Grade 6 Study Guide 1/2 Mathematics by Impaq

Intermediate Phase Grade 6 • Study Guide 1/2

Mathematics CAPS IEB Mathematics

• Comprehensive explanations of concepts in simple language. everyday examples with visuals and diagrams to help • Practical, master concepts. • Learners work at their own pace. • Activities that test learners’ knowledge application and reasoning. • The facilitator’s guide contains step-by-step calculations and answers. • Use in school or at home.

home classroom college workplace

9 781990

946486

Study Guide 1/2

2106-E-MAM-SG01

Mathematics Study guide 1/2

CAPS aligned

Y Neuhoff M Prinsloo

2006-E-MAM-SG01

Í4&È-E-MAM-SG01MÎ

Grade 6

Study Guide 1/2 G06 ~ Mathematics

CONTENTS PREFACE ............................................................................................................................ 5 INTRODUCTION ................................................................................................................. 5 LESSON ELEMENTS.......................................................................................................... 6 YEAR PLAN ........................................................................................................................ 7 UNIT 1.1: Whole numbers ............................................................................................... 12 Lesson 1.1: Whole numbers ......................................................................... 14 Lesson 1.2: Whole numbers ......................................................................... 17 Mental maths 1 ........................................................................ 17 Activity 1 .................................................................................. 18 Lesson 1.3: Whole numbers ......................................................................... 19 Mental maths 2 ........................................................................ 19 Activity 2 .................................................................................. 20 Lesson 1.4: Counting and subtracting with 10, 100 and 1 000 ..................... 23 Lesson 1.5: Counting and subtracting with 10, 100 and 1 000 ..................... 25 Mental maths 3 ........................................................................ 25 Activity 3 .................................................................................. 26 UNIT 1.2: Numbers ........................................................................................................... 34 Lesson 1.6: Number sentences, counting and subtraction of numbers ........ 35 Lesson 1.7: Whole numbers: counting, ordering, comparing, representing and place value ....................................................................... 36 Mental maths 4 ........................................................................ 36 Activity 4 .................................................................................. 37 Lesson 1.8: Vertical and horizontal ............................................................... 39 Mental maths 5 ........................................................................ 40 Activity 5 .................................................................................. 41 Lesson 1.9: Rounding off .............................................................................. 43 Mental maths 6 ........................................................................ 43 Activity 6 .................................................................................. 44 Mental maths 7 ........................................................................ 45 Activity 7 .................................................................................. 46 Lesson 1.10: Divide by 10, 100 and 1 000 .................................................... 49 Mental maths 8 ........................................................................ 50 Activity 8 .................................................................................. 51 Lesson 1.11: Revision .................................................................................. 54 Lesson 1.12: Revision .................................................................................. 57 UNIT 2.0: Fractions .......................................................................................................... 66 Lesson 2.1: Fractions ................................................................................... 67 Mental maths 9 ........................................................................ 68 1

Study Guide 1/2 G06 ~ Mathematics

Activity 9 .................................................................................. 69 Lesson 2.2: Common fractions ..................................................................... 72 Mental maths 10 ...................................................................... 72 Activity 10 ................................................................................ 74 Lesson 2.3: Common fractions ..................................................................... 76 Mental maths 11 ...................................................................... 77 Activity 11 ................................................................................ 78 Lesson 2.4: Equivalent fractions ................................................................... 80 Mental maths 12 ...................................................................... 81 Activity 12 ................................................................................ 82 Lesson 2.5: Solving fractions ........................................................................ 85 Mental maths 13 ...................................................................... 85 Activity 13 ................................................................................ 86 Lesson 2.6: Revision .................................................................................... 90 UNIT 3.0: Time .................................................................................................................. 93 Lesson 3.1: 12-hour time and 24-hour time .................................................. 94 Mental maths 14 ...................................................................... 95 Activity 14 ................................................................................ 96 Lesson 3.2: Calculate time ........................................................................... 98 Mental maths 15 .................................................................... 100 Activity 15 .............................................................................. 101 Lesson 3.3: Calendar and time zones ........................................................ 103 Mental maths 16 .................................................................... 104 Activity 16 .............................................................................. 105 UNIT 4.0: 2D shapes ...................................................................................................... 109 Lesson 4.1: Sides of a 2D shape ................................................................ 110 Mental maths 17 .................................................................... 112 Activity 17 .............................................................................. 113 Lesson 4.2: 2D different angles .................................................................. 116 Mental maths 18 .................................................................... 122 Activity 18 .............................................................................. 123 Lesson 4.3: 2D parallelograms and rectangles ........................................... 126 Mental maths 19 .................................................................... 127 Activity 19 .............................................................................. 128 UNIT 5.0: Data handling................................................................................................. 129 Lesson 5.1: Data handling .......................................................................... 130 Mental maths 20 .................................................................... 132 Activity 20 .............................................................................. 133 Lesson 5.2: Data handling .......................................................................... 134 Mental maths 21 .................................................................... 135

