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MATHEMATICS STUDY GUIDE 1/2 Grade 6
A member of the FUTURELEARN group
Mathematics Study guide 1/2
1806-E-MAM-SG01
Í2&È-E-MAM-SG01KÎ
Grade 6
CAPS aligned
Y Neuhoff M Prinsloo
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 ........ 34 Lesson 1.7: Whole numbers ......................................................................... 36 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: Fractions ............................................................................................................. 66 Lesson 2.1: Fractions ................................................................................... 67 Mental maths 9 ........................................................................ 68 Activity 9 .................................................................................. 69 Lesson 2.2: Common fractions ..................................................................... 72 Mental maths 10 ...................................................................... 72 1
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Study Guide 1/2 G06 ~ Mathematics
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: 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: 2-D Shapes ........................................................................................................ 109 Lesson 4.1: Sides of a 2-D shape .............................................................. 110 Mental maths 17 .................................................................... 112 Activity 17 .............................................................................. 113 Lesson 4.2: 2-D Different angles ................................................................ 116 Mental maths 18 .................................................................... 122 Activity 18 .............................................................................. 123 Lesson 4.3: 2-D – Parallelograms and rectangles ...................................... 126 Mental maths 19 .................................................................... 127 Activity 19 .............................................................................. 128 UNIT 5: 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 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
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Study Guide 1/2 G06 ~ Mathematics
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 ..................................................................... 169 Lesson 6.6: Multiplication ........................................................................... 170 Mental maths 28 .................................................................... 173 Activity 28 .............................................................................. 174 Lesson 6.7: Multiplication ........................................................................... 178 Mental maths 29 .................................................................... 180 Activity 29 .............................................................................. 181 UNIT 7.1: Shapes: Properties of 3-D objects ............................................................... 185 Lesson 7.1: 3-D objects .............................................................................. 185 Mental maths 30 .................................................................... 188 Activity 30 .............................................................................. 190 Lesson 7.2: 3-D objects .............................................................................. 194 Activity 31 .............................................................................. 194 UNIT 7.2: Shapes: Geometric problems....................................................................... 196 Lesson 7.3: Geometric problems ................................................................ 197 Mental maths 31 .................................................................... 197 Activity 32 .............................................................................. 198 UNIT 7.3: Shapes: symmetry ........................................................................................ 202 Lesson 7.4: Geometric problems ................................................................ 203 Mental maths 32 .................................................................... 203 Activity 33 .............................................................................. 204 UNIT 8.1: Division .......................................................................................................... 207 Lesson 8.1: Division.................................................................................... 207 Mental maths 33 .................................................................... 208 Activity 34 .............................................................................. 209 Lesson 8.2: Division.................................................................................... 210 Mental maths 34 .................................................................... 212 Activity 35 .............................................................................. 213
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Study Guide 1/2 G06 ~ Mathematics
UNIT 8.2: Decimal fractions .......................................................................................... 217 Lesson 8.3: Decimal fractions ..................................................................... 217 Mental maths 35 .................................................................... 220 Activity 36 .............................................................................. 221 Lesson 8.4: Decimal fractions ..................................................................... 224 Mental maths 36 .................................................................... 226 Activity 37 .............................................................................. 227 Lesson 8.5: Decimal fractions ..................................................................... 232 Mental maths 37 .................................................................... 232 Activity 38 .............................................................................. 233 UNIT 9.1: Capacity: Volume .......................................................................................... 236 Lesson 9.1: Capacity and volume ............................................................... 237 Mental maths 38 .................................................................... 