contents - tom newby school€¦ · grade 6 maths: term 4 . contents . unit 1: whole numbers:...
TRANSCRIPT
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Grade 6 Maths: Term 4 Contents Unit 1: Whole numbers: counting and ordering .................................................................... 3
Activity 1 ........................................................................................................................... 3 Number Patterns........................................................................................................... 3
Unit 2: Multiplication: 4 digits by 3 digits. ............................................................................. 5
Activity 1 ........................................................................................................................... 5 Working with 2 and 3 digit numbers .............................................................................. 5
Activity 2 ........................................................................................................................... 6 Multiples ....................................................................................................................... 6
Activity 3 ........................................................................................................................... 6 Factors and prime factors ............................................................................................. 6
Activity 4 ........................................................................................................................... 7 Multiply 4 digits by 3 digits ............................................................................................ 7
Activity 5 ........................................................................................................................... 8 Word Problems. ............................................................................................................ 8
Unit 3: Common Fractions ................................................................................................... 9
Activity 1 ........................................................................................................................... 9 Simplifying Fractions ..................................................................................................... 9
Activity 2 ......................................................................................................................... 10 Comparing and ordering fractions............................................................................... 10
Activity 3 ......................................................................................................................... 10 Add and subtract fractions with the same denominators. ........................................... 10
Add and subtract mixed numbers. .............................................................................. 11
Activity 4 ......................................................................................................................... 11 Simplifying fractions. ................................................................................................... 11
Activity 5 ......................................................................................................................... 12 Comparing fractions .................................................................................................... 12
Activity 6 ......................................................................................................................... 12 Add and subtract fractions with different denominators. ............................................. 12
Activity 7 ......................................................................................................................... 13 Fractions, decimals and percentages ......................................................................... 13
Informal Assessment ......................................................................................................... 15
Unit 4: Properties of 3-D shapes. ....................................................................................... 17
Activity 1 ......................................................................................................................... 17 Identifying 3-D objects ................................................................................................ 17
Activity 2 ......................................................................................................................... 17 Building 3-D objects .................................................................................................... 17
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Activity 3 ......................................................................................................................... 18 Faces, vertices and edges .......................................................................................... 18
Activity 4 ......................................................................................................................... 19 3-D objects and nets ................................................................................................... 19
Unit 5: Perimeter and area ................................................................................................. 20
Activity 1 ......................................................................................................................... 20 Perimeter of 2-D shapes ............................................................................................. 20
Activity 2 ......................................................................................................................... 22 Area of 2-D shapes ..................................................................................................... 22
Unit 6: Perimeter, Area, Volume & History of Measurement. ............................................. 24
Activity 1 ......................................................................................................................... 24 Activity 2 ......................................................................................................................... 24
Perimeter and Area ..................................................................................................... 24
Activity 3 ......................................................................................................................... 25 Doubling and halving 2-D shapes ............................................................................... 25
Activity 4 ......................................................................................................................... 26 Volume ....................................................................................................................... 26
Activity 5 ......................................................................................................................... 28 The History of Measurement ...................................................................................... 28
Assessment ....................................................................................................................... 29
Unit 7: Division (4 digit by 3 digit numbers.) ....................................................................... 31
Activity 1 ......................................................................................................................... 31 Activity 2 ......................................................................................................................... 31 Activity 3 ......................................................................................................................... 32
Factors ........................................................................................................................ 32
Activity 4 ......................................................................................................................... 33 Practise Division ......................................................................................................... 33
Activity 5 ......................................................................................................................... 34 Revision of 4 digit by 2 digit division ........................................................................... 34
Activity 6 ......................................................................................................................... 34 Dividing 4 digit numbers by 3 digit numbers. .............................................................. 34
Activity 7 ......................................................................................................................... 35 Fun with Division......................................................................................................... 35
Unit 8: Number Sentences. ................................................................................................ 37
Activity 1 ......................................................................................................................... 37 Properties of Numbers ................................................................................................ 37
Activity 2 ......................................................................................................................... 38 Solving equations ....................................................................................................... 38
Activity 3 ......................................................................................................................... 39 Problem solving .......................................................................................................... 39
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Unit 1: Whole numbers: counting and ordering Activity 1 Number Patterns Copy and complete each number pattern: 1. a. 24 300 23 700 ____ ____ ____ ____ 20 700 b. ____ 47 500 47 750 48 000 ____ ____ ____ c. 310 040 ____ 310 120 ____ ____ 310 240 ____ d. ____ 720 ____ ____ ____ 1 040 1 120 e. 46 250 46 750 ____ ____ ____ ____ 49 250 2. Write these words as numbers: a. two hundred and seventy thousand nine hundred and sixty four. b. three hundred and five thousand seven hundred and eighty nine. c. five hundred and eighty one thousand four hundred and twelve. d. nine hundred and twenty seven thousand and sixty three. 3. Copy and complete the table: Number Expanded Notation Words Example: 21 360 20 000+ 1 000+
300+ 60 twenty one thousand three hundred and sixty.
