Solutions for all
Mathematics
Grade 4
Learner’s Book
Schools Development Unit
Kaashief Hassan
Mthunzi Nxawe
Connie Skelton
Sari Smit
Solutions for all Mathematics Grade 4 Learner’s Book
© Schools Development Unit 2012
© Illustrations and design Macmillan South Africa (Pty) Ltd, 2012
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First published 2012
13 15 17 16 14 12
2 4 6 8 10 9 7 5 3 1
Published by
Macmillan South Africa (Pty) Ltd
Private Bag X19
Northlands
2116
Gauteng
South Africa
Cover design by Deevine Design
Cover image from Digital Source
Illustrations by Geoff Walton
The publishers have made every effort to trace the copyright holders.
If they have inadvertently overlooked any, they will be pleased to make the necessary arrangements at the first
opportunity.
ISBN: 978 1 4310 0972 5
WIP: 4069M000
e-ISBN: 978-1-4310-2318-9
It is illegal to photocopy any page of this book
without written permission from the publishers.
Contents
Term 1 ..................................................................................................................
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Counting and number sentences ......................................................................
Addition and subtraction of whole numbers ......................................................
Number patterns ...............................................................................................
Whole number multiplication and division ........................................................
Telling time .......................................................................................................
Data handling 1 .................................................................................................
Data handling 2 .................................................................................................
Properties of 2-D shapes ...................................................................................
More multiplication and division ........................................................................
Revision .............................................................................................................
1
1
10
18
27
38
49
57
64
73
83
Term 2 .................................................................................................................. 91
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Moving on to bigger numbers ............................................................................
Common fractions..............................................................................................
Length ................................................................................................................
Whole number multiplication .............................................................................
Properties of 3-D objects ...................................................................................
Shape patterns and symmetry ..........................................................................
Whole number addition and subtraction ............................................................
Whole number multiplication and division .........................................................
Revision .............................................................................................................
91
98
107
119
128
137
146
154
161
Term 3 .................................................................................................................. 170
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Unit 11
Capacity and volume ........................................................................................
Comparing and calculating with fractions .........................................................
Counting, addition and subtraction ...................................................................
Views and 2-D shapes ......................................................................................
Data handling ...................................................................................................
Numeric patterns ..............................................................................................
Addition and subtraction ...................................................................................
Whole number multiplication ............................................................................
Number sentences ...........................................................................................
Transformations ................................................................................................
Revision ............................................................................................................
170
179
189
194
201
207
215
221
229
235
240
Term 4 .................................................................................................................. 248
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Counting, addition and subtraction of whole numbers ......................................
Mass .................................................................................................................
More about 3-D objects ....................................................................................
More common fractions ....................................................................................
Whole number division .....................................................................................
Perimeter, area and volume .............................................................................
Grids, tiling patterns and shape patterns ..........................................................
Whole number addition and subtraction ...........................................................
Probability .........................................................................................................
Revision ............................................................................................................
248
254
263
271
281
288
299
309
313
316
Mental mathematics ...................................................................................................... 328
Term
1
Unit 1 Counting and
number sentences
In this unit you will:
count forwards and backwards in 2s, 3s, 5s, 10s, 25s, 50s and 100s between
0 and at least 10 000
order, compare and represent numbers to at least 4-digit numbers
recognise the place value of digits in whole numbers to at least 4-digit
numbers
round off to the nearest 10, 100 and 1 000
write number sentences to describe problem situations
solve and complete number sentences.
Getting started
Counting
1. Count the bottle tops.
2. Each flower has eight petals. How many petals are there altogether? (You
may count in 2s if you like.)
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1
3. Look at the following flow diagram. Fill in the missing numbers.
Activity 1
Whole numbers
1. Find the numbers represented by the letters a) to k). Count on.
81
91
i)
82
92
j)
83
93
k)
a)
94
104
b)
95
105
c)
96
106
d)
97
107
2. Copy and complete.
a)
b)
3. Write the following numbers from biggest to smallest:
a) 237; 148; 108; 180; 303; 481
b) 2 001; 1 202; 2 009; 1 999; 2 900; 2 100
4. Are the following statements true or false?
a) 12 is closer to 10 than to 20
b) 56 is closer to 50 than to 60
c) 967 is closer to 1 000 than to 950
d) 220 is closer to 240 than to 210
5. Use the digits 8, 9 and 6.
a) What is the biggest number you can make?
b) What is the smallest number you can make?
c) What other numbers can you make from 8, 9 and 6?
2
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e)
f)
108
89
g)
109
90
h)
110
6. Write the following numbers in words:
a) 369
b) 709
c) 7 708
7. Write the following number names. Use number symbols.
a) five hundred and twenty-nine
b) four hundred and nine
c) one thousand three hundred and sixty-one
d) one thousand and fifty-seven
Exercise 1
Counting patterns
1. a) Count in 2s from 300 to 330.
b) Copy and complete.
332; 334;
;
;
;
; 344;
;
;
2. a) Count in 3s from 500 to 530.
b) Copy and complete.
533; 536;
;
; 545;
;
;
;
3. a) Count in 25s from 110 to 335.
b) Copy and complete.
360; 385; 410;
;
; 485;
;
;
;
4. Cool drink is sold in packs of six. How many cool drinks are there in
eight packs?
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Activity 2
Writing number sentences
1. a) Mrs Green bakes 24 cookies. She wants to sell 40 cookies at the cake
sale. How many more must she bake? Show your problem in a number
sentence.
b) This is how Niyaaz and Sally worked out the answer.
Niyaaz wrote
Sally wrote
40 – 20 = 20
24 + 6 = 30
20 – 4 = 16
30 + 10 = 40
She must bake 16 cookies.
She must bake another
10 + 6 = 16 cookies.
Explain how Sally and Niyaaz worked out their answers.
2. a) Write down five different number sentences that are equal to 248.
b) Compare your number sentences with the number sentences of a friend.
c) Compare your number sentences with Motlalepule’s. Are all his number
sentences correct?
