The Wyze Maths Workbooks are the only Workbooks available according to the exact prescribed CAPS Educational Department requirements. In order to verify the educational correctness of any educational related book for this Grade there are only two options available: Option 1 to visit the Educational Curriculum website to compare the index of the book in question against the Curriculum CAPS requirements, or Option 2 to compare the book in question according to the index of our Wyze Workbook. Although the Wyze Workbooks were developed with Parental assistance in mind (see Parent involvement on ANA link) by, for the first time ever, giving informative definitions and examples to assist the Parent and Learner with correct Educational terminology per Grade, this Wyze Workbook also adhere to the Educational Curriculum requirements, i.e. a. National Curriculum Statement (NCS), Currculum Assessment Policy Statement (CAPS); b. CAPS required progressive distribution per term; c. Teachers guidelines per Grade as per the CAPS requirements. WYZE EDUCATIONAL PUBLISHERS i
MATHS WORKBOOK GRADE 3 This book belongs to: REMEMBER: You should never be afraid of making mistakes, because that s the only way of gaining confidence and knowledge. Maths Workbook for Grade 3 WYZE Educational Publications PO Box 41683 Moreletapark 0044 Fax: (012) 997 5335 First Edition, First Impression ISBN: 978-0-920259-10-8 All rights reserved. No part of this publication may be reproduced. ii WYZE EDUCATIONAL PUBLISHERS
MATHS GRADE 3 LEARNING SKILLS NUMBERS, OPERATIONS AND RELATIONSHIPS We will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and to check answers with competence and confidence. PATTERNS, FUNCTIONS AND ALGEBRA We will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. SPACE AND SHAPE (GEOMETRY) We will be able to describe and represent characteristics of and relationships between twodimensional shapes and three-dimensional objects in a variety of orientations and positions. MEASUREMENT We will be able to use appropriate measuring units, instruments and formulae in a variety of situations. DATA HANDLING We will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation. My class Boys Girls WYZE EDUCATIONAL PUBLISHERS iii
Assessment Index Page Term 1 1 NUMBERS, OPERATIONS AND RELATIONSHIPS 1 1. Count objects. 1 1.1 Group to at least 200 objects to estimate and count reliably. 1 1.2 Give a reasonable estimate of a number of objects that can be checked by counting. 2 2. Count forwards and backwards. 2 2.1 Count forwards and backwards in the intervals specified in grade 2 from any given number between 0 and 200. 2 2.2 Count forwards and backwards in 100s to at least 500. 5 3. Number symbols and number names. 3.1 Recognise, identify and read numbers. 5 5 4. Describe, compare and order numbers. 4.1 Describe, compare and order numbers to 99. 5. Place value. 5.1 Recognise the place value of numbers to 99. 6. Problem-solving techniques. 6.1 Use the following techniques when solving problems and explain solutions to problems. 7. Addition and subtraction. 7.1 Solve word problems in context and explain own solution to problems involving addition, subtraction leading answers up to 99. 8. Repeated addition leading to multiplication. 8.1 Solve number problems in context and explain own solution to problems involving multiplication with answers up to 50. 9. Grouping and sharing leading to division. 9.1 Solve and explain solutions to practical problems that involve equal sharing and grouping up to 50 with answers that may include remainders. 10. Fractions. 10.1 Solve and explain solutions to practical problems that involve equal sharing leading to solutions that include unitary and non-unitary fractions e.g.,,, etc. 11. Money. 11.1 Recognise and identify the South African coins and banknotes. 11.2 Solve money problems involving totals and change in Rand or cents. 12. Techniques (methods or strategies). 12.1 Use the following techniques when performing the following operations. 13. Addition and subtraction. 13.1 Add up to 99. 13.2 Subtract from 99. 13.3 Use appropriate symbols (+, -, =). 13.4 Practise number bonds to 20. 7 7 8 8 10 10 13 13 14 14 16 16 17 17 18 18 19 20 20 22 22 25 28 29 iv WYZE EDUCATIONAL PUBLISHERS
