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MATHEMATICS STUDY GUIDE 2/2 Grade 6
A member of the FUTURELEARN group
Mathematics Study guide 2/2
CAPS aligned
Y Neuhoff M Prinsloo
2006-E-MAM-SG02
Í4&È-E-MAM-SG02[Î
Grade 6
Study Guide 2/2 G06 ~ Mathematics
CONTENTS PREFACE ............................................................................................................................ 5 INTRODUCTION ................................................................................................................. 5 LESSON ELEMENTS.......................................................................................................... 6 YEAR PLAN ........................................................................................................................ 7 UNIT 10.0: Whole numbers: Addition and subtraction ................................................. 12 Lesson 10.1: Whole numbers ....................................................................... 13 Mental maths 42 ...................................................................... 15 Activity 43 ................................................................................ 16 Lesson 10.2: Whole numbers ....................................................................... 19 Mental maths 43 ...................................................................... 19 Activity 44 ................................................................................ 20 Lesson 10.3: Patterns ................................................................................... 22 Mental maths 44 ...................................................................... 23 Activity 45 ................................................................................ 24 UNIT 11.1: Shapes: Viewing objects .............................................................................. 26 Lesson 11.1: Viewing objects ....................................................................... 26 Mental maths 45 ...................................................................... 28 Activity 46 ................................................................................ 29 UNIT 11.2: Shapes: Properties of 2D shapes ................................................................ 34 Lesson 11.2: Properties of 2D shapes .......................................................... 35 Mental maths 46 ...................................................................... 37 Activity 47 ................................................................................ 38 Lesson 11.3: Viewing objects ....................................................................... 41 Mental maths 47 ...................................................................... 42 Activity 48 ................................................................................ 43 UNIT 11.3: Transformation .............................................................................................. 45 Lesson 11.4: Transformation ........................................................................ 45 Mental maths 48 ...................................................................... 48 Activity 49 ................................................................................ 49 UNIT 11.4: Shapes: Length ............................................................................................. 53 Lesson 11.5: Length ..................................................................................... 53 Mental maths 49 ...................................................................... 56 Activity 50 ................................................................................ 57 Lesson 11.6: Length ..................................................................................... 60 Mental maths 50 ...................................................................... 61 Activity 51 ................................................................................ 62
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Study Guide 2/2 G06 ~ Mathematics
UNIT 12.0: Temperature................................................................................................... 64 Lesson 12.1: Temperature ............................................................................ 65 Mental maths 51 ...................................................................... 66 Activity 52 ................................................................................ 67 Lesson 12.2: Percentage .............................................................................. 69 Mental maths 52 ...................................................................... 71 Activity 53 ................................................................................ 72 Lesson 12.3: Percentage .............................................................................. 74 Mental maths 53 ...................................................................... 76 Activity 54 ................................................................................ 77 UNIT 13.0: Data handling................................................................................................. 81 Lesson 13.1: Data handling .......................................................................... 81 Mental maths 54 ...................................................................... 82 Activity 55 ................................................................................ 83 Lesson 13.2: Data handling .......................................................................... 87 Mental maths 55 ...................................................................... 88 Activity 56 ................................................................................ 89 Lesson 13.3: Data handling .......................................................................... 89 Mental maths 56 ...................................................................... 92 Activity 57 ................................................................................ 93 UNIT 14.1: Whole numbers ............................................................................................. 97 Lesson 14.1: Whole numbers ....................................................................... 98 Mental maths 57 ...................................................................... 99 Activity 58 .............................................................................. 100 Lesson 14.2: Whole numbers ..................................................................... 102 Mental maths 58 .................................................................... 103 Activity 59 .............................................................................. 104 UNIT 14.2: Whole numbers ........................................................................................... 106 Lesson 14.3: Whole numbers ..................................................................... 106 Mental maths 59 .................................................................... 108 Activity 60 .............................................................................. 109 UNIT 14.3: Whole numbers ........................................................................................... 114 Lesson 14.4: Whole numbers ..................................................................... 114 Mental maths 60 .................................................................... 117 Activity 61 .............................................................................. 118 UNIT 14.4: Whole numbers ........................................................................................... 126 Lesson 14.5: Whole numbers ..................................................................... 127 Mental maths 61 .................................................................... 128 Activity 62 .............................................................................. 130