Motlalepule wrote
248 = 240 + 8
= 200 + 40 + 8
= 250 – 2
= double 124
= half of 496
= 62 + 62 + 62 + 62
= 31 × 8
d) Make 10 number sentences that are equal to 350. Use doubling, halving,
adding, subtracting and multiplying.
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Exercise 2
Building up and breaking down numbers
1. Write five number sentences for each of the following numbers:
a) 97
b) 120
c) 145
d) 460
2. Match the number sentences in Column A with the answers in Column B.
a)
b)
c)
d)
Column A
100 + 80 + 1
49 – 7
double 132
9+9+9+9
Column B
264
36
181
42
3. Use the picture to help solve the following problem:
How much do four 25c stamps cost?
25c + 25c + 25c + 25c =
25c × 4 =
Activity 3
How adding and subtracting work together
Andrew represents number sentences using diagrams.
25 + 5 = 30
30 – 5 = 25
34 – 34 = 0
0 + 34 = 34
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5
345 + 0 = 345
345 – 0 = 345
32 + 16 = 48
16 + 32 = 48
Complete the following. Draw diagrams to help you.
1. a) If 420 + 30 = 450 then 450 –
= 420.
b) If 200 – 50 = 150 then
+
= 200.
c) If 135 +
= 145 then
–
=
.
d) What do you notice about adding and subtracting numbers?
2. a) 55 – 55 = 0 so 55 +
= 55.
b)
c)
– 168 = 0 so
+ 0 = 168.
+ 0 = 532 so 532 – 532 =
d) What do you notice about adding and subtracting zero?
3. a) If 23 + 17 = 40 then
+ 23 = 40.
b) If 540 + 15 =
then
+ 540 = 555.
c) 124 +
= 224 =
+
d) What do you notice about adding numbers in a different order?
4. a) If 201 + 0 = 201 then 201 – 0 =
.
b) If 0 + 37 =
then 37 –
= 37.
c) 243 + 0 =
– 0
d) What do you notice about adding and subtracting zero?
6
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Activity 4
Order of operations
Gary, Norman and Gilbert are doing a natural
sciences investigation. They record the heights of
three bean plants that are growing in the classroom.
Gary measures the bean plants:
A = 74 mm, B = 97 mm and C = 111 mm.
1. Round off the length of each bean plant to the nearest 10 mm. Then add them
together.
2.
I first add 74 mm and
97 mm to get 171 mm.
Then I find the sum of
171 mm and 111 mm to get
a total of 282 mm.
This is Gary’s calculation:
(74 mm + 97 mm) + 111 mm = 171 mm + 111 mm = 282 mm
Explain why your estimate in Question 1 is different from Gary’s answer.
3. Norman measures the length of the bean plants, but in a different order. He first
measures bean plant A, then C and then B. Norman’s number sentence looks
like this:
(74 mm + 111 mm) + 97 mm = total length of the bean plants
a) Do you think Norman will get the same answer as Gary?
b) Complete Norman’s calculation. Is his answer the same?
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7
4. Gilbert’s measurements are recorded as follows:
(111 mm + 74 mm) + 97 mm = total length of the bean plants
a) What is the total length of the bean plants in Gilbert’s calculation?
b) Do you need to calculate the answer? Give a reason.
c) Write a number sentence. Show the problem in a different way from Gary’s,
Norman’s and Gilbert’s methods.
d) What happens when you change the order in which you add the numbers?
Key ideas
You can make many different number sentences for a given number.
When you add zero or subtract zero from a number, the total stays the same.
You can use addition to check your subtraction. You can use subtraction to
check your addition.
You can add two or more numbers in any order and get the same answer.
Check what you know
1. Count the blocks in each of these diagrams.
a)
b)
2. Copy and complete.
a)
b)
c) 912; 812; 712; 612;
;
;
;
;
;
d) 1 035; 1 085; 1 135; 1 185;
;
;
;
;
;
8
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3. a) Arrange the following numbers from smallest to biggest:
212; 731; 197; 371; 712; 317
b) Arrange the following numbers from biggest to smallest:
1 009; 897; 355; 1 052; 987; 548; 829
4. Write four different number sentences that are equal to:
a) 24
b) 1 000
c) 750
d) 253
5. Fill in the missing numbers.
a) If 50 + 15 = 65 then 65 –
= 50.
b) If 250 –
= 0 then 250 +
= 250.
c) You can add
to 375 and your answer will be 375.
d) 45 +
= 100 = 55 +
6. Vusi calculates the sum of the ages of the members of his family. Vusi is 10
years old. His father is 40 years old. His mother is 35 years old. His brother
is 15 years old. His sister is 13 years old. Write three different number
sentences you could use to calculate the sum of the family’s ages.
Word bank
a b
calculate:
number sentence:
sum:
digit:
ow diagram:
c
work out the answer
a mathematical sentence you write with numbers
and operation signs
the total after you add
a symbol you use to make a numeral (we use
the digits 0 to 9 to make numerals, e.g. 475 has
three digits)
a diagram showing a sequence of operations
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9
Term
1
Unit 2 Addition and
subtraction of
whole numbers
In this unit you will:
revise addition and subtraction of 3-digit whole numbers
use a range of strategies to perform and check mental and written
calculations, including:
{ estimation
{ rounding off and compensating
{ building up and breaking down numbers
{ using addition and subtraction as inverse operations
solve word problems that involve addition and subtraction of whole numbers.
Getting started
Place value
Kobus builds numbers with number cards. He writes number sentences. They
show how Kobus made the numbers. He then writes each number in words.
5 243 = 5 000 + 200 + 40 + 3
5 003 = 5 000 + 3
5 243 = five thousand
5 003 = five thousand
two hundred and
and three
forty-three
1. Use number cards to build the numbers in a) to e):
a) 3 679
b) 7 021
d) 9 030
e) 6 363
c) 5 555
2. Write number sentences to show how you made the numbers.
3. Write each number in words.
10
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Activity 1
Breaking down numbers to calculate
Lynn breaks down numbers. This makes it easier to calculate.