14. Repeated addition leading to multiplication. 14.1 Multiply numbers 1 to 10 by 2, 5, 3 and 4. 14.2 Use appropriate symbols (x, =). 15. Division. 15.1 Divide numbers to 50 by 2, 5 and 10. 15.2 Use appropriate symbols (, =). 16. Mental mathematics. 16.1 Number concept: Range 200. 16.2 Rapid recall. 17. Fractions. 17.1 Apply and name fractions in familiar contexts including halves, quarters, eighths, thirds, sixths and fifths. 17.2 Recognise fractions in diagrammatic form. 17.3 Write fractions as 1 half, 1 third. 29 29 32 33 33 35 35 36 37 39 39 39 40 PATTERNS, FUNCTIONS AND ALGEBRA 41 1. Geometric patterns. 41 1.1 Copy, extend and describe in words. 41 1.2 Create and describe own geometric patterns. 43 2. Number patterns. 43 2.1 Copy, extend and describe simple number sequences up to at least 200. Sequences should show counting forwards and backwards in. 44 SPACE AND SHAPE 45 1. 2-D shapes. 45 1.1 Range of shapes. 45 1.2 Features of shapes. 47 MEASUREMENT 48 1. Time. 48 1.1 Telling the time. 48 2. Capacity/volume. 53 2.1 Informal measurement. 54 2.2 Introduction formal measurement. DATA HANDLING 57 1. Collect and organise data. 57 1.1 Collect data about the class or school to answer questions posed by the teacher. 57 2. Represent data. 58 2.1 Represent data through tables and bar graphs. 58 3. Analyse and interpret data. 60 3.1 Talk about and answer questions about data in tables and bar graphs. 60 WYZE EDUCATIONAL PUBLISHERS v
Term 2 61 NUMBERS, OPERATIONS AND RELATIONSHIPS 61 1. Counting objects. 61 1.1 Group to at least 500 objects to estimate and count reliable. 61 1.2 Give a reasonable estimate of a number of objects that can be checked by counting. 61 2. Count forwards and backwards. 62 2.1 Count forwards and backwards in the intervals specified in grade 2 with increased number ranges. 62 2.2 Count forwards and backwards in 50s and 100s up to at least 1 000. 63 3. Number symbols and number names. 63 3.1 Recognise, identify and read numbers. 63 4. Describe, compare and order numbers. 65 4.1 Describe, compare and order numbers to 500. 65 5. Place value. 66 5.1 Recognise the place value of numbers up to 500. 66 6. Problem-solving techniques. 68 6.1 Use the following techniques when solving problems. 68 7. Addition and subtraction. 71 7.1 Solve word problems in context and explain own solution to problems involving addition and subtraction with answers up to 400. 71 8. Repeated addition leading to multiplication. 72 8.1 Solve number problems in context and explain own solution to problems involving multiplication with answers up to 75. 72 9. Grouping and sharing leading to division. 73 9.1 Solve number problems in context and explain own solution to problems that involve equal sharing and grouping with answers up to 75. Answers may include remainders. 73 10. Fractions. 74 10.1 Solve and explain solutions to practical problems that involve equal sharing leading to solutions that include unitary and non-unitary fractions, e.g.,,, etc. 74 11. Money. 11.1 Recognise and identify the South African coins and banknotes. 11.2 Solve money problems involving totals and change in rand or cents. 12. Techniques (methods or strategies). 12.1 Use the following techniques when performing calculations. 13. Addition and subtraction. 13.1 Add up to 400. 13.2 Subtract from 400. 13.3 Use appropriate symbols (+, -, =). 13.4 Practise number bonds to 30. 14. Repeated addition leading to multiplication. 14.1 Multiply 2, 3, 4, 5, 10 to a total of 50. 14.2 Use appropriate symbols (x, =). 75 75 76 77 77 80 80 84 87 88 88 88 91 vi WYZE EDUCATIONAL PUBLISHERS
15. Division. 15.1 Divide numbers to 50 by 2, 4, 5 and 10. 15.2 Use appropriate symbols (, =). 16. Mental mathematics. 16.1 Number concept: Range 500. 16.2 Rapid recall. 17. Fractions. 17.1 Use and name unitary fractions including halves, quarters, eighths, thirds, sixths and fifths. 17.2 Recognise fractions in diagrammatic form. 17.3 Write fraction as 1 half, 1 third. 91 91 93 94 94 96 98 98 98 99 PATTERNS, FUNCTIONS AND ALGEBRA 100 1. Geometric patterns. 100 1.1 Copy, extend and describe in words. 100 1.2 Create and describe own geometric patterns. 101 2. Number patterns. 102 2.1 Copy, extend and describe simple number sequences up to at least 500. 102 SPACE AND SHAPE 104 1. Position, orientation and views. 1.1 Position and views. 1.2 Position and directions. 2. 3-D objects. 2.1 Range of objects. 2.2 Features of objects. 2.3 Focused activities. 3. Symmetry. 3.1 Determine line of symmetry through paper folding and reflection. 3.2 Suggested focus of Term 2. 104 104 106 108 108 110 113 113 113 115 MEASUREMENT 115 1. Time. 115 1.1 Telling the time calendars, 12 hour time on analogue clocks and digital clocks, etc. 115 1.2 Calculate length of time and passing of time. 117 2. Length. 2.1 Informal measuring. 2.2 Introducing formal measurement. 3. Mass. 3.1 Informal measuring. 3.2 Introducing formal measurement. 118 119 120 121 121 122 DATA HANDLING 125 1. Analyse and interpret data. 125 1.1 Analyse data from representations provided. 125 WYZE EDUCATIONAL PUBLISHERS vii