a. 327 548 b. 804 913 c. 64 882 d. 12 951 e. 348 752
4. Place Value: What is the place value of the 4 in each of these numbers? a. 946 517 b. 280 470 c. 493 517 d. 149 832 e. 106 493 f. 534 782 g. 363 794 h. 698 546 5. Arrange these numbers from smallest to biggest: a. 64 464 66 446 66 464 64 664 64 446 b. 373 113 377331 373 131 377 133 c. 195 059 195 095 195 950 195 509 195 905 d. 2 543 334 2 544 434 2 543 343 2 543 443 2 544 334 e. 188 680 008 188 670 008 188 660 008 188 650 008
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6. Write each digit in the correct column: Number HTH TTH TH H T U Example: 158 046 1 5 8 0 4 6 a. 208 547 b. 716 949 c. 230 554 d. 852 164 e. 195 735
7. Round off to the nearest 5, 10, 100 and 1 000. Number 5 10 100 1 000 Example: 156 203 156 205 156 200 156 200 156 000 a. 629 131 b. 548 706 c. 116 489 d. 307 774 e. 872 945
8. Use the numbers in the block: Use each number once. a. Make the smallest 6 digit number. b. Make the biggest 6 digit number. c. Find the difference between the 2 numbers you made.
8 2 4 0 6 1
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Unit 2: Multiplication: 4 digits by 3 digits. Activity 1 Working with 2 and 3 digit numbers 1. Copy and complete each diagram:
2. Use the example below to complete each calculation.
Number sentence Round off to nearest 10 Working out 274 x 26 270 x 30 = 8 100 274
x 26 1 644 + 5 540 7 184
a. 135 x 32 b. 216 x 23 c. 189 x 16 d. 347 x 24 e. 268 x 19 f. 199 x 12 g. 234 x 25 h. 479 x 46 i. 423 x 33 j. 352 x 42 k. 758 x 26 l. 455 x39 3. 127 books were sold for R25 each. Calculate the total amount of money received for these books.
a. b. c.
9 90 900 9 000
9 90 900 9 000
9 90 900 9 000
X 10 X 100 X 1 000
d. e.
7 70 700 9 90 900
8 80 800 6 60 600
X 100 ÷ 10 X 1000 ÷100
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Activity 2 Multiples When we say the multiples of a number, it’s like counting in that number. 1. Write the first 10 multiples of each number:
a. 7 70 700 b. 5 50 500 c. 2 20 200 d. 9 90 900 e. 10 100 1 000 f. 4 40 400 2. Copy and complete the table.
x 10 20 30 40 50 60 70 80 90 100 100 200 300 400 500 600 700 800 900 1 000
Write the first 10 multiples of: 1 250; 3 200; 750. Activity 3 Factors and prime factors A factor is a number which divides exactly into a given number. The factors of 30 are all the numbers which divide exactly into 30. Factors of 30: 1 2 3 5 6 10 15 30 The factor pairs of 30: 1 x 30 = 30 2 x 15 = 30 3 x 10 = 30 5 x 6 = 30
Challenge!
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• Write the factors of each number. • Join the factor pairs in a number sentence.
a. 24 b. 40 c. 18 d. 32 e. 20 f. 16 g. 15 h.12 i. 100 j.120 k. 150 l. 200 A prime number has only 2 factors: 1 and itself.
2. Write the factors of each number, then circle the prime numbers. (You have then circled the prime factors.) a. 9 b. 10 c. 12 d. 15 e. 18 f. 20 g. 21 h. 24 i. 16 Activity 4 Multiply 4 digits by 3 digits 1. Round off each number to the nearest 10, 100 and 1 000.