Study Guide 1/2 G06 ~ Mathematics

Activity 21 .............................................................................. 136 Lesson 5.3: Data handling .......................................................................... 137 Mental maths 22 .................................................................... 138 Activity 22 .............................................................................. 139 Lesson 5.4: Data handling .......................................................................... 140 Mental maths 23 .................................................................... 140 Activity 23 .............................................................................. 141 UNIT 6.1: Number patterns ............................................................................................ 145 Lesson 6.1: Number patterns ..................................................................... 147 Mental maths 24 .................................................................... 147 Activity 24 .............................................................................. 148 Lesson 6.2: Number patterns ..................................................................... 152 Mental maths 25 .................................................................... 152 Activity 25 .............................................................................. 153 UNIT 6.2: Whole numbers ............................................................................................. 156 Lesson 6.3: Whole numbers ....................................................................... 157 Mental maths 26 .................................................................... 157 Activity 26 .............................................................................. 158 Lesson 6.4: Whole numbers ....................................................................... 162 Mental maths 27 .................................................................... 162 Activity 27 .............................................................................. 163 Lesson 6.5: Whole numbers ....................................................................... 166 UNIT 6.3: Whole numbers: Multiplication .................................................................... 168 Lesson 6.6: Multiplication ........................................................................... 169 Mental maths 28 .................................................................... 172 Activity 28 .............................................................................. 173 Lesson 6.7: Multiplication ........................................................................... 177 Mental maths 29 .................................................................... 179 Activity 29 .............................................................................. 180 UNIT 7.1: Shapes: Properties of 3D objects ................................................................ 184 Lesson 7.1: 3D objects ............................................................................... 184 Mental maths 30 .................................................................... 187 Activity 30 .............................................................................. 189 Activity 31 .............................................................................. 193 UNIT 7.2: Shapes: Geometric problems....................................................................... 195 Lesson 7.2: Geometric patterns .................................................................. 196 Mental maths 31 .................................................................... 196 Activity 32 .............................................................................. 197 3

Study Guide 1/2 G06 ~ Mathematics

UNIT 7.3: Shapes: Symmetry ........................................................................................ 201 Lesson 7.3: Geometric problems ................................................................ 202 Mental maths 32 .................................................................... 202 Activity 33 .............................................................................. 203 UNIT 8.1: Division .......................................................................................................... 206 Lesson 8.1: Division.................................................................................... 206 Mental maths 33 .................................................................... 207 Activity 34 .............................................................................. 208 Lesson 8.2: Division .................................................................................... 209 Mental maths 34 .................................................................... 211 Activity 35 .............................................................................. 212 UNIT 8.2: Decimal fractions .......................................................................................... 216 Lesson 8.3: Decimal fractions ..................................................................... 216 Mental maths 35 .................................................................... 219 Activity 36 .............................................................................. 220 Lesson 8.4: Decimal fractions ..................................................................... 223 Mental maths 36 .................................................................... 225 Activity 37 .............................................................................. 226 Lesson 8.5: Decimal fractions ..................................................................... 231 Mental maths 37 .................................................................... 231 Activity 38 .............................................................................. 232 UNIT 9.1: Capacity: Volume .......................................................................................... 235 Lesson 9.1: Capacity and volume ............................................................... 236 Mental maths 38 .................................................................... 237 Activity 39 .............................................................................. 238 Lesson 9.2: Capacity and volume ............................................................... 240 Mental maths 39 .................................................................... 240 Activity 40 .............................................................................. 241 Lesson 9.3: Capacity and volume ............................................................... 244 Mental maths 40 .................................................................... 244 Activity 41 .............................................................................. 245 UNIT 9.2: Capacity: Mass .............................................................................................. 249 Lesson 9.4: Capacity and volume ............................................................... 250 Mental maths 41 .................................................................... 251 Activity 42 .............................................................................. 252