238 Activity 39 .............................................................................. 239 Lesson 9.2: Capacity and volume ............................................................... 241 Mental maths 39 .................................................................... 241 Activity 40 .............................................................................. 242 Lesson 9.3: Capacity and volume ............................................................... 245 Mental maths 40 .................................................................... 245 Activity 41 .............................................................................. 246 UNIT 9.2: Capacity: Mass .............................................................................................. 250 Lesson 9.4: Capacity and volume ............................................................... 251 Mental maths 41 .................................................................... 252 Activity 42 .............................................................................. 253
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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 2-D 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)
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Study Guide 1/2 G06 ~ Mathematics
Whole numbers Counting, ordering, comparing, representing and place value 6.2
(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
(Lesson 6.6–6.7 , Mental maths 28– 29, Activity 28–29) Properties of 3-D objects (Lesson 7.1–7.2, Mental maths 30, Activity 30–31) Geometric problems (Lesson 7.3, Mental maths 31, Activity 32) Symmetry (Lesson 7.4, Mental maths 32, Activity 33) Whole numbers Division (Lesson 8.1–8.2, Mental maths 33–34, Activity 34–35) Decimal fractions
8.2
Unit 9 Units 9.1
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(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)
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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 2-D 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)
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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
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(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 3-D objects (Lesson 16.1–16.3, Mental maths 64– 66, Activity 65–67)
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Study Guide 1/2 G06 ~ Mathematics
Area, perimeter and volume 16.2
16.3
Unit 17 Units 17.1
17.2
Unit 18 Probability
(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) Location and directions (Lesson 17.2, Mental maths 70, Activity 71) Probability (Lesson 18.1, Mental maths 71, Activity 72) Extra exercises
Unit 19 Mental maths (Lesson 19.1, Mental maths 72–82) November examination (Unit 1–19)
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Unit
Study Guide 1/2 G06 ~ Mathematics
1.1
UNIT 1.1: Whole numbers LEARNING AIMS After you have completed Unit 1, you must be able to do the following: • • • • •
Know what even numbers and uneven numbers are. Know what will happen when you add even and uneven numbers. Identify place values. Break up 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)
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Study Guide 1/2 G06 ~ Mathematics
Unit
1.1
Recognise place values of digits in whole numbers to at least 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 with at least 5 digits. 46 546 - 9 789 36 757
46 546 + 9 789 56 335
Multiplication of at least 3-digit numbers by 2-digit numbers. 543 × 84 45 612 Division of at least 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
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Halve original number (54 ÷ 2) = 27 (272 ÷ 2) = 136
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Unit
Study Guide 1/2 G06 ~ Mathematics
1.1
Lesson 1.1: Whole numbers IMPORTANT Whole numbers and counting numbers mean exactly the same. It is just another name, just like for example plus, count and add up, which all have the same meaning. When we start counting, we count from 0. That’s why we talk about counting numbers when we start counting at 0. When you speak, you don’t say you have “zero” apples. It doesn’t sound natural. You say you have no apples. Therefore we talk about natural numbers when we start counting at 1. A whole number can be an even number or an uneven number. Even numbers Even numbers always end on 2, 4, 6, 8 or 0. An even number is divided by 2 and can be divided into equal parts without a fraction. For example: 8 ÷ 2 = 4 Uneven numbers Uneven numbers always end on 1, 3, 5, 7 or 9. An uneven number cannot be divided by 2. If you divide uneven numbers by 2, you get fractions. For example: 7 ÷ 2 = 3,5
Place values The value of a digit depends on its position or place 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
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Study Guide 1/2 G06 ~ Mathematics
Unit
1.1
Expanded notation There are three ways in which a number can be written in expanded notation or expanded form. 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 number. When a number ends on 5, 6, 7, 8 or 9, it goes to the next number. For example:
To the nearest 100 When a number of the Tens ends on 2, 3 or 4, it goes to the previous number. When a number of the Tens ends on 5, 6, 7, 8 or 9, it goes to the next number. For example:
Even number + even number = even number Even number + uneven number = uneven number Uneven number + uneven number = even number 15
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Unit
Study Guide 1/2 G06 ~ Mathematics
1.1
Prime numbers A prime number is a number that can only be divided by 1 and itself. E.g. 1, 2, 3, 5, 7, 11 11 ÷ 1 = 11 11 ÷ 11 = 1 × by 10 Any number × 10 = put a 0 at the back 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 = : > : < : ≠ : ≈ : & : 2-D shape : 3-D object :
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equal to greater than less than not equal to almost equal to and two-dimensional shape three-dimensional object
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Study Guide 1/2 G06 ~ Mathematics
Unit
1.1
Lesson 1.2: Whole numbers Counting, ordering, comparing, representing and place value Mental maths 1 You have to do mental maths every day. Work as quickly and correctly as possible. Only write down the answers. 1.
4×7=
21. 1 × 2 =
2.
8×7=
22. 5 × 2 =
3.
6×7=
23. 8 × 3 =
4.
1×7=
24. 7 × 4 =
5.
3×7=
25. 9 × 2 =
6.
5×7=
26. 2 × 2 × 2 =
7.
0×7=
27. 3 × 3 =
8.
10 × 7 =
28. 4 × 4 =
9.