Number Nearest 10 Nearest 100 Nearest 1 000 Example: 47 543 47 540 47 500 48 000 a. 36 242 b. 51 375 c. 74 951 d. 33 688
2. Use the example below to complete each calculation.
Number sentence Round off to nearest
10 Round off to nearest 100
Work out
1 364 x 256 1 360 x 260 = 353 600
1 400 x 300 = 420 000
1 364 x 256 8 184 + 68 200 272 800 349 184
a. 4 532 x 167 b. 3 951 x 234 c. 1 762 x 234 d. 2 768 x 159 e. 3 218 x 256 f. 1 385 x 123 g. 2 986 x 193 h. 5 307 x 159 i. 1 386 x 352 j. 6 573 x 382 k. 5 463 x 258 l. 3 796 x 354
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Activity 5 Word Problems. 1. The taxi takes 14 pensioners to collect their money. Each person gets R1 725. How
much money do they collect altogether?
2. Dad travels 1 245 km each week. How far does he travel in 28 days? 3. 684 new cars need to be filled with petrol. Each petrol tank has a capacity of 55 litres.
How much petrol is needed for all the cars? 4. Zwi collected 132 bottles for recycling. Her friend collected 11
12 of this number of bottles.
How many bottles did her friend collect? 5. One bag of cement has a mass of 50 kg. A builder orders 238 bags of cement. What is
the total mass of cement that needs to be delivered? 6. There are 3 600 seconds in one hour and 168 hours in a week. How many seconds are
there in a week?
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Unit 3: Common Fractions Activity 1 Simplifying Fractions
34 14
5
When we write a fraction in its simplest form, we use the smallest numbers we can…
612
= 3 6
= 12
1. Copy and complete the table.
Shape Fraction
shaded Fraction in simplest form
Fraction unshaded
Fraction in simplest form
a.
24
12
24
12
b.
c.
d.
e.
f.
2. Write the fractions in their simplest form.
a. 8
12 b. 10
20 c. 40
50 d. 8
10
e. 8
20 f. 20
100 g. 75
100 h. 25
100
Remember:
numerator
denominator
A mixed number consists of a whole number and a common fraction.
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Activity 2 Comparing and ordering fractions 1. Replace * with ˂, ˃ or =. a. 1
7 * 1
6 b. 5
7 * 4
5 c. 1
3 * 2
6 d. 4
8 * 1
2
e. 7
7 * 1 f. 3
12 * 1
4 g. 3
9 * 1
3 h. 6
8 * 5
7
2. Write the fractions from smallest to largest. a. 1
5 1
4 1
6 b. 1
3 1
4 1
5 c. 1
2 2
6 1
3
d. 1
11 1
12 1
10 e. 1
8 1
10 1
6 f. 2
6 2
7 2
5
3. Count on and simplify the fractions where possible. a. 2 21
8 21
4 23
8 21
2 _____ _____ _____ _____ _____
b. 0 1
12 1
6 1
4 1
3 5
12 _____ _____ _____ _____ _____
c. 1 1 1
10 11
5 1 3
10 12
5 _____ _____ _____ _____ _____
4. Word Problem. Gogo is baking a cake. She needs 13
4 cups of raisins and 13
4 cups of nuts.
How many cups of nuts and raisins does she need altogether? Activity 3 Add and subtract fractions with the same denominators.
Examples: 49 + 7
9 = 11
9 10
11 - 2
11 = 8
11
= 9
9 + 2
9
=12
9
1. Copy and calculate. a. 4
9 + 3
9 b. 5
6 - 3
6 c. 4
5 + 2
5 d. 8
11 - 2
11
e. 3
4 + 3
4 f. 7
8 - 3
8 g. 4
6 + 2
6 h. 9
12 + 7
12
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Add and subtract mixed numbers.
Examples: 235 + 14
5 = 37
5 11
8 - 5
8 = (8
8 + 1
8) - 5
8
= 3 + 5
5 + 2
5 = 9
8 - 5
8
= 42
5 = 4
8
= 1
2
Remember to always write your fractions in simplest form… 2. Copy and calculate. Show your working out. a. 12
3 + 12
3 b. 25
6 - 13
6 c. 25
8 + 17
8 d. 22
5 - 4
5
e. 31
4 - 13
4 f. 14
7- 57 g. 2 7
10 + 1 2
10 h. 2 7
12 + 1 5
12
Activity 4 Simplifying fractions. 1. Simplify as far as possible. a. 2
6 = b. 6
12 =
c. 4
10 = d. 4
8 =
e. 6
8 = f. 6
9 =
g. 4
6 = h. 8
12 =
i. 4
12 = j. 2
10 =
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Activity 5 Comparing fractions
Examples: 316
* 12 4
5 * 7
10
316
* 816
8 10
* 710
316
˂ 12 4
5 ˃ 7
10
1. Replace * with ˃, ˂ or =. a. 1
2 * 5
8 b. 3
4 * 9
12 c. 2
3 * 5
9 d. 7
10 * 70
100
e. 2
5 * 5
10 f. 9
10 * 89
100 g. 1
4 * 2
12 h. 5
6 * 11
12
i. 8
100 * 8
10 j. 1
10 * 1
100 k. 3
10 * 33
100 l. 5
10 * 50
100
Activity 6 Add and subtract fractions with different denominators. Examples: 34 + 5
8 = 6
8 + 5
8 9
10 - 3
5 = 9
10 - 6
10
= 11
8 = 3
10
= 8
8 + 3
8
= 13
8
Fractions must have the same denominators before you can compare them.
