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MATHEMATICS STUDY GUIDE 2/2 Grade 6
A member of the FUTURELEARN group
Mathematics Study guide 2/2
1806-E-MAM-SG02
Í2&È-E-MAM-SG02YÎ
Grade 6
CAPS aligned
Y Neuhoff M Prinsloo
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 2-D shapes ................................................................34 Lesson 11.2: Properties of 2-D shapes .........................................................35 Mental maths 46 ......................................................................36 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 UNIT 12.0: Temperature ...................................................................................................65 Lesson 12.1: Temperature ............................................................................66 Mental maths 51 ......................................................................67 Activity 52 ................................................................................68
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Study Guide 2/2 G06 ~ Mathematics
Lesson 12.2: Percentage ..............................................................................70 Mental maths 52 ......................................................................72 Activity 53 ................................................................................73 Lesson 12.3: Percentage ..............................................................................75 Mental maths 53 ......................................................................77 Activity 54 ................................................................................78 UNIT 13.0: Data handling .................................................................................................82 Lesson 13.1: Data handling ..........................................................................82 Mental maths 54 ......................................................................83 Activity 55 ................................................................................84 Lesson 13.2: Data handling ..........................................................................87 Mental maths 55 ......................................................................88 Activity 56 ................................................................................89 Lesson 13.3: Data handling ..........................................................................90 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 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 3-D objects ............................................................143 Lesson 16.1: Shapes – Properties of 3-D objects .......................................143 Mental maths 64 ....................................................................143 Š Impaq
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Study Guide 2/2 G06 ~ Mathematics
Activity 65 ..............................................................................145 Lesson 16.2: Shapes – Properties of 3-D shapes .......................................147 Mental maths 65 ....................................................................147 Activity 66 ..............................................................................148 Lesson 16.3: Shapes – Properties of 3-D shapes .......................................151 Mental maths 66 ....................................................................151 Activity 67 ..............................................................................152 UNIT 16.2: Shapes: Perimeter and volume ..................................................................157 Lesson 16.4: Perimeter, area and volume ..................................................157 Mental maths 67 ....................................................................162 Activity 68 ..............................................................................163 Lesson 16.5: Perimeter, 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 & 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 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
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 2/2 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 2/2 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 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 3-D 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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Unit 17 Units 17.1
17.2
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
Unit 18 Probability
(Lesson 18.1, Mental maths 71, Activity 72) Extra exercises Unit 19 Mental (Lesson 19.1, Mental maths 72–82) maths 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
46 546
– 9 789
+
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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1 9
2
5 to 9 move up
3
4
10
14
5
6
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Study Guide 2/2 G06 ~ Mathematics
Unit
10.0
Opposite or inverse operations = Determine if your answer is correct Example Addition: Subtract to see if the answer is correct.
Subtraction: Add to see if the answer is correct.
Mental maths 42 You have to do mental maths every day. Work as quickly and correctly 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 following 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
10.0
Round off the following numbers 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 the following numbers 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
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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Study Guide 2/2 G06 ~ Mathematics
6.7
742 264 – 12 273
6.8
348 939 – 94 283
Unit
10.0
Lesson 10.2: Whole numbers Sometimes it helps to draw pictures to make word sums easier to understand and solve. Word sums have five steps: Step 1: Write down an open number sentence. Step 2: Write down the information that has been given. Step 3: Write down what has been asked. Step 4: Do the calculations. Step 5: Calculate the answer and write down what you have calculated.
Mental maths 43 You have to do mental maths every day. Work as quickly and correctly as possible. Only write down the answers. 1.
5 × 14 =
21.
50 × 30 =
2.
30 × 12 =
22.
400 ÷ 4 =
3.
6 × 30 =
23.
4 × 120 =
4.
90 × 12 =
24.
7 × 120 =
5.
2 × 20 =
25.
9 × 20 =
6.
200 ÷ 5 =
26.
7 × 60 =
7.
45 ÷ 9 =
27.
6 × 60 =
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Unit
Study Guide 2/2 G06 ~ Mathematics
10.0
8
10 × 100 =
28.
8 × 80 =
9.
60 × 8 =
29.
9 × 90 =
10.
60 × 4 =
30.
70 × 7 =
11.
90 × 10 =
31.
70 × 10 =
12.
1 000 ÷ 10 =
32.
700 ÷ 10 =
13.
10 × 120 =
33.
30 × 10 =
14.
10 × 60 =
34.
300 ÷ 10 =
15.
8 × 40 =
35.
80 × 10 =
16.
120 + 40 =
36.
800 ÷ 10 =
17.
3 × 40 =
37.
50 × 10 =
18.
0 × 12 222 =
38.
500 ÷ 10 =
19.
5 × 50 =
39.
90 × 10 =
20.
50 × 12 =
40.
900 ÷ 10 =
Activity 44 1.
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The circus is in town. During a performance 600 people can sit in the tent. All the tickets were sold out for the first three evenings. They sold only half the tickets on the fourth evening and they sold 450 tickets on the fifth evening. 1.1
How many tickets did they sell in total?
1.2
If they were able to sell all their tickets on all five days, how many tickets would they have sold?
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Study Guide 2/2 G06 ~ Mathematics
1.3
2.
Unit
10.0
What is the difference between the number of tickets they could have sold and the number of tickets they really sold?
The Grade 6 learners all joined the school’s library. They set a goal to read 2 000 books by the end of the year, together with the Grade 4, 5 and 7 learners. By the end of the year they’ve collected the following information: Class Grade 4 Grade 5 Grade 6 Grade 7 Grade 4 Grade 5 Grade 6 Grade 7 Grade 4 Grade 5 Grade 6 Grade 7 Grade 4 Grade 5 Grade 6 Grade 7
Term 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4
Books read 92 176 372 536 83 163 401 487 85 198 448 473 78 176 396 426
2.1
How many books have the Grade 4 learners read altogether?
2.2
How many books have the Grade 5 learners read altogether?
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Unit
Study Guide 2/2 G06 ~ Mathematics
10.0 2.3
How many books have the Grade 6 learners read altogether?
2.4
How many books have the Grade 7 learners read altogether?
2.5
How many books have all the grades read in total?
2.6
Have the learners reached their goal? Give a reason for your answer.
2.7
By how many were they below or above their goal?
3.
What is the sum of: 584 934 and 273 823?
4.
What is the difference of 732 337 and 832 327?
Lesson 10.3: Patterns · ·
·
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When we start counting, we count from 0 = counting numbers. 0 is not a natural number and you don’t say “I have zero apples”. You say you have no apples or you don’t have any apples. We therefore talk about natural numbers when we start counting from 1. 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 4. When you divide 4 by 2, the answer is 2. Uneven numbers always end on 1, 3, 5, 7 or 9. An uneven number cannot be divided by 2 without a remainder. If you divide uneven 22