| B | Fractions that add to one (whole) | 112 | (118) | |
| C | Finding a fraction of a quantity | 114 | (120) | |
| D | Improper fractions and mixed numbers | 116 | (122) | |
| E | Equivalent fractions | 119 | (125) | |
| F | Fractions as division | 123 | (128) | |
| G | Addition and subtraction of fractions | 124 | (129) | |
| Skill tester: Fractions | 129 | |||
| Mental set 5A | 130 | |||
| Mental set 5B | 130 | |||
| Mental set 5C | 130 | |||
| Review exercise 5A | 131 | |||
| Review exercise 5B | 132 | |||
| 6 | DECIMALS | 133 | (139) | |
| A | Tenths as decimals | 134 | (140) | |
| B | Hundredths | 136 | (143) | |
| C | Decimals on a number line | 139 | (146) | |
| D | Place value | 142 | (148) | |
| E | Order of size | 143 | (150) | |
| F | Adding decimal numbers | 146 | (157) | |
| G | Subtracting decimal numbers | 148 | (159) | |
| H | Multiplication by 10, 100 and 1000 | 149 | (162) | |
| I | Using a calculator | 151 | (163) | |
| J | Percentage | 152 | (164) | |
| Activity: The game of equality | 154 | |||
| Mental set 6A | 155 | |||
| Mental set 6B | 155 | |||
| Mental set 6C | 155 | |||
| Skill tester: Decimals | 157 | |||
| Review exercise 6A | 157 | |||
| Review exercise 6B | 158 | |||
| 7 | MONEY | 159 | ||
| A | Money | 160 | (153) | |
| B | Adding and subtracting with money | 164 | ||
| C | Multiplying and dividing | 166 | ||
| D | Problem solving | 168 | ||
| E | Using a calculator | 169 | ||
| F | Budgets | 170 | ||
| Skill tester: Money | 173 | |||
| Mental set 7A | 173 | |||
| Mental set 7B | 173 | |||
| Review exercise 7A | 174 | |||
| Review exercise 7B | 174 | |||
| 8 | PATTERNS AND ALGEBRA | 175 | ||
| A | Number patterns | 177 | (175) | |
| B | Patterns with matchsticks | 179 | (176) | |
| C | Number crunching machines | 181 | (178) | |
| D | Other patterns | 182 | (183) | |
| E | Finding missing numbers | 184 | (184) | |
| Skill tester: Number patterns | 187 | |||
| Mental set 8A | 188 | |||
| Mental set 8B | 188 | |||
| Mental set 8C | 188 | |||
| Review exercise 8A | 189 | |||
| Review exercise 8B | 190 | |||
| 9 | MEASUREMENT | 191 | (191) | |
| A | Length | 192 | (192) | |
| B | Conversion of length units | 195 | ||
| C | Perimeter | 197 | (196) | |
| D | Area | 200 | (199) | |
| E | Volume | 205 | (202) | |
| F | Capacity | 207 | (204) | |
| G | Mass | 211 | (210) | |
| Activity: Net mass | 215 | |||
| Mental set 9A | 216 | |||
| Mental set 9B | 216 | |||
| Mental set 9C | 216 | |||
| Review exercise 9A | 217 | |||
| Review exercise 9B | 218 | |||
| 10 | TIME AND TEMPERATURE | 219 | ||
| A | Telling the time | 220 | (213) | |
| B | Conversion of units | 225 | ||
| C | Using a calendar | 227 | (268) | |
| D | Using timetables | 229 | ||
| E | Problem solving | 233 | ||
| F | Temperature | 233 | ||
| Skill tester: Measurement | 237 | |||
| Mental set 10A | 238 | |||
| Mental set 10B | 238 | |||
| Review exercise 10A | 238 | |||
| Review exercise 10B | 239 | |||
| 11 | DATA COLLECTION AND GRAPHING | 241 | ||
| A | Collecting and recording data | 242 | (228) | |
| B | Column and bar graphs | 245 | (230) | |
| C | Composite graphs | 249 | ||
| D | Using technology to graph data | 250 | ||
| E | Pie graphs | 251 | ||
| F | Pictograms (pictographs) | 253 | (232) | |
| G | Line graphs | 254 | ||
| H | Surveys | 257 | (237) | |
| I | Statistical activity | 259 | (239) | |
| J | Reading charts and tables | 260 | (276) | |
| Skill tester: Sam’s super survey | 263 | |||
| Mental set 11A | 264 | |||
| Mental set 11B | 264 | |||
| Mental set 11C | 264 | |||