This is how Lynn calculates 423 + 265:
423 + 265
= (400 + 20 + 3) + (200 + 60 + 5)
¤ first break down each number
= (400 + 200) + (20 + 60) + (3 + 5) ¤ add the hundreds, tens and units
¤ add the answers
= 600 + 80 + 8
= 688
Lynn calculates a subtraction problem 597 – 346. She uses the same way:
597 – 346
= (500 + 90 + 7) – (300 + 40 + 6)
¤ first break down each number
7–6
= 1
¤ subtract the units
90 – 40
= 50
¤ subtract the tens
500 – 300
= 200
¤ subtract the hundreds
= 200 + 50 + 1
¤ add the answers
= 251
1. Calculate the following. Use Lynn’s method:
a) 525 + 473
b) 965 – 855
c) 659 + 340
d) 688 – 467
Roger found that Lynn’s method did not work to calculate 586 – 377.
Roger added a step to her method.
Roger did this:
586 – 377
=
=
(500 + 80 + 6) – (300 + 70 + 7) ¤ break down each number
(500 + 70 + 16) – (300 + 70 + 7) ¤ compensate by breaking down
86 into 70 + 16
16 – 7 = 9 ¤ subtract the last numbers
70 – 70 = 0 ¤ subtract the tens
500 – 300 = 200 ¤ subtract the hundreds
200 + 0 + 9 = 209 ¤ add the answers
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11
2. a) Calculate 624 – 416. Use Lynn’s method. Can you get the answer?
b) Now add Roger’s step to the method. Calculate 624 – 416. Can you get the
answer?
c) Write a subtraction sum that needs the extra step from Roger’s method. Ask
a friend to find the answer.
Exercise 1
Adding and subtracting
1. Break down the following numbers:
a) four hundred and ninety-four
b) six thousand five hundred and twelve
c) twenty-six thousand eight hundred and thirty-seven
d) nine thousand and forty-eight
2. Add the numbers in the bricks to work out the numbers for A, B and C.
For example, in the second row of a):
30 + 28 = 58 and 28 + 18 = A = 46
a)
b)
3. Anele has read 75 pages of his book. The book has 120 pages. How
many more pages must Anele still read?
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4. Calculate.
a) 378 + 243 =
b) 645 + 324 =
c) 701 + 199 =
d) 967 – 432 =
e) 621 – 407 =
f) 693 – 584 =
5. Copy and complete.
+
78
52
14
36
115
136
219
479
Key ideas
We can round off numbers to the nearest 10, 100 or 1 000.
We can round off the number 332 to 330 (nearest 10).
We can round off the number 337 to 340 (nearest 10).
The number 335 is halfway between 330 and 340. But we always round 5
up, so 335 becomes 340 (nearest 10).
We can round off the number 332 to 300 (nearest 100).
We can round off the number 378 to 400 (nearest 100).
The number 350 is halfway between 300 and 400. But we always round 5
up, so 350 becomes 400 (nearest 100).
We can round off the number 2 234 to 2 000 (nearest 1 000).
We can round off the number 2 789 to 3 000 (nearest 1 000).
Activity 2
Estimating answers by rounding off
Akhona needs to calculate 324 – 57. He knows that it will be less than 300. This is
because 24 is less than 57.
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13
Akhona estimates the answer. He rounds off the numbers and then subtracts the
numbers.
324 rounded off to the nearest 10 is 320
57 rounded off to the nearest 10 is 60
320 – 60 = 320 – (20 + 40) = 300 – 40 = 260
1. Calculate 324 – 57.
2. What is the difference between Akhona’s estimation and the correct answer?
Activity 3
Checking solutions
Sandra works out that 568 – 342 = 226. She checks her answer using addition.
568 – 342 = 226
If my answer is right, then 568 = 342 + 226.
Check:
568 = (300 + 40 + 2) + (200 + 20 + 6)
568 = (300 + 200) + (40 + 20) + (2 + 6)
568 = 500 + 60 + 8
Both sides are the same. So, my calculation is correct.
Busi checks the answer to her addition problem. She uses subtraction.
387 + 253 = 640
If my answer is right, then 640 – 253 = 387.
Check:
640 – 253
(600 + 40) – (200 + 50 + 3)
(600 + 30 + 10) – (200 + 50 + 3)
(500 + 130 + 10) – (200 + 50 + 3)
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10 – 3
= 7
130 – 50
= 80
500 – 200
= 300
300 + 80 + 7
= 387
So my calculation is correct.
Calculate the answers to the following sums. Check the solutions using the method
of addition or subtraction.
1. 376 + 632 =
2. 892 – 375 =
3. 638 + 176 =
4. 709 – 344 =
Addition and subtraction are inverse operations
Addition and subtraction are inverse operations. This means:
what you do with subtraction you can undo with addition, e.g.
10 – 3 = 7 can be undone by saying 7 + 3 = 10
what you do with addition you can undo with subtraction, e.g.
7 + 3 = 10 can be undone by saying 10 – 3 = 7.
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15
Exercise 2
Estimating and checking
Look at the following sums:
1. 548 + 154
2. 707 – 313
3. 485 + 37
4. 628 – 333
a) Estimate the answers by rounding off the numbers to the nearest 10.
b) Calculate the answers.
c) Calculate the difference between your estimates and the actual
answers.
d) Check the answers by using the inverse operations.