Term 3 127 NUMBERS, OPERATIONS AND RELATIONSHIPS 127 1. Count objects. 127 1.1 Group to at least 700 objects to estimate and count reliably. 127 1.2 Give a reasonable estimate of a number of objects that can be checked by counting. 127 2. Count forwards and backwards. 128 2.1 Count forwards and backwards in the intervals specified in grade 2 with increased number ranges. 128 2.2 Count forwards and backwards in 20s, 25s, 50s, 100e to at least 1 000. 128 3. Number symbols and number names. 3.1 Recognise, identify and read numbers. 4. Describe, compare and order numbers. 4.1 Describe, compare and order numbers to 700. 4.2 Use ordinal numbers to show order, place or position. 5. Place value. 5.1 Recognise the place value of numbers to 700. 6. Problem-solving techniques. 6.1 Use the following techniques when solving problems and explain solutions to problems. 7. Addition and subtraction. 7.1 Solve word problems in context and explain own solution to problems involving addition, subtraction leading answers up to 800. 8. Repeated addition leading to multiplication. 8.1 Solve number problems in context and explain own solution to problems involving multiplication with answers up to 100. 9. Grouping and sharing leading to division. 9.1 Solve and explain solutions to practical problems that involve equal sharing and grouping up to 150 with answers that my include remainders. 10. Fractions. 10.1 Solve and explain solutions to practical problems that involve equal sharing leading to solutions that include unitary and non-unitary fractions, e.g.,,, etc. 129 129 131 131 132 133 133 136 136 139 139 140 140 141 141 142 142 11. Money. 11.1 Recognise and identify the South African coins and banknotes. 11.2 Solve money problems involving totals and change in Rand and cents. 11.3 Convert between rand and cents. 12. Techniques (methods or strategies). 12.1 Use the following techniques when performing the operations. 13. Addition and subtraction. 13.1 Add up to 800. 13.2 Subtract from 800. 13.3 Use appropriate symbols (+, -, =). 13.4 Practice number bonds to 30. 142 142 144 145 146 146 149 149 151 154 154 viii WYZE EDUCATIONAL PUBLISHERS
14. Repeated addition leading to multiplication. 14.1 Multiply 2, 3, 4, 5, 10 to a total of 99. 14.2 Use appropriate symbols (x, =). 15. Division. 15.1 Divide numbers to 99 by 2, 4, 5, 10 and 3. 15.2 Use appropriate symbols (, =). 16. Mental mathematics. 16.1 Number concept: Range 750. 16.2 Rapid recall. 17. Fractions. 17.1 Apply and name fractions in familiar contexts including halves, quarters, eighths, thirds, sixths and fifths. 17.2 Recognise fractions in diagrammatic form. 17.3 Begin to recognise that two halves or three thirds make one whole and that 1 half and 2 quarters are equivalent. 17.4 Write fractions as 1 half, 2 thirds. 155 155 160 161 161 163 164 164 167 168 168 169 169 171 PATTERNS, FUNCTIONS AND ALGEBRA 171 1. Geometric patterns. 1.1 Copy, extend and describe in words. 1.2 Create and describe own geometric patterns. 2. Number patterns. 2.1 Copy, extend and describe simple number sequences to at least 750. 2.2 Create and describe own number patterns. 171 171 172 173 173 174 SPACE AND SHAPE 174 1. Position, orientation and views. 174 1.1 Position and views. 174 1.2 Position and directions. 176 2. 3-D objects. 2.1 Range of objects. 2.2 Features of objects. 2.3 Focused activities. 3. 2-D shapes. 3.1 Range of shapes: circles, triangles, squares, rectangles. 3.2 Features of shapes: shape, straight sides, rounded sides. 178 178 179 180 180 180 181 MEASUREMENT 183 1. Time. 183 1.1 Telling the time. 183 1.2 Calculate length of time and passing of time. 186 2. Length. 2.1 Introducing formal measuring. 3. Perimeter. 3.1 Investigate the distance around 2-D shapes and 3-D objects using direct comparison or informal units. 188 188 193 193 WYZE EDUCATIONAL PUBLISHERS ix