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Study Guide 2/2 G06 ~ Mathematics
UNIT 15.0: Common fractions ....................................................................................... 134 Lesson 15.1: Fractions ............................................................................... 134 Mental maths 62 .................................................................... 135 Activity 63 .............................................................................. 136 Lesson 15.2: Fractions ............................................................................... 139 Mental maths 63 .................................................................... 139 Activity 64 .............................................................................. 140 UNIT 16.1: Shapes: Properties of 3D objects .............................................................. 143 Lesson 16.1: Properties of 3D objects ........................................................ 143 Mental maths 64 .................................................................... 143 Activity 65 .............................................................................. 145 Lesson 16.2: Properties of 3D shapes ........................................................ 147 Mental maths 65 .................................................................... 147 Activity 66 .............................................................................. 148 Lesson 16.3: Properties of 3D shapes ........................................................ 151 Mental maths 66 .................................................................... 151 Activity 67 .............................................................................. 152 UNIT 16.2: Shapes: Perimeter and volume .................................................................. 157 Lesson 16.4: Perimeter, surface area and volume ..................................... 157 Mental maths 67 .................................................................... 162 Activity 68 .............................................................................. 163 Lesson 16.5: Perimeter, surface area and volume ..................................... 166 Mental maths 68 .................................................................... 166 Activity 69 .............................................................................. 167 UNIT 16.3: Shapes: Transformation ............................................................................. 170 Lesson 16.6: Transformation ...................................................................... 170 Mental maths 69 .................................................................... 174 Activity 70 .............................................................................. 175 UNIT 17.1: Time .............................................................................................................. 177 Lesson 17.1: Time and geometry ............................................................... 177 UNIT 17.2: Location and direction ................................................................................ 182 Lesson 17.2: Location and direction ........................................................... 182 Mental maths 70 .................................................................... 187 Activity 71 .............................................................................. 188 UNIT 18.0: Probability .................................................................................................... 190 Lesson 18.1: Probability ............................................................................. 190 Mental maths 71 .................................................................... 191 Activity 72 .............................................................................. 192
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Study Guide 2/2 G06 ~ Mathematics
UNIT 19.0: Quick exercises ........................................................................................... 195 Lesson 19.1: Mental maths – extra exercises ............................................. 195 Mental maths 72 .................................................................... 195 Mental maths 73 .................................................................... 196 Mental maths 74 .................................................................... 197 Mental maths 75 .................................................................... 198 Mental maths 76 .................................................................... 199 Mental maths 77 .................................................................... 200 Mental maths 78 .................................................................... 201 Mental maths 79 .................................................................... 202 Mental maths 80 .................................................................... 203 Mental maths 81 .................................................................... 204 Mental maths 82 .................................................................... 205
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Study Guide 2/2 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 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)!
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Study Guide 2/2 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.
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Study Guide 2/2 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)
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Study Guide 2/2 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
9.2
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(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) Mass (Lesson 9.4, Mental maths 41, Activity 42) June examination (Unit 1–9.2)
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Study Guide 2/2 G06 ~ Mathematics
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
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)
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Study Guide 2/2 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
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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 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)
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Study Guide 2/2 G06 ~ Mathematics
Unit 17 Units 17.1
17.2
Unit 18 Probability Unit 19 Mental maths
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 (Lesson 19.1, Mental maths 72–82) November examination (Unit 1–19)
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Unit
Study Guide 2/2 G06 ~ Mathematics
10.0
UNIT 10.0: Whole numbers: Addition and subtraction LEARNING AIMS After you have completed Unit 10, you must be able to do the following: • • • • • •
Work with 6-digit numbers. Know how addition and subtraction problems are asked. Know what the different words for ‘add’ and ‘subtract’ are. Know what expanded notation is. Apply inverse operations to check answers. Solve word problems.
REVISION Revise addition, subtraction and expanded notation of 5-digit numbers and multiplication and division of 2-digit numbers and 3-digit numbers. Addition and subtraction of whole numbers with at least 5 digits 46 546 – 9 789
46 546 +
36 757
9 789 56 335
Expanded notation of whole numbers with at least 5 digits 35 974 30 000 + 5 000 + 900 + 70 + 4 (3 × 10 000) + (5 × 1 000) + (9 × 100) + (7 × 10) + (4 × 1) 3TTh + 5Th + 9H + 7T + 4U © Impaq
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Study Guide 2/2 G06 ~ Mathematics
Unit
10.0
Multiplication and division of 2-digit numbers and 3-digit numbers 2 400 ÷ 60 = 40 2 400 × 60 = 144 000
Lesson 10.1: Whole numbers There are many different words that mean the same as ‘add’ and ‘subtract’. It is very important that you know all the different words and expressions. It will especially help you when you are doing word sums. Addition • Make more • Double • What will it be together? • How much more? • Also • The sum of • Plus • Increase • Total Subtraction • Make less • Halve • Decrease • Take away • Deduct • The difference • Minus • Less than • How much less?
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Unit
Study Guide 2/2 G06 ~ Mathematics
10.0
Horizontal addition and subtraction by expanded notation Example Addition
Subtraction
Rounding off 1 to 4 move down
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2
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5 to 9 move up
4
5
14
6
7
8
9
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Study Guide 2/2 G06 ~ Mathematics
Unit
10.0
Inverse operations = Check if your answer is correct Example Addition: Subtract to check if the answer is correct.
Subtraction: Add to check if the answer is correct.
Mental maths 42 You have to do mental maths every day. Work as quickly and accurately as possible. Only write down the answers. Write the smallest number you can make with the digits:
Double:
1.
7; 2; 6; 8; 3; 1
21.
72 816
2.
3; 8; 0; 9; 6; 4
22.
46 254
3.
5; 7; 2; 8; 1; 6
23.
100 500
4.
3; 1; 6; 8; 4; 0
24.
32 648
5.
7; 9; 2; 1; 4; 2
25.
18 438
6.
5; 0; 6; 1; 7; 4
26.
50 072
7.
2; 5; 3; 4; 6; 5
27.
64 804
8.
9; 3; 1; 7; 2; 6
28.
36 290
9.
3; 5; 6; 1; 4; 9
29.
80 234
10.
2; 3; 8; 7; 4; 6
30.
71 234
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Unit
Study Guide 2/2 G06 ~ Mathematics
10.0 Round off to the nearest 100:
Calculate:
11.
3 874
31. 380 ÷ 5 =
12.
1 217
32. 45 ÷ 15 =
13.
29 704
33. 24 ÷ 8 =
14.
15 599
34. 18 ÷ 6 =
15.
15 972
35. 16 ÷ 4 =
16.
11 604
36. 410 ÷ 10 =
17.
13 421
37. 40 ÷ 10 =
18.
20 005
38. 440 ÷ 10 =
19.
8 556
39. 940 ÷ 10 =
20.
8 544
40. 21 ÷ 7 =
Activity 43 1.
Solve the addition and subtraction sums. 1.1
1.2 293 482 32 395 + 47 734
928 463 43 273 + 6 382
1.3
1.4 372 392 – 52 483
823 283 – 87 421
1.5
1.6 646 235 36 388 + 18 282
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293 119 – 199 283
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Study Guide 2/2 G06 ~ Mathematics
2.
3.
4.
5.
Unit
Round off to the nearest 1 000. 2.1 3 784 __________
2.2
8 372
2.3
4 938 __________
2.4
9 998
2.5
7 364 __________
2.6
2 511
Round off to the nearest 10 000. 3.1 63 347 3.2
28 483
3.3
93 837
3.4
37 953
3.5
73 743
3.6
93 929
Round off to the nearest 100 000. 4.1 737 398 4.2
277 211
4.4
632 162
4.4
362 833
4.5
998 243
4.6
452 543
10.0
First round off to the nearest 100 000 and then solve the problem. 5.1
434 887 + 633 282 __________________________________________________ __________________________________________________
5.2
783 374 – 372 373 __________________________________________________ __________________________________________________
5.3
128 483 + 843 399 __________________________________________________ __________________________________________________
5.4
974 432 – 346 824 __________________________________________________ __________________________________________________
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Unit
Study Guide 2/2 G06 ~ Mathematics
10.0
6.
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Calculate the sum and then do the inverse (opposite) to check the answer. 6.1
382 372 + 822 477
6.2
753 263 + 193 843
6.3
637 374 + 273 192
6.4
561 372 + 374 496
6.5
843 236 – 74 263
6.6
462 273 – 273 338
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