Check what you know
1. Break down the following numbers. Use the place value of their digits.
a) 298
b) 349
d) 444
e) 1 010
c) 1 093
2. Now write the numbers in Question 1 a) to e) in words.
3. Complete.
a) 385 + 113 = (300 +
+ 5) + (
+ 10 + 3)
= (300 + 100) + (80 +
) + (5 +
)
= 400 +
+
=
b) 687 – 253 = (600 + 80 +
) – (
+ 50 + 3)
(7 –
) ¤ calculate the 1s
(
– 50) ¤ calculate the 10s
(600 –
) ¤ calculate the 100s
= 400 +
+ 4
=
c) 486 + 378 = (
+ 80 + 6) + (300 +
+ 8)
= (400 +
) + (80 +
) + (6 + 8)
= 700 + (
+ 50) + (10 +
)
=
16
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4. Use the digits 1, 2, 3, 4 and 5. Make the biggest number that you can.
5. Copy and complete.
b)
a)
6. Copy and complete.
+
546
47
101
581
73
729
764
801
179
7. Estimate the answers to the following:
a) 677 + 118
b) 815 – 428
c) 888 + 222
d) 709 – 556
8. Now calculate the answers to Question 7 a) to d). Use any method.
9. Calculate the difference between your estimations in Question 7 and your
answers in Question 8.
10. Calculate.
a) 457 – 84 =
b) 558 – 237 =
c) 600 – 438 =
11. Check your answers to Question 10 a) to c). Use the inverse operation.
Word bank
a b
estimate:
round off:
inverse operation:
difference:
c
do a rough calculation
change a number to the nearest 10, 100 or 1 000
the opposite or reverse of an operation
the difference between two numbers (subtraction)
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17
Term
1
Unit 3 Number patterns
In this unit you will:
use input values, output values and rules to complete flow diagrams and
tables
look for relationships or rules to describe and extend number patterns
create your own number patterns using a rule or relationship between the
numbers
use flow diagrams to learn more about:
{ relationships between multiplication and division
{ multiples of 10
{ rules of multiplication that make calculations easier.
Getting started
Number patterns
We can use tables to work out number patterns.
1. Theunis rides 5 km on his bicycle each day. How many kilometres does he
ride in seven days?
You can work this out using a table. In one day, Theunis rides 5 km. So, in
two days he will ride 10 km. We can continue with this pattern to find out how
many kilometres Theunis rides in seven days. Copy and complete the table.
Days
Distance in km
1
5
2
10
3
4
5
6
7
Input numbers and output numbers
In the table, the days are the input numbers. The kilometres are the output
numbers.
2. We use the rule (× 4) in this flow diagram. The first input number is 1.
The first output number is 4 because 1 × 4 = 4. The second input number
is 2. The second output number is 8 because 2 × 4 = 8. Copy and complete
the flow diagram.
1
2
input
3
4
rule
×4
4
5
18
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8
12
output
Activity 1
Input and output
Thabang wants to buy a new bicycle. He does odd jobs on weekends. He manages
to save R25 each week.
1. How much will Thabang save in four weeks?
2. Thabang uses a table. He wants to see how many weeks it will take him to save
enough money to buy the bicycle. Copy and complete Thabang’s table.
Weeks
Savings (R)
2
50
4
6
8
10
12
14
16
18
3. The bicycle costs R399. How many weeks will Thabang need to save
enough money?
4. Thabang brings home a good report from school. His father gives him R50.
How many weeks will Thabang now need to save?
Activity 2
Flow diagrams
1. Nicole is asked by her teacher to help prepare paint for the art lesson. The
powder paint is mixed with water to create a paste. Nicole needs to mix one
spoonful of water with three spoonfuls of paint to make the paste. Nicole draws
the following flow diagram to help her remember.
water
1
3
2
6
3
9
paint
4
5
Nicole looks at her flow diagram. Nicole can see that if she puts two spoonfuls
of water into the mixing bowl, she needs to add six spoonfuls of paint. Nicole
can also see that if she uses three spoonfuls of water, she needs to add nine
spoonfuls of paint.
a) Copy and complete the flow diagram.
b) Nicole notices that the numbers on the paint side of the flow diagram form
the three times table. The numbers are all multiples of 3. What rule do we
use to get the numbers on the paint side from the numbers on the water
side? Write the answer in the box in the middle of the flow diagram.
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19
c) Nicole uses 10 spoonfuls of water. How many spoonfuls of paint does she
need to use?
2. Copy and complete the following flow diagram:
1
5
rule
3
input
×5
5
25
output
8
10
3. Draw a flow diagram with input numbers. Draw your own rule in the box in the
middle of the diagram. Ask a friend to fill in the output numbers. Use only single
digit numbers for your rule and your input numbers.
Exercise 1
Finding output numbers
1. Copy and complete the following flow diagrams:
2
input
3
2
4
1
a)
b)
rule
input
output
×4
d)
3
input 10
15
22
÷2
output
10
5
7
6
8
4
c)
4
1
rule
rule
7
12
output
+5
20
13
input 17
rule
–5
12 output
11
22
2. Siphiwe gets R6 from her father every week for washing dishes on a
Sunday. Siphiwe’s father puts the money into her savings account. Draw
a flow diagram. Help Siphiwe to see how much money she can earn in
seven weeks.
3. Create flow diagrams with the following rules (choose your own input
numbers):
a) (+ 7)
b) (× 11)
c) (– 8)
20
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Activity 3
Flow diagrams that work together
1. a) Copy and complete the following flow diagrams:
5
1
3
input
5
rule
15
×5
input 25
output
10
50
15
75
rule
÷5
output
b) Use the flow diagrams. Complete the following number sentences:
5 × 5 =
and
÷ 5 = 5
15 × 5 =
and
÷ 5 = 15
c) Complete the sentences:
i)
If I multiply a number by 5 and then take the answer and divide it by 5, I
end up with _______.
ii) I can check that I divided by 5 correctly by _________.
Key ideas
Use multiplication to find the input numbers for a division flow diagram.
Use multiplication to check that the output numbers to a division flow diagram
are correct.
2. Look at the following flow diagram. It has some of the input numbers missing.
a) Copy and complete the flow diagram.
6
12
rule
÷6
input
4
output
18
b) How did you find the missing input numbers?
c) Write a number sentence. It uses 12 as the input. The rule is (÷ 6).
d) Write a number sentence. It has 4 as the output. The rule is (÷ 6).
e) The rule from input to output is (÷ 6). When you move from output to input,
does the rule stay the same? Explain.