| Review exercise 11A | 265 | |||
| Review exercise 11B | 265 | |||
| 12 | 3-DIMENSIONAL SHAPES | 267 | ||
| A | Names of special solids | 268 | (246) | |
| B | Sketching solids | 271 | (248) | |
| C | Making solids | 272 | (250) | |
| D | Views from different directions | 275 | (254) | |
| E | Making cylinders and cones | 276 | (256) | |
| F | The platonic solids | 278 | (260) | |
| G | The platonic solids (extension) | 273 | ||
| Skill tester: Solid geometry | 280 | |||
| Mental set 12A | 281 | |||
| Mental set 12B | 281 | |||
| Review exercise 12 | 281 | |||
| 13 | CHANCE | 284 | (285) | |
| A | Words describing chance | 285 | (287) | |
| B | What do you expect? | 287 | (289) | |
| C | Possible outcomes | 289 | (294) | |
| D | Probability by experiment | 291 | ||
| Mental set 13A | 292 | |||
| Mental set 13B | 292 | |||
| Review exercise 13A | 293 | |||
| Skill tester: ‘Dealing with chance’ | 295 | |||
| Investigation: Tossing a coin | 296 | |||
| Review exercise 13B | 296 | |||
| 14 | TRANSFORMATIONS | 297 | ||
| A | Transforming shapes | 298 | (32) | |
| B | Translations | 299 | ||
| C | Rotations | 301 | ||
| D | Reflections | 302 | ||
| E | Enlarging and reducing | 304 | ||
| F | Tessellations | 306 | (28) | |
| Mental set 14A | 311 | |||
| Mental set 14B | 311 | |||
| Review exercise 14 | 312 | |||
| ANSWERS | 313 | |||
| INDEX | 339 | |||
Mathematics for Year 5 (second edition) presents a comprehensive and rigorous course in mathematics at Year 5 level. The book provides students with the structure and content to work efficiently at their own rate, with the help of worked examples, exercises, activities and answers, and the support of the interactive Student CD.
The book and CD package can supplement classroom practice and give teachers time to explore other creative strategies, according to the needs of their students. It is not the Year 5 Mathematics Curriculum, nor does it proclaim to provide the most effective teaching program.
The knowledge, skills and understandings summarised at the beginning of each chapter reflect the descriptors used in the R-7 SACSA Mathematics Teaching Resource for Primary Years. We hope that this will be a helpful guide for Year 5 teachers who may wish to use the book to support their teaching practice.
This second edition is a general revision and updating of the original text, with some reorganisation of chapters. Changes include:
In the table of contents, page numbers for corresponding sections in the first edition are given in brackets. This is intended as a guide for teachers who may wish to use the first and second editions within the same classroom. A glance at the contents pages will show how both books correlate (the absence of a page number in brackets denotes the introduction of a new section).
The interactive Student CD 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. But more than that, by clicking on the ‘active icons’ within the text, students can access a range of interactive features: graphing and geometry packages, video clips, computer demonstrations and simulations, and worksheets.
The CD is ideal for independent study. Students can revisit concepts taught in class and explore new ideas for themselves. It is fantastic for teachers to use for demonstrations and simulations in the classroom.
In summary, the book offers structure and rigour, and the CD makes maths come alive.
We have endeavoured to provide as broad a base of activity and learning styles as we can, 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
Web: www.haeseandharris.com.au