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 =
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Unit
Study Guide 1/2 G06 ~ Mathematics
1.1 Activity 1
1.
Indicate whether the following statements are true or false. If the statement is false, correct the statement so that itâ&#x20AC;&#x2122;s 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 uneven number and any other uneven number will be an uneven number.
___________________________________________________ 2.
Circle all the even numbers. 26 57 89 32 127 0
3.
28
93
127
Circle all the uneven numbers. 69 52 73 21 11 67 59 33 22
4.
Colour in the uneven numbers. 23
8
16
91
10
53
64
89
69
27
55
102
261
72
75
32
37
40
623
16
5.
Colour in the even numbers. 28
34
63
25
91
73
84
6
67
21
19
16
37
83
74
81
20
69
90
93
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Study Guide 1/2 G06 ~ Mathematics
Unit
1.1
Lesson 1.3: Whole numbers Mental maths 2 You have to do mental maths every day. Work as quickly and correctly as possible. Only write down the answers. 1.
8×6=
21. 1 × 4 =
2.
5×4=
22. 1 × 10 =
3.
9×8=
23. 2 × 2 =
4.
7 × 10 =
24. 3 × 5 =
5.
4×8=
25. 6 × 3 =
6.
5 × 10 =
26. 4 × 2 =
7.
9×4=
27. 3 × 3 =
8.
6×9=
28. 8 × 2 =
9.
8×7=
29. 9 × 9 =
10. 7 × 6 =
30. 10 × 11 =
11. 4 × 7 =
31. 12 × 3 =
12. 10 × 6 =
32. 4 × 12 =
13. 6 × 6 =
33. 6 × 12 =
14. 4 × 6 =
34. 11 × 8 =
15. 10 × 10 =
35. 4 × 2 × 2 =
16. 180 ÷ 10 =
36. 3 × 7 =
17. 100 ÷ 10 =
37. 4 × 8 =
18. 220 ÷ 10 =
38. 10 × 3 =
19. 2 200 ÷ 100 =
39. 1 × 5 × 1 × 8 =
20. 6 300 ÷ 10 =
40. 2 × 20 =
19
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Unit
Study Guide 1/2 G06 ~ Mathematics
1.1 Activity 2
The value of a digit depends on its position or place in a number. For example: The value of 7 in 54 723 is 7 hundreds. We can represent the number on a counting frame as follows: HTh
TTh
Th
H
T
U
54 723 Use the counting frame as indicator of the positions, namely HTh (hundred thousands), TTh (ten thousands), Th (thousands), H (hundreds), T (tens) and U (units) to answer the following questions. 1.
2.
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How many units are there in the following?
1.1
1 ten
_____________________
1.2
1 thousand
_____________________
1.3
1 ten thousand
_____________________
1.4
1 hundred
______________________
How many thousands are there in the following?
2.1
1 ten thousand
_____________________
2.2
1 hundred thousand
_____________________
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Study Guide 1/2 G06 ~ Mathematics
3.
Unit
1.1
Write in the simplest form:
3.1
(5 × 1 000) + (3 × 100) + (7 × 10) + (4 × 1)
___________________________________________________
3.2
(9 × 10 000) + (8 × 1 000) + (7 × 10) + (5 × 1)
___________________________________________________
3.3
84 tens + 43 ten thousands
___________________________________________________
3.4
8 hundred thousands + 28 hundreds
___________________________________________________
3.5
34 hundreds + 45 units + 76 thousands
___________________________________________________
4.
Write the following as expanded notation: 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 + 5T + 9H + 7T + 4U
4.1
89 346
________________________________________________________ ________________________________________________________ ____________________________________________________
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Unit
Study Guide 1/2 G06 ~ Mathematics
1.1 4.2
600 831
________________________________________________________ ________________________________________________________ ________________________________________________________ 4.3
8 437
________________________________________________________ ________________________________________________________ ________________________________________________________ 4.4
356 980
________________________________________________________ ________________________________________________________ ________________________________________________________ 4.5
65 874
________________________________________________________ ________________________________________________________ ________________________________________________________
5.
Analyse the number 3 261 267 and answer the questions that follow.
5.1
How many times bigger in value is the underlined 6 than the 6 in bold?
_______________________________________________________
5.2
The digit 1 plus the value of the digit 3 is equal to?
_______________________________________________________
5.3
The digit 2 on the left-hand side is how many times the value of the digit 2 on the right?
_______________________________________________________
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