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21
3. Look at the following flow diagram. It uses two rules with different operations.
a) Copy and complete the flow diagram.
1
5
rule
3
×3
input
+2
17
output
10
20
b) How did you find the missing input number?
c) Use the same method you used in b). Check the rest of your
output numbers.
d) Complete the number sentences for each input and output number.
1×3+2=
3×3+2=
× 3 + 2 = 17
10 × 3 + 2 =
20 × 3 + 2 =
Activity 4
Combining rules
1. a) Complete this table.
The rule is (× 10)
Input
Output
1
10
2
20
3
30
4
40
5
7
b) Multiply the input number by 10. What happens to it?
2. a) Copy and complete the following flow diagrams:
1
30
rule
2
input
3
× 3
5
10
22
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× 10
output
10
15
150
50
30
1
2
input
3
rule
output
× 30
5
10
b) What do you notice about these two flow diagrams?
c) The first flow diagram shows a quick way to multiply numbers by 30.
Explain why.
d) Draw another flow diagram. Use two multiplication rules. Show a quick way
to multiply numbers by 50.
3. a) Copy and complete the following flow diagrams:
2
16
rule
5
input
3
× 4
× 2
output
10
15
2
16
rule
5
input
3
× 2
× 4
output
10
15
b) What do you notice about the outputs of these two flow diagrams?
c) Complete.
If 2 × (4 × 2) = 2 × (2 × 4) then 5 × (4 × 2) =
× (
× 4)
d) Write similar number sentences. Use the two flow diagrams. Use the input
numbers 3, 10 and 15.
e) Look at these flow diagrams. What can you say about the order of
multiplication of numbers?
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23
Check what you know
1. Copy and complete the following tables:
a) The rule is (× 7):
Input
Output
1
7
2
14
3
4
5
7
10
11
15
2
12
3
4
5
7
9
10
12
6
2
9
12
15
24
30
39
45
b) The rule is (× 6):
Input
Output
1
6
c) The rule is (÷ 3):
Input
Output
3
1
2. Create a table. Use the rule (× 5).
Use the following inputs: 1; 2; 3; 4; 5; 9; 10; 13; 15 and 19. Complete the
outputs for this table.
3. Copy and complete the following flow diagrams. For c), fill in the missing rule.
a)
9
1
3
input
5
rule
×9
45 output
8
10
b)
1
3
input
5
rule
9
output
+6
8
14
10
c)
2
4
10
input
rule
output
6
18
9
24
4. Create your own flow diagram. Use subtraction in your rule. Make sure your
outputs are single-digit numbers.
24
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5. Copy the following tables. Fill in the missing rules. Complete the tables.
a) The rule is ________
Input
Output
5
1
10
2
15
3
30
6
40
8
45
9
50
10
65
13
80
16
3
30
5
50
9
10
13
19
25
3
4
44
5
6
8
9
99
10
110
b) The rule is ________
Input
Output
1
10
2
20
c) The rule is ________
Input
Output
1
11
2
22
6. Copy and complete the following flow diagrams:
a)
6
12
input
rule
+6
8
output
18
15
b)
3
10
rule
× 9
input
45
output
12
72
c)
1
10
rule
3
× 5
input
+5
30
output
10
20
d)
1
11
rule
3
×4
input
19
31 output
10
20
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25
Word bank
a b
input:
output:
rule:
ow diagram:
26
IZgb& Jc^i(
c
the number to which you apply a rule and that will
decide what the answer or output will be
the number you get after you have applied a rule to
the input number
an instruction that has one or more operations
(+, –, × or ÷) that you need to do on an input
number
a diagram that gives a rule used on input numbers
to make output numbers
Term
1
Unit 4 Whole number
multiplication and
division
In this unit you will:
use skip counting and repeated addition to find the patterns in multiplication
tables
multiply 1-digit numbers by numbers up to 10
practise and extend multiplication tables
use tables and flow diagrams for multiplication
multiply numbers in any order to get the same answer
solve problems using sharing and grouping.
Activity 1
Skip counting and repeated addition
1. a) Count in 4s. Complete this counting pattern.
4; 8; 12;
;
;
;
;
; 36; 40
b) Use the counting pattern. Complete the following:
1×4=4
2×4=8
3 × 4 = 12
4×4=
5×4=
6×4=
7×4=
8×4=
9×4=
10 × 4 =
c) Count in 4s. Complete this counting pattern.
40; 44; 48;
;
;
;
;
;
;
;
d) Use the counting pattern. Complete the following:
11 × 4 =
14 × 4 =
19 × 4 =
20 × 4 =
17 × 4 =
2. a) Count in 5s. Complete this counting pattern.
5; 10; 15;
;
;
;
;
;
;
b) Use the counting pattern. Complete the following:
1×5=5
2 × 5 = 10
3×5=
4×5=
5×5=
6×5=
7×5=
8×5=
9×5=
10 × 5 =
IZgb& Jc^i)
27
c) Count in 5s. Complete this counting pattern.
50; 55; 60;
;
;
;
;
;
;
;
d) Use the counting pattern. Complete the following:
12 × 5 =
15 × 5 =
18 × 5 =
20 × 5 =
16 × 5 =
3. a) Copy and complete the following:
7+7=
7×2=
7+7+7=
7×3=
7+7+7+7=
7×4=
7+7+7+7+7=
7×5=
7+7+7+7+7+7=
7×6=
7+7+7+7+7+7+7=
7×7=
7+7+7+7+7+7+7+7=
7×8=
7+7+7+7+7+7+7+7+7=
7×9=
7+7+7+7+7+7+7+7+7+7=
7 × 10 =
b) Copy and complete the same pattern as in Question 3 a). Use 6 this time.
Start with 6 + 6 = 12 and 6 × 2 = 12.
c) Copy and complete the same pattern as in Question 3 a). Use 8 this time.