Study Guide 1/2 G06 ~ Mathematics

PREFACE You can use the internet and various other textbooks to practise Mathematics. These books and websites are suggested: Platinum Mathematics Math in Focus www.math-play.com www.mathsplayground.com www.funbrain.com www.ixl.com

INTRODUCTION Each unit in this Mathematics book consists of five elements: 1. Outcomes 2. What I have learnt 3. Introduction 4. Lesson content 5. Activities and a revision exercise. Remember: Do each day’s mental maths as quickly as possible before you start with the activity. Everything you learn are building blocks that build on each other. Make sure that you understand each unit with its activities well before moving on to the next unit. It is important that you don’t fall behind. You will to learn to build numbers with digits, count and subtract and make sketches with the help of digits. Yes, graphs are sketches. We are even going to build objects with cubes (mathematical building blocks)!

Study Guide 1/2 G06 ~ Mathematics

LESSON ELEMENTS LEARNING AIMS What learners should know at the end of the lesson. Taken from CAPS.

IMPORTANT TERMINOLOGY New terminology to extend understanding of the subject as part of the lesson.

DEFINE Definitions of concepts to understand the content.

IMPORTANT Explain misunderstandings; possible confusion regarding existing knowledge.

ACTIVITY Questions that must be done in order to test the knowledge of the completed lesson.

STUDY/REVISION Time spent to study the content in conclusion of the unit and in preparation for the test or examination.

Study Guide 1/2 G06 ~ Mathematics

YEAR PLAN Remember: Mental maths is part of every day’s programme. UNIT

Term 1 Unit 1 Numbers 1.1

DATE STARTED

LESSONS

DATE COMPLETED

Whole numbers Counting, ordering, comparing, representing and place value (Lesson 1.1–1.5, Mental maths 1–3, Activity 1–3 and Revision exercise 1.1) Whole numbers Number sentences, counting and subtraction

1.2 (Lesson 1.6–1.12, Mental maths 4–8, Activity 4–8 and Revision exercise 1.2.1 and 1.2.2) Common fractions Unit 2 Fractions

Unit 3 Units

Unit 4 Shapes

Unit 5 Data

Term 2 Unit 6 Numbers 6.1

(Lesson 2.1–2.6, Mental maths 9–13, Activity 9–13 and Revision exercise 2.1) Time (Lesson 3.1–3.3, Mental maths 14–16, Activity 14–16) Properties of 2D shapes (Lesson 4.1–4.3, Mental maths 17–19, Activity 17–19) Data handling (Lesson 5.1–5.4, Mental maths 20–23, Activity 20–23) (Time allocation – 10 weeks) Term 1 test: Unit 1–5 Number patterns (Lesson 6.1–6.2, Mental maths 24–25, Activity 24–25)

Study Guide 1/2 G06 ~ Mathematics

6.2

Whole numbers Counting, ordering, comparing, representing and place value (Lesson 6.3–6.5, Mental maths 26–27, Activity 26–27 and Revision exercise 3) Whole numbers Multiplication

6.3

Unit 7 Shapes 7.1

7.2

7.3

Unit 8 Numbers 8.1

8.2

Unit 9 Units 9.1

(Lesson 6.6–6.7, Mental maths 28–29, Activity 28–29) Properties of 3D objects (Lesson 7.1, Mental maths 30, Activity 30–31) Geometric patterns (Lesson 7.2, Mental maths 31, Activity 32) Symmetry (Lesson 7.3, Mental maths 32, Activity 33) Whole numbers Division (Lesson 8.1–8.2, Mental maths 33–34, Activity 34–35) Decimal fractions (Lesson 8.3–8.5, Mental maths 35–37, Activity 36–38) Capacity Volume (Lesson 9.1–9.3, Mental maths 38–40, Activity 39–41)