DATA HANDLING 196 1. Collect and organise data. 196 1.1 Re-organise data provided in a list or tally or table in a bar graph. 196 2. Data presentation. 196 2.1 Represent data on bar graph. 196 3. Analyse and interpret data. 197 3.1 Answer questions on the data in the bar graph. 197 Term 4 199 NUMBERS, OPERATIONS AND RELATIONSHIPS 199 1. Count objects. 199 1.1 Group to at least 1 000 objects to estimate and count reliable. 1.2 Give a reasonable estimate of a number of objects that can be checked by counting. 199 2. Count forwards and backwards. 200 2.1 Count forwards and backwards in the intervals specified in grade 2 within increased number ranges. 200 2.2 Count forwards and backwards in 20s, 25s, 50s, 100s to at least 1 000. 201 3. Number symbols and number names. 201 3.1 Recognise, identify and read numbers. 201 4. Describe, compare and order numbers. 202 4.1 Describe, compare and order numbers to 99. 202 5. Place value. 203 5.1 Recognise the place value of numbers to 999. 203 6. Problem-solving techniques. 205 6.1 Use the following techniques when solving problems and explain solutions to problems. 205 7. Addition and subtraction. 208 7.1 Solve word problems in context and explain own solution to problems involving addition and subtraction with answers up to 999. 208 8. Repeated addition leading to multiplication. 209 8.1 Solve number problems in context and explain own solution to problems involving multiplication with answers up to 100. 209 9. Grouping and sharing leading to division. 210 9.1 Solve and explain solutions to practical problems that involve equal sharing and grouping up to 100 with answers that may include remainders. 210 10. Fractions. 211 10.1 Solve and explain solutions to practical problems that involve equal sharing leading to solutions that include unitary and non-unitary fractions, e.g.,,, etc. 211 11. Money. 11.1 Recognise and identify the South African coins and bank notes. 11.2 Solve money problems involving totals and change in rand and cents. 11.3 Convert between rand and cents. 213 213 213 215 x WYZE EDUCATIONAL PUBLISHERS
12. Techniques (methods or strategies). 12.1 Use techniques when performing calculations. 13. Addition and subtraction. 13.1 Add up to 999. 13.2 Subtract from 999. 13.3 Use appropriate symbols (+, -, =). 13.4 Practise number bonds to 30. 14. Repeated addition leading to multiplication. 14.1 Multiply 1, 2, 3, 4, 5, 10 to a total of 100. 14.2 Use appropriate symbols (x, =). 15. Division. 15.1 Divide numbers to 99 by 2, 3, 4, 5 and 10. 15.2 Use appropriate symbols (, =). 16. Mental mathematics. 16.1 Number concept: Range 999. 16.2 Rapid recall. 17. Fractions. 17.1 Apply and name fractions in familiar contexts including halves, quarters, eighths, thirds, sixths and fifths. 17.2 Recognise fractions in diagrammatic form. 17.3 Begin to recognise that two halves or three thirds make one whole and that 1 half and 2 quarters are equivalent. 17.4 Write fractions as 1 half, 2 thirds. 215 215 217 217 220 222 223 223 223 226 226 226 229 230 230 232 234 234 235 236 237 PATTERNS, FUNCTIONS AND ALGEBRA 238 1. Geometric patterns. 238 1.1 Patterns around us. 238 2. Number patterns. 240 2.1 Copy, extend and describe simple number sequences up to at least 1 000. 240 2.2 Create and describe own number patterns. 241 SPACE AND SHAPE 241 1. 3-D objects. 1.1 Range of objects. 1.2 Features of objects. 2. Symmetry. 2.1 Recognise and draw line of symmetry in 2-D geometrical and nongeometrical shapes. 241 241 242 243 MEASUREMENT 245 1. Time. 1.1 Telling the time. 1.2 Calculate length of time and passing of time. 2. Mass. 2.1 Introducing formal measuring. 3. Capacity / volume. 3.1 Introducing formal measuring. 4. Area. 4.1 Investigate the area using tiling. 243 245 245 246 249 249 250 250 252 252 WYZE EDUCATIONAL PUBLISHERS xi
DATA HANDLING 254 1. Analyse and interpret data. 1.1 Analyse data from representations provided. 254 254 xii WYZE EDUCATIONAL PUBLISHERS
Will term 1 differ much from the rest of the year? In term 1 of the workbook, we endeavour to address all assessments as required by the curriculum (CAPS)'s teachers guidelines, by way of explanations. The purpose of term 2 is to support these explanations progressively with an increased number of exercises and operations. In term 3 we investigate the required assessments with more progressive exercises and calculations. This is also illustrated with relevant examples and tips. To revise all the compulsory assessments, term 4 continues with many more exercises and calculations to prepare the learner for the final exams. Therefore, term 4 will determine whether the learner has conquered the assessments required by the curriculum. We strongly advise the learners to review the explanations introduced in term 1. WYZE EDUCATIONAL PUBLISHERS xiii