Remember, we can only + and - fractions when their denominators are the same.
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1. Copy and complete. Show all your working.
a. 6
6 + 7
12 b. 2
3 + 1
6 c. 3
4 + 3
8 d. 7
10 + 1
5
e. 7
8 - 3
4 f. 4
5 - 3
10 g. 2
3 - 5
12 h. 1
2 - 1
6
i. 7
9 - 2
3 j. 9
10 - 1
2 k. 7
8 + 1
2 l. 5
6 + 2
3
2. Word problem. Paul, Tom and Ruth share a packet of 24 biscuits. Paul ate 1
3, Tom ate 1
6 and Ruth ate 1
4.
How many biscuits were left in the packet?
Activity 7 Fractions, decimals and percentages 1. Copy and complete the table.
Percentage: Fraction in simplest
form: Decimal:
Example: 50% 50100
= 12 0,50
a. 25% b. 3
10
c. 0,2 d. 0,75 e. 60% f. 4
5
g. 17100
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2. Calculate: a. 1
4 of R36. b. 50% of 2 400 litres. c. 1
3 of 24 kg.
d. 30% of R100. e. 2
5 of 40 m. f. 9
10 of R500.
3. Word problems. There are 64 children in the athletics team. The pie chart shows the size of the tracksuits a. Write the fraction of the team who wear:
• small • medium • large • extra large
b. Calculate how many tracksuits they need of each size. Hint: remember that there are 64 athletes in the team. 4. Themba ran an 800 m race. After 1
10 of the race he had run ____m. He still had to run ____m.
After 1
4 of the race he had run ____m. He still had to run ____m.
After 2
5 of the race he had run ____m. He still had to run ____m.
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Informal Assessment Whole Numbers 1. Copy and complete the number patterns. a. ____ 12,375 ,12,5 ____ ____ ____ 13 ____ b. 12 150 ____ ____ 9 150 8 150 ____ ____ ____ 2. Copy and complete the table. Number Expanded Notation Number in words a. 524 106 b. 735 882 c. 942 718
3. Use the digits 5 6 0 4 9 and 2: a. use each digit once and make the biggest 6 digit number. b. use each digit once and make the smallest 6 digit number. c. you may use 1 digit twice to make the smallest 6 digit number. d. you may use 1 digit twice to make the biggest 6 digit number. e. Arrange your 4 numbers from biggest to smallest. f. Round your 4 numbers off to the nearest 10, 100 and 1 000. 4. Number ≈ 10 ≈ 100 ≈ 1 000 a. 32 476 b. 53 869 c. 45 743
Multiplication 5. X 10 20 30 40 50 60 70 80 90 100 a. 200 b. 500 c. 800 d. 1
000
6. Write the factors of each number. Circle the prime factors. a. 18 b. 12 c. 24 7. Calculate and use the inverse operation to check your answer. a. 234 x 15 b. 427 x 18 c. 1 385 x 123 d. 5 463 x 258 8. The taxi driver travels 1 586 km each week. How far does he travel in 126 days?
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Fractions 9. Replace * with ˃, ˂ or =. a. 3
12 * 1
4 b. 5
6 * 11
12
c. 3
10 * 33
100 d. 5
10 * 2
5
e. 2
3 * 5
9 f. 7
7 * 1.
10. Write the fractions from smallest to largest. a. 2
6 27 2
5 1
2 b. 1
8 1
10 1
6 1
12
11. Add and subtract. a. 4
5 - 3
10 b. 7
10 + 1
5 c. 7
8 - 34
d. 5
6 + 2
3 e. 5
6 + 7
12 f. 2
3 - 1
6
12. Copy and complete the table. % Fraction in simplest
form. Decimal.
a. 25% b. 3
5
c. 0,2 13. Word problem. Themba ran a 1 000 m race. How far had he run after 2
5 of the race?