Study Guide 1/2 G06 ~ Mathematics

Mass 9.2

Term 3 Unit 10 Numbers 10.1

10.2

Unit 11 Shapes 11.1

11.2

11.3

11.4

Unit 12 Units 12.1

12.2

Unit 13 Data

(Lesson 9.4, Mental maths 41, Activity 42) June examination (Unit 1–9.2) Whole numbers Counting and subtraction (Lesson 10.1–10.2, Mental maths 42–43, Activity 43–44) Number patterns (Lesson 10.3, Mental maths 44, Activity 45) Viewing objects (Lesson 11.1, Mental maths 45, Activity 46) Properties of 2D shapes (Lesson 11.2–11.3, Mental maths 46–47, Activity 47–48) Transformation (Lesson 11.4, Mental maths 48, Activity 49) Length (Lesson 11.5–11.6, Mental maths 49–50, Activity 50–51) Temperature (Lesson 12.1, Mental maths 51, Activity 52) Percentages (Lesson 12.2–12.3, Mental maths 52–53, Activity 53–54) Data handling (Lesson 13.1–13.3, Mental maths 54–56, Activity 55–57)

Study Guide 1/2 G06 ~ Mathematics

Unit 14 Numbers 14.1

Whole numbers Counting, ordering, comparing, representing and place value (Lesson 14.1–14.2, Mental maths 57–58, Activity 58–59) Whole numbers Multiplication

14.2 (Lesson 14.3, Mental maths 59, Activity 60) Whole numbers Division 14.3 (Lesson 14.4, Mental maths 60, Activity 61) Number sentences

14.4

Term 4 Unit 15 Fractions Unit 16 Shapes 16.1

16.2

16.3

Unit 17 Units 17.1

(Lesson 14.5, Mental maths 61, Activity 62) (Time allocation – 10 weeks) Term 3 test: Unit 10–14.4 Common fractions (Lesson 15.1–15.2, Mental maths 62–63, Activity 63–64) Properties of 3D objects (Lesson 16.1–16.3, Mental maths 64–66, Activity 65–67) Area, perimeter and volume (Lesson 16.4–16.5, Mental maths 67–68, Activity 68–69) Transformation (Lesson 16.6, Mental maths 69, Activity 70) The history of measuring units (Lesson 17.1, Videos that can be watched)

Study Guide 1/2 G06 ~ Mathematics

Location and directions 17.2

Unit 18 Probability Unit 19 Mental maths

(Lesson 17.2, Mental maths 70, Activity 71) Probability (Lesson 18.1, Mental maths 71, Activity 72) Extra exercises (Lesson 19.1, Mental maths 72–82) November examination (Unit 1–19)

Unit

Study Guide 1/2 G06 ~ Mathematics

1.1

UNIT 1.1: Whole numbers LEARNING AIMS After you have completed Unit 1.1, you must be able to do the following: • • • • •

Know what even numbers and odd numbers are. Know what will happen when you add even and odd numbers. Identify place value. Break down numbers using expanded notation. Round off to the nearest 5, 10, 100 and 1 000.

REVISION OF GRADE 5 Recognise and represent numbers so that it can be described and compared. 74 383 74 383

Seventy-four thousand three hundred and eighty-three (Describe) = 70 000 + 4 000 + 300 + 80 + 3 (Compare) = 7TTh + 4Th + 3H + 8T + 3U (Compare) = (7 × 10 000) + (4 × 1 000) + (3 × 100) + (8 × 10) + (3 × 1) (Compare)

Whole numbers to at least 6-digit numbers. 746 039 (Read, compare and write)

Study Guide 1/2 G06 ~ Mathematics

Unit

1.1

Recognise place value of digits in whole numbers up to 6-digit numbers. 746 039 = Place values HTh TTh 7 4

Th 6

H 0

T 3

U 9

Rounding off to the nearest 5, 10, 100 or 1 000. 9 583 9 583

= Rounding off to the nearest: 5 10 100 9 585 9 580 9 600

1 000 10 000

Addition and subtraction of whole numbers up to 5 digits. 46 546 – 9 789 36 757

46 546 + 9 789 56 335

Multiplication of 3-digit numbers by 2-digit numbers. 543 × 84 45 612 Division of 3-digit numbers by 2-digit numbers. 32 remainder 11 21 683 Double and halve whole numbers. Number 54 272

Double original number (54 + 54) or (54 × 2) = 108 (272 + 272) or (272 × 2) = 544