Start with 8 + 8 = 16 and 8 × 2 = 16.
Activity 2
Using tables for multiplication
1. Copy and complete the following tables:
a) The rule is (× 2).
Input
Output
1
2
2
4
3
4
5
10
15
20
50
2
6
3
4
5
10
15
20
50
2
18
3
4
5
10
15
20
50
b) The rule is (× 3).
Input
Output
1
3
c) The rule is (× 9).
Input
Output
28
1
9
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d) The rule is (× 10).
Input
Output
1
10
2
20
3
4
5
10
15
20
50
2. a) Look at the inputs of 10 and of 20 in each table. What do you notice about
the output numbers each time?
b) The rule is (× 6). What will the output be for 10 and for 20?
c) The rule is (× 8). What will the output be for 10 and for 20?
Activity 3
Multiplying with rows and columns
1. a) Place 24 counters in rows and columns in a rectangle pattern.
b) Write a number sentence about your pattern of counters.
c) Compare your pattern with a friend’s pattern.
2. Use 24 counters. Show the following:
a) 4 groups of 6 counters is 24 so 4 × 6 = 24.
b) 2 rows of 12 counters is 24 so
×
= 24.
c) 8 rows of 3 counters is 24 so
×
= 24.
3. Zenobia and Angelina made these patterns with triangles.
How are Zenobia’s and Angelina’s patterns the same? How are these
patterns different?
IZgb& Jc^i)
29
If you turn Zenobia’s pattern around you get Angelina’s pattern.
If you turn Angelina’s pattern around you get Zenobia’s pattern.
We can see that 4 × 6 = 24 and 6 × 4 = 24, so 4 × 6 = 6 × 4.
4. a) Use 36 counters in rows and columns. Arrange them to show as
many different patterns as you can. Write down number sentences for
each pattern.
b) Does it matter what order you use to multiply two numbers? Explain.
Key ideas
You can multiply two numbers in any order and get the same answer.
For example, 4 × 6 = 6 × 4 = 24.
30
IZgb& Jc^i)
Activity 4
Finding easy ways to multiply
1. Copy and complete.
2×1=2
double 2 × 1 is 4
¤
4×1=4
2×2=4
double 2 × 2 is 8
¤
4×2=8
2×3=6
double 2 × 3 is
¤
4×3=
2×4=8
double 2 × 4 is
¤
4×4=
2 × 5 = 10
double 2 × 5 is
¤
4×5=
Continue this pattern up to 4 × 10 = 40.
2. Use doubling of the (4 ×) table. Work out the (8 ×) table. Here is the first one:
4×1=4
double 4 × 1 is 8
¤
8×1=8
3. Copy and complete.
3×2=6
double 3 × 2 is 12
¤
6 × 2 = 12
3×3=9
double 3 × 3 is 18
¤
6 × 3 = 18
3×4=
double 3 × 4 is
¤
6×4=
3 × 5 = 15
double 3 × 5 is
¤
6×5=
Continue this pattern up to 6 × 10 = 60.
Exercise 1
Multiplying
1. Copy and complete the following table by multiplying. Use doubling where
you can.
×
2
4
8
3
6
5
10
2. Copy and complete the following tables:
a) The rule is (× 5).
Input
Output
1
5
2
10
3
4
5
10
15
20
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50
31
b) The rule is (× 8).
Input
Output
1
8
2
16
3
4
5
10
15
20
50
3. Use 30 counters. Show the following:
a) 6 groups of 5 counters is
so 6 ×
=
.
b) 5 groups of 6 counters is
so 5 ×
=
.
c) 3 rows of
counters is 30 so
×
=
.
d)
rows of 3 counters is
so
×
= 30.
4. Work out the following. Use any quick way.
a) 4 × 6 =
b) 4 × 3 =
c) 6 × 9 =
d) 8 × 4 =
e) 8 × 8 =
f) 8 × 5 =
g) 3 × 6 =
h) 4 × 9 =
i)
4×7=
6×5=
k) 8 × 3 =
l)
8×9=
m) 6 × 6 =
n) 4 × 3 =
o) 6 × 7 =
p) 3 × 4 =
q) 8 × 6 =
r) 8 × 2 =
j)
Activity 5
Ten times and five times
1. Complete the following:
a) 6 × 10 =
b) 9 × 10 =
c) 2 × 10 =
d) 16 × 10 =
e) 19 × 10 =
f) 22 × 10 =
2. You multiply a number by 10. What happens to it?
3. Connie says:
I multiply a number by 10. I just put a zero
on the end of the number.
So 8 × 10 = 80 and 18 × 10 = 180.
Do you agree with Connie? Show why she is right or wrong. Give examples.
4. Complete the following:
a) 6 × 5 =
b) 9 × 5 =
c) 2 × 5 =
d) 16 × 5 =
e) 19 × 5 =
f) 22 × 5 =
32
IZgb& Jc^i)
5. Shollay says:
When I multiply a number by 5, I first multiply by 10.
Then halve my answer or divide by 2.
So 12 × 5 = (12 × 10) ÷ 2
= 120 ÷ 2
= 60
What do you know about multiplying by 10 and multiplying by 5?
Key ideas
When you multiply a whole number by 10, you put a zero at the end of the
number.
For example: 4 × 10 = 40
40 × 10 = 400
45 × 10 = 450
400 × 10 = 4 000
Five is half of 10. So here is an easy way to multiply by 5. First multiply
by 10. Then halve your answer.
For example, find 9 × 5. Say to yourself: ‘Half of (9 × 10) is half of 90.
So that is 45.’