Checked GM 2016
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GM 2017
Unit 4: Properties of 3-D shapes Activity 1 Identifying 3-D objects 1. Write the letter of each 3-D object with the correct name. Example: a. cylinder.
rectangular prism sphere hexagonal pyramid pentagonal pyramid cone octagonal pyramid square based pyramid tetrahedron cube cylinder triangular prism hexagonal prism octagonal prism pentagonal prism
Activity 2 Building 3-D objects Play time! Using straws, string and jelly tots, see how many of the following 3-D shapes you can make…
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Activity 3 Faces, vertices and edges
Pyramids. • All pyramids have 1 base. • All pyramids have triangular faces which meet at 1 vertex (point). • We name a pyramid according to its base. If the base is a triangle, we name the
pyramid a triangular based pyramid or tetrahedron. 1. Copy and complete the table.
Name the 3-D object.
Number of faces.
Shape of each face.
Number of edges.
Number of vertices.
vertex (where edges meet)
face (a flat surface)
edge (where 2 faces meet)
a.
b.
c.
d.
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Activity 4 3-D objects and nets 1. Write the name of each 3-D object with the letter of the matching net.
2. Write the name of each 3-D object, shape of the face and name the face angles. ________ ________ ________ ________
3-D object Shape of base Name the angles
Checked GM 2016
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Unit 5: Perimeter and area To calculate the perimeter of this rectangle… Perimeter is the distance all the way around the outside of a 2-D shape. Activity 1 Perimeter of 2-D shapes 1. Chumani was asked to calculate the perimeter of the soccer field to make sure that the markings were correct. This is how he did it. Calculate the perimeter of the soccer field. 2. Calculate the perimeter of the rectangle.
start 3,5 cm
3,5 cm
2,5 cm 2,5 cm P = ℓ + ℓ + ℓ + ℓ = 3,5 cm + 2,5 cm +3,5 cm + 2,5 cm = 12 cm
start
2,3
cm 16,4 cm 2,3 cm
16,4 cm
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3. Write down the measurement of each side in mm. Add up the measurements to calculate the perimeter of the triangle. Example:
4. 5. Calculate the perimeter of each square. 6. You are given the perimeter of 6 squares. Calculate the length of a single side in each square. a. 68 m d. 36 mm b. 8,8 cm e. 28,6 cm c.24,5 cm f. 40 km
Remember that these lines show that the sides are of = length.
18,2 cm 76,7 cm
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7. Measure the length of the sides and diagonal of these squares and record your answers. a. b. c. Activity 2 Area of 2-D shapes
1. Calculate the area of each 2-D shape by counting the number of squares.
What would we do if there are half blocks? 2. Find the area of each shape.
We can calculate the area of this rectangle by counting the number of squares.
Area is the size of the surface of a shape and is measured in squares. The area of this rectangle is 8 squares.
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How do I calculate the area of this shape?
3. Count the squares to calculate the area of the shape below.
Count all the squares that are half or more as full squares. Don’t count squares that are less than half. I have put a on each square that I have counted I get an area of 8 squares.
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Unit 6: Perimeter, Area, Volume & History of Measurement.
Activity 1 Calculate the area of squares and rectangles. 1. Use your favourite method to calculate the area of these 2-D shapes.
Activity 2 Perimeter and Area Each of these rectangles below has a perimeter of 16 cm but they have different area.
Brenda’s method.
I counted all the squares and I got a total of 36 squares.
What method would you use?
Siya’s method.
I multiplied the length of the rectangle (9 squares) by the breadth (4 squares) and got 36 squares. Length x breadth = 36 squares.
area = 12 squares area = 7 squares area = 15 squares
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GM 2017
1.a. Draw 4 different rectangles each with a perimeter of 20 cm. Write the area of each rectangle. b. Draw 4 different rectangles with a perimeter of 18 cm. Write the area of each rectangle. Activity 3 Doubling and halving 2-D shapes Doubling a 2-D shape means making the area twice as big… The length of the rectangle has doubled. What has happened to the area of the rectangle? 1. Double the area of each of these rectangles and squares. 2. Draw the same 2-D shapes as above. Halve the length of 1 pair of opposite sides. What do you notice about the area of the shape?
Challenge! Draw 1 rectangle with a perimeter of 22 cm and an area of 30 cm.
3 cm
3 cm
2 cm
2 cm
area = 6 squares.
Double the length of 1 pair of opposite sides.
6 cm
6 cm
2 cm 2
cm
Example:
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Activity 4 Volume Volume is the amount of space an object occupies. It is measured in cubes. 1. Count cubes.
a. Estimate how many containers will fit into the container on the teacher’s desk. b. Take turns to pack the cubes into a shoebox. Keep count as you pack the cubes. c. The volume of the shoebox is ____ cubes. d. Repeat this activity using other containers, for example ice-cream boxes.
2. Take turns to make stacks with your cube:
• Estimate the number of cubes in the stack. • Count the cubes in each stack.
Homework.
Make 2 cubes from the net. Bring them to school tomorrow.
• Trace this net onto paper.
• Write your name on 1 of the outward faces.
• Cut, fold and paste the net to form a cube.
• The first layer has 10 cubes. • The second layer has 6 cubes. • The third layer has 6 cubes. • The fourth layer has 2 cubes.
I counted the cubes in layers. The volume of the stack is 24 cubes.
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3. Write the volume of each stack.
4. How many matchboxes in each stack?
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Activity 5 The History of Measurement Use your handspan as the unit of measurement. Follow these steps to work out how many times your handspan fits into your height. Step 1: Make your handspan: take a strip of paper and stretch your hand along it. Make a mark where your thumb starts and your little finger ends. Step 2: Cut the paper on the mark on each end. You now have a strip of paper the same length as your handspan. Measure your handspan. Step 3: Measure your height against a wall. See how many times your handspan fits into your height. Calculate your height.
The Egyptians were skilled builders. They did not have measuring instruments like
rulers or builders’ tapes. The Egyptians used body parts as units of measurement. These
measurements were copied onto wood, metal or stone so that
everyone used the same measure.
These are some of the non-standard units of measurement
that people used long ago…
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Assessment Properties of 3-D objects 1. Copy and complete the table.
3-D object
Name of 3-D object.
Number of faces.
Shape of each face.
Number of edges.
Number of vertices.
Perimeter and Area 2. Find the perimeter and area of each shape.
3. Find the area of each shape.
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Volume 4. Write the volume of each stack of cubes.
5. Name the non-standard units of measurement.
Checked GM 2016
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Unit 7: Division (4 digit by 3 digit numbers.) Activity 1 1. Copy and complete the flow diagrams. 2. Copy and complete the table.
1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000 a. ÷ 10 100 b. ÷ 20 50 c. ÷ 25 40 d. ÷ 50 20 e. ÷ 100 10 f. ÷ 500 2 g. ÷ 1 000 1
3. Number families. Write 4 number sentences for each group of numbers. Copy and
complete.
Example: 63; 9; 7 7 x 9 = 63 9 x 7 = 63 63 ÷ 7 = 9 63 ÷ 9 = 7 a. 60; 70; 420 b. 8 400; 200; 42 c. 40; 800; 20 d. 800; 25; 32
Activity 2 RemembeR: A multiple of 12 (12 times table) is any number which divides exactly by 12. It’s like counting in 12s… example: 12; 24; 36; 48; 60; 72; 84; 96; 108; 120; 132; 144. 1. Write the first 10 multiples of these numbers. a. 15 b. 8 c. 25 d. 30 e. 60 f. 100
a.
b.
c.
d.
e.
f.
45 450 4 500
630 6 300 63 000
4 800 48 000 480 000
450 4 500 45 000
6 300 63 000 630 000
8 000 80 000 800 000
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GM 2017
When you list the multiples of 2 or more numbers and find the same number in both, then it is a common multiple. 2. Copy and complete the table. Write down the first 12 multiples for the following
numbers. Circle the common numbers for the 2 multiples.
Number Multiples 3 3; 6; 9; 12; 15; 18; 21; 24; 27; 30; 33; 36 9 9; 18; 27; 36; 45; 54; 63; 72; 81; 90; 99; 108 a. 5 8 b. 10 12 c. 4 7
3. Use the table from Q2. Write the lowest common multiple for each pair of numbers. Example: the LCM of 3 and 9 is 9. a. The LCM of 5 and 8 is ____. b. The LCM of 10 and 12 is ____. c. The LCM of 4 and 7 is ____. Activity 3 Factors RemembeR: Any number that divides exactly into a given number is a factor of that number. example: Factors of 42 are: 1; 2; 3; 6; 7; 14; 21; 42. Factor pairs: 1 x 42; 2 x 21; 3 x 14; 6 x 7. 1. Copy and complete the table. Write the factors and factor pairs of the following numbers. Number Factors Factor pairs No. of factors Example: 20 1; 2; 4; 5; 10;20 1x20; 2x10; 4x5 6 a. 24 b. 45 c. 18 d. 60 e. 17
Remember: numbers with only 2 factors are prime numbers.
LCM is the short way to write Lowest Common Multiple.
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GM 2017
Example: 13 x 1 = 13. Number Factors No. of factors Prime no?
Yes/No. Example: 19 1; 19 2 Yes a. 23 b. 57 c. 41
Activity 4 Practise Division 1. Copy and complete the table.
Example: 42 ÷ 2 63 ÷ 2 142÷ 2 253÷ 2 Answers: 21 31 rem 1 71 126 rem 1 a. 26 ÷ 3 271 ÷ 3 406÷ 3 24 000 ÷ 3 Answers b. 91 ÷ 7 270÷ 7 820 ÷ 7 216 ÷ 7 Answers c. 96÷ 10 249÷ 10 342÷ 10 2 040÷ 10 Answers
2. Inverse operations. Complete each number sentence. Check your answers using inverse operations. Example: ÷7=4 rem 5. Check: 7x4+5=33 33÷7=4 rem 5 a. ÷9=7 rem 7 i. ÷15=7 rem 7 b. ÷6=8 rem 3 j. 159÷ =10 rem 9 c. ÷7= 4 rem 5 k. 205÷ =15 rem 10 d. 70÷ =6 rem 4 l. ÷25=8 rem 13 e. 97÷ =7 rem 6 m. 762÷ =95 rem 2 f. 123÷ =10 rem 3 n. 106÷ =9 rem 7 g. ÷12=9 rem 8 o. ÷12=12 rem 9 h. 104 ÷ =9 rem 5 p. ÷20=7 rem 18
Remember that division and multiplication are inverse (opposite) operations, andcan be used to check answers.
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Activity 5 Revision of 4 digit by 2 digit division Long division: 1 316÷12
1. Calculate. Use the method you prefer. Check your answer by using the inverse
operation.
a. 2 014 ÷ 17 b. 3 716 ÷ 22 c. 4 691 ÷ 13 d. 1 168 ÷ 16
e. 9 603 ÷ 27 f. 7 834 ÷ 19 g. 5 186 ÷ 21 h. 6 437 ÷ 14
2. Solve these problems.
a. A farmer needs to plant 1 346 apple trees in rows of 15.
How many full rows can he plant?
b. The school is going on an outing. There are 1 196 learners.
If each bus can take 65 learners, how many buses will the school need to transport
the learners?
Activity 6 Dividing 4 digit numbers by 3 digit numbers. 1. Calculate. Use any method. Check your answers by using multiplication.
a. 2 968÷203 b. 5 892÷144 c.3 864÷314 d. 4 381÷361
e. 6 302÷164 f. 5 847÷318 g. 7 819÷511 h. 5 926÷261
i. 8 649÷129
109 12 1 316 1. divide -1 2 2. multiply 11 3. subtract - 0 4. bring down 116 - 108 8
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GM 2017
2. Solve these word problems. Use any method you like.
Activity 7 Fun with Division 1. Copy and complete, filling in the missing digits with a coloured pencil.
a. A company donated boxes of calculators to a school. Each box has 165 calculators in it. If there are 4 455 calculators altogether, how many boxes were donated?
b. A shop sells bouncy balls. If a box of 144 bouncy balls cost R2 016, how much will 10 balls cost?
c. The Grade 6 learners collected cans for a recycling project. The total mass of the cans collected was 3 648 kg. If there are 152 learners in Grade 6, how many kilograms did each learner collect?
d. The school shop buys 224 pairs of shorts. The total cost was R9 744. How much did 1 pair of shorts cost?
a. 1 rem 2 9 281 - 27 11 -
b. 2 rem 3 8 179 - 6 19 - 6 3
c. 42 rem 6 8 342 -32 2 - 6
d. 3 rem 11 399 - 3 69 - 66 3
e. 11 rem 24 271 -2 1 - 2 7
f. 2 rem 17 28 633 - 6 7 - 6 17
g. 4 rem 23 323 -2 3 - 92 1
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GM 2017
2. Copy and complete the table.
a. 650 ÷ 10 = f. 50 500 ÷ 100 = b. 9 200 ÷ 100 = g. 120 000 ÷ 1 000 = c. 3 010 ÷ 10 = h. 100 800 ÷ 100 = d. 93 000 ÷ 1 000 = i. 720 ÷ 10 = e. 2 700 ÷ 10 = j. 47 000 ÷ 100 =
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GM 2017
Unit 8: Number Sentences Activity 1 Properties of Numbers Remember: brackets mean you must do that part first. 1. Determine if the following number expressions are equal to each other. Fill in = if they are the same and ≠ if they are not equal. Example: 80 + 60 ≠ 80 – 60 a. 2 + (4 + 3) (2 +4) + 3 e. 13 + 16 16 - 13 b. (10 ÷ 1) x 4 10 ÷ 2 (2 x 4) f. (15 x 10) x 2 15 x 10 x 2 c. 3 + (5 x 4) (3 x 4) + (5 x 4) g. (15 + 30) + 20 15 + (30 + 20) d. (9 x 1) + 2 (9 + 1) x 2 h. 4 x 5 5 x 4
2. Fill in the missing number to make the number sentence true. Copy and complete. Example: 60 + 200 = 200 + 60 a. 400 + 500 = + 400 e. (30 + 5) x 2 = 30 x +5 x 2 b. (50 x 10) x 2 = 50 x (10 x ) f. (25 + 75) + 50 = + (25 + 75) c. + 455 = 455 + 725 g. 30 + 40 + 5 = 30 + + 5 d. (35 + 20) + 10 = 20 + (35 + ) h. 1 x 4 x 5 = 5 x 1 x
3. Calculate. Example: (a + b) + c = a + (b + c) (20 + 50) + 2 = 20 + (50 + 2) 70 + 2 = 20 + 52 72 = 72 a. (a + b) x c = a x c + b x c d. b – a + c = b. c x b = b x c e. a x 0 = c. (a x c) x b = a x (c x b) f. c x a = a x c
a=20 b=50 c=2
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GM 2017
Activity 2 Solving equations 1. Copy and complete the table. ....remember to do the brackets first… a. Number 0 1 3 5 10 25 50 100 x2 +15 b. Number 0 1 3 5 10 25 50 100 +5 x3 c. Number 0 1 3 5 10 25 50 100 (+20) ÷1 d. Number 0 1 3 5 10 25 50 100 x10 +5 e. Number 0 1 3 5 10 25 50 100 (+15) x2
2. Find the value of . a.
+ = 54 d. x = 144 g. 75 - = 22
b.
72 ÷ 9= e. 80 + = 150 h. x 20 = 160
c.
+ 15 = 70 f. 12 x = 108 i. - 55 = 35
3. Choose the correct number sentence. a. What is 20 more than 55? A. 55-20 B. 20+55 C. 55÷20 D. 20x55 b. Find the product of 9 and 6. A. 9+6 B. 9÷6 C.9-6 D. 9x6 c. What number is 5 times bigger than 7-3? A. (7-3)x5 B. (7-3)+5 C. 7-3x5 D. 5x7-3 d. What number is 10 times smaller than 50 + 20? A. 50+20÷10 B.50+20-10 C.(50+20) ÷10 D. (50+20)-10 e. You and two friends need to share R3,60. A. R3,60÷3 B. R3,60÷2 C. R3,60x3 D. R3,60x2
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GM 2017
Activity 3 Problem solving 1. Solve the following equations. a. (5x8)÷4= b. 9x(8+4)= c. 50+(20x5)= d. 27+18-26= e. (7x6)÷2= f. 12-(28÷4)= g. (5+6)x(8-1)= h. 30x (9-2)= i. (108÷9)x4= 2. Determine if the following are = to each other. Fill in = if they are and ≠ if they are not
equal. Copy and complete. Example: 15x3≠15+3 a. 5x(3x9) (5x3)x9 e. 100-10+5 100-(10+5) b. (60÷6)x8 60÷(6x8) f. 4+8x2 (4+8)x2 c. (15x29)+(15x1) 15x30 g. (50x10)x2 50x(10x2) d. (15x8)+(15x2) 150 h. (12x3)+10 (12+3)x10
3. Write a number sentence for each problem. Calculate the answer. a. Lizzy gets R20 a week for walking her neighbour’s dog. How much money will she be able to save in a year? b. Didi and her 2 friends get R100 to share. If Didi must get R10 more than her friends, How much money must each child get?
Remember these rules:
You can swap numbers around and still get the same answer when you add or multiply.
It does not matter how you
group the number when you
add or multiply.
Checked GM 2016