Halve original number (54 ÷ 2) = 27 (272 ÷ 2) = 136

Unit

Study Guide 1/2 G06 ~ Mathematics

1.1

Lesson 1.1: Whole numbers IMPORTANT Whole numbers are numbers without fractions or decimals. Whole numbers are always positive and never negative. Remember, 0 is also a whole number. Whole numbers are also called counting numbers. A whole number can be an even or odd number. Natural numbers are all numbers that are not negative, a fraction or 0. The number 0 is excluded from natural numbers. Even numbers Even numbers always end on 2, 4, 6, 8 or 0. When an even number is divided by 2, it is divided into equal parts without a remainder. For example: 8 ÷ 2 = 4 Odd numbers Odd numbers always end on 1, 3, 5, 7 or 9. An odd number cannot be divided by 2. When an odd number is divided by 2, you get remainders. For example: 7 ÷ 2 = 3,5 Place value The value of a digit depends on its position in the number. For example: Th, H, T, U Th = Thousands H = Hundreds T = Tens U = Units For example: 2 496 Th H T U 2 4 9 6 Expanded notation There are three ways to write a number in expanded notation or expanded form.

Study Guide 1/2 G06 ~ Mathematics

Unit

1.1

For example: 35 974 1. 30 000 + 5 000 + 900 + 70 + 4 2. (3 × 10 000) + (5 × 1 000) + (9 × 100) + (7 × 10) + (4 × 1) 3. 3TTh + 5Th + 9H + 7T + 4U Rounding off Rounding off means that a number is taken to the nearest 10, 100 or 1 000. To the nearest 10 When a number ends on 1, 2, 3 or 4, it goes to the previous 10. When a number ends on 5, 6, 7, 8 or 9, it goes to the next 10. For example:

To the nearest 100 When a number of the Tens ends on 1, 2, 3 or 4, it goes to the previous 100. When a number of the Tens ends on 5, 6, 7, 8 or 9, it goes to the next 100. For example:

30 40

50 60 70

80 90 100

Unit

Study Guide 1/2 G06 ~ Mathematics

1.1 Even number + even number = even number Even number + odd number = odd number Odd number + odd number = even number

Prime numbers A prime number is a number that can only be divided by 1 and itself. It is a number that has exactly two factors. E.g. 1, 2, 3, 5, 7, 11 11 ÷ 1 = 11 ✓ 11 ÷ 11 = 1 ✓ × by 10 Any number × 10 = tag a 0 on the end of the number. For example: 8 × 10 = 80 112 × 10 = 1 120 × by 0 Any number × 0 = always 0 For example: 1×0=0 999 × 0 = 0

IMPORTANT TERMINOLOGY = > < ≠ ≈ & 2D shape 3D object

: : : : : : : :

equal to greater than less than not equal to approximately equal to and two-dimensional shape three-dimensional object

Study Guide 1/2 G06 ~ Mathematics

Unit

1.1

Lesson 1.2: Whole numbers Mental maths 1 You have to do mental maths every day. Work as quickly and accurately as possible. Only write down the answers. 1.

4×7=

21. 1 × 2 =

8×7=

22. 5 × 2 =

6×7=

23. 8 × 3 =

1×7=

24. 7 × 4 =

3×7=

25. 9 × 2 =

5×7=

26. 2 × 2 × 2 =

0×7=

27. 3 × 3 =

10 × 7 =

28. 4 × 4 =

7×7=

29. 5 × 3 =

10. 9 × 7 =

30. 2 × 6 =

11. 2 × 7 =

31. 5 × 5 =

12. 63 ÷ 7 =

32. 2 × 2 =

13. 35 ÷ 7 =

33. 6 × 3 =

14. 14 ÷ 7 =

34. 9 × 4 =

15. 42 ÷ 7 =

35. 6 × 6 =

16. 28 ÷ 7 =

36. 7 × 7 =

17. 70 ÷ 7 =

37. 4 × 2 × 2 =

18. 56 ÷ 7 =

38. 1 × 0 =

19. 49 ÷ 7 =

39. 9 × 5 =

20. 21 ÷ 7 =

40. 10 × 3 =

Unit

Study Guide 1/2 G06 ~ Mathematics

1.1 Activity 1

Indicate whether the following statements are true or false. If the statement is false, correct the statement to make it true. 1.1

0, 1 and 2 are natural numbers.

___________________________________________________ 1.2

1, 2 and 3 are counting numbers.

___________________________________________________ 1.3

The product of any odd number and any other odd number will be an odd number.

___________________________________________________ 2.

Circle all the even numbers. 26 57 89 32 127 0

127

Circle all the odd numbers. 69 52 73 21 11 67 59 33 22

Colour the odd numbers. 23

102

261

623

Colour the even numbers. 28