Exercise 2
Fives and tens
1. Complete the following:
a) 14 × 10 =
d)
× 10 = 310
b) 27 × 10 =
e)
c) 211 × 10 =
× 10 = 980
2. Complete the following:
a) 13 × 10 =
half of 130 =
13 × 5 =
b) 20 × 10 =
half of 200 =
20 × 5 =
c) 48 × 10 =
half of 480 =
48 × 5 =
d) 37 × 10 =
half of 370 =
37 × 5 =
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33
3. Complete the following:
a) 21 × 10 =
21 × 5 =
b) 140 × 10 =
140 × 5 =
c) 356 × 10 =
356 × 5 =
4. Complete the following:
a) 43 × 5 =
b) 84 × 5 =
c) 65 × 5 =
d) 17 × 5 =
Activity 6 Problem solving
1. There are seven players in a netball team. How many players are there in nine
netball teams?
a) Complete:
×
=
b) Copy and complete the flow diagram. It shows the relationship between the
number of netball teams and the number of players.
2
3
input
5
rule
×
8
9
34
IZgb& Jc^i)
output
2. Ma Gocini bought five cool drinks for R3 each. How much did she pay for
them altogether?
3. There are six eggs in a box.
a) How many eggs are there in seven boxes?
b) Write a number sentence to show your working.
4. Look at the prices of the cool drinks and the boxes of eggs:
Number of items
1
Cost of cool drinks
R3
Cost of boxes of
eggs
R6
2
3
R9
R12
4
5
10
R30
R60
15
20
50
R60
R300
a) Copy and complete the table.
b) You want to work out the cost of eggs. How can you use the cost of cool
drinks to help you?
IZgb& Jc^i)
35
Check what you know
1. Copy and complete the following multiplication table:
×
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
2. Complete the following tables. Use the table in Question 1 to help you:
a) The rule is (× 7).
Input
Output
1
7
2
14
3
4
5
10
15
20
50
2
10
3
4
5
10
15
20
50
2
16
3
4
5
10
15
20
50
b) The rule is (× 5).
Input
Output
1
5
c) The rule is (× 8).
Input
Output
1
8
3. Copy and complete the following flow diagrams:
2
a)
12
rule
3
input
5
10
15
36
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output
×2
60
b)
9
2
rule
3
input
output
× 3
5
10
90
15
4. Create tables that use one operation or rule to get the same output as in the
flow diagrams for Questions 3 a) and 3 b). Use the tables that follow.
a) The rule is × 6
Input
Output
2
3
5
10
15
3
5
10
15
b) The rule is × 9
Input
Output
2
5. Complete the following:
a) 2 × 15 =
b) Double 30 =
d) Double 60 =
e) 8 × 15 =
c) 4 × 15 =
6. Complete the following:
a) 2 × 20 =
b) Double 40 =
d) Double 80 =
e) 8 × 20 =
c) 4 × 20 =
7. Complete the following:
a) 6 × 10 =
b) 9 × 10 =
c) 2 × 10 =
d) 16 × 10 =
e) 19 × 10 =
f) 22 × 10 =
a) 6 × 5 =
b) 9 × 5 =
c) 2 × 5 =
d) 16 × 5 =
e) 19 × 5 =
f) 22 × 5 =
8. Complete the following:
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37
Term
1
Unit 5 Telling time
In this unit you will:
read, tell and write time in 12-hour and 24-hour forms
calculate the number of days or weeks between any two dates
calculate time intervals in minutes or hours
learn about an old way of measuring time.
Getting started
12-hour time
We can tell the time using a clock or a watch with a
long hand and a short hand. The numbers 1 to 12
around the clock tell us the hour. The short hand
shows the hour. We count the minutes in 5s around
the clock. The long hand shows the minutes. This is
called an analogue clock.
This clock shows twenty-five past one. If this is
morning time, we write 1:25 a.m.
If this is afternoon time, we write 1:25 p.m.
This clock shows fifteen minutes before four o’clock.
We say ‘quarter to four’.
38
IZgb& Jc^i*
Activity 1
What is the time?
1. Each clock shows a different time. Write down the time, in words, for each
clock. The first one is done for you.
half past six
2. The times shown on clocks 1 to 5 are before 12 o’clock midday (a.m.).
The times shown on clocks 6 to 10 are after midday (p.m.). Each clock shows
a time of an activity in Owen’s daily routine during the school week.
Match the following activities with the times on the clocks. Write them in
analogue time. The shaded activities take place after midday.
IZgb& Jc^i*
39
leave home
eat sandwiches
leave school
do homework
arrive home
7:30 a.m.
arrive at school
wake up
eat breakfast
go to bed
eat supper
24-hour time
Litha works out the times before midday (a.m.) and the times after midday (p.m.) in
digital time. There are 24 hours in the day. Litha starts counting from midnight.
I wake up at 6 o’clock in
the morning. The first six hours
of the new day have passed
already. So the time is 6:00 a.m.
In 24-hour time I can write
06h00 or 06:00.
I usually have
supper at six in the
evening. By this time,
twelve hours plus
another six hours of the
new day have passed.
So the time is 6:00 p.m.
In 24-hour time, the
time is 18h00
or 18:00.
So six o’clock in the morning is 06h00 (or 06:00). Six o’clock in the evening is
18h00 (or 18:00).
40
IZgb& Jc^i*
For the first twelve hours of the day, the digital clock shows the hours as 00; 01; 02
up to 12.
For the second twelve hours of the day, the digital clock shows the hours as 13; 14;
15 up to 23.
One minute before midnight is 23h59. We write midnight as 00h00.
Activity 2
Twenty-four hours in a day
Write the following times in 24-hour time:
1. quarter past nine in the morning
2. 11:45 a.m.
3. 1:30 p.m.
4. 5:45 p.m.
5. seven o’clock in the evening
Exercise 1
Telling the time
1. Copy the clocks. Draw in the long hand and the short hand to show the
correct times.
6:15 a.m.
2:35 p.m.
7:50 p.m.
10:05 a.m.
12:40 a.m.
IZgb& Jc^i*
41
2. Copy the table. Match the times written in words to the digital times. Draw
lines between the matching times.
05:53
08:46
12:16
04:33
02:11
sixteen minutes past twelve
twenty-seven minutes to five
seven minutes to six
eleven minutes past two
fourteen minutes to nine
3. Write the following times in 24-hour time:
a) ten past twelve in the afternoon
b) 8:00 a.m.
c) 3:35 p.m.
d) eleven o’clock in the morning
e) 9:10 p.m.
4. Convert the following 24-hour times to 12-hour times. Say whether the
time is before midday (a.m.) or after midday (p.m.).
a) 16:15
b) 09:30
c) 10:50
d) 19:20
e) 22:00
Activity 3
Passing time
Look at the table that follows. It shows the timetables for Fatima and Michelle for
their afternoon activities.
Days of the week
Monday
Tuesday
Wednesday
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Fatima’s schedule
14:00–15:30:
Drama
15:45–17:45:
Extra Maths classes
14:00–15:30:
Netball
15:45–17:45:
Extra English classes
14:00–15:30:
Girls’ soccer
15:45–17:45:
Extra Maths classes
Michelle’s schedule
13:00–14:00:
Girls’ soccer
15:45–17:45:
Extra Maths classes
13:00–14:00:
Violin lessons
15:45–17:45:
Extra English classes
13:00–14:00:
Tennis
15:45–17:45:
Extra Maths classes
Days of the week
Thursday
Friday
Fatima’s schedule
14:00–15:30:
Tennis
15:45–17:45:
Extra English classes
14:00–15:30:
Swimming
Michelle’s schedule
13:00–14:00:
Art
15:45–17:45:
Extra English classes
14:00–15:30:
Girls’ cricket
1. How long is Fatima’s drama class?
2. How many hours a week does Fatima play sport?
3. How many hours a week does Michelle play sport?
4. How many hours a week do Fatima and Michelle spend in extra Mathematics
classes altogether?
Activity 4
Counting days and weeks
Kevin’s birthday is on 25 August. Kevin’s mother
plans a party with his friends. Kevin hands out
invitations to his friends on Monday, 1 August.
1. a) How many days are there from Monday,
1 August to Kevin’s birthday?
b) What is the date two weeks after 1
August?
c) How long is this in days?
2. Kevin’s birthday party is planned for the first
Saturday after his birthday.
a) On what date is Kevin’s birthday?
b) How many days after his birthday is the
party?
c) Kevin wants to make masks for the party. He needs three days to make
them. By when should Kevin start making the masks?
IZgb& Jc^i*
43
3. Simphiwe is Kevin’s friend. Simphiwe celebrates his birthday two weeks and
one day before Kevin’s birthday.
a) On what date in August does Simphiwe celebrate his birthday?
b) On what day of the week is Simphiwe’s birthday?
c) How many days after Simphiwe’s birthday does Kevin celebrate his
birthday?
4. It will be Simphiwe’s crown birthday. Crown birthday means that the date of
Simphiwe’s birthday is the same number as his age this year. Kevin is turning
11 on his birthday. How many years will Kevin have to wait to celebrate his
crown birthday?
Activity 5
Telling time in the past
People have measured time in many ways over time. They have
used different kinds of sundials, candles, hourglasses, water
clocks and pendulum clocks. Here is an hourglass.
The hourglass uses the flow of sand to measure the flow of time.
The sand in the hourglass takes one hour to fall from the top
glass bulb, through the neck of the hourglass to the bottom bulb
of the hourglass. You can measure the next hour by turning the
hourglass over and starting again.
1
4
3
4
2
4
1
4
3
4
2
4
1
4
3
4
2
4
There are dotted lines on each hourglass. The dotted lines measure the fraction of
the sand that has fallen through to the bottom of the hourglass.
1. a) Which hourglass shows the least amount of time passed in the hour?
b) Which hourglass shows the most time passed in the hour?
44
IZgb& Jc^i*
2. There are 60 minutes in 1 hour. How many minutes have passed:
a) on hourglass C
b) on hourglass B?
3. Hourglass C started measuring the time at 9.00 a.m. What time is shown on
hourglass C?
4. How much time has passed on hourglass A? Why do you say so?
5. You want to measure the length of a full day and night. How many times will
you have to turn the hourglass over?
6. Can you use the hourglass to measure the time it takes you to brush your
teeth? Why do you say so?
Exercise 2
How long does it take?
1. Look at the following calendar. Answer the questions that follow.
April
S
May
M
T
W
T
F
S
S
M
1
2
3
4
5
6
7
8
9
10
11
12
13
5
6
14
15
16
17
18
19
20
12
21
22
23
24
25
26
27
28
29
30
T
W
T
F
S
1
2
3
4
7
8
9
10
11
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
a) How many days are there in April and May altogether?
b) If the date today is 29 April, what was the date three weeks ago?
c) What is the date 12 days after 24 April?
d) Alex is given a project at school on 22 April. He must finish it by 20
May. How many weeks does Alex have to complete the project?
e) Convert your answer in d) into days.
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45
2. The following candles all burn at the same rate. Each candle takes 6
hours to burn out from start to finish.
2 hrs
4 hrs
6 hrs
A
B
C
Each of the candles has been burning for different lengths of time.
a) For how long has candle A been burning?
b) For how long has candle B been burning?
c) After how many minutes will candle C be burnt out?
Check what you know
1. a) Copy the following clocks. Draw in the hands to show the times.
7:30 a.m.
3:45 p.m.
5:20 p.m.
9:15 a.m.
11:55 a.m.
b) Write down the times in order from the earliest time to the latest time.
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2. Buses leave the bus stop every 45 minutes. The first bus leaves at five past
five in the morning (5:05 a.m.). Copy and complete the departure times in
digital time and on the clock faces.
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47
3. Look at the following calendar. Answer the questions.
a) How many days are there from 10 September to 10 October?
b) Convert your answer in a) into weeks and days.
c) Which date is two weeks and 3 days after 19 September? What day of
the week is that date?
d) What day of the week is 15 November?
4. Mathilda has boiled eggs for breakfast each morning.
Mathilda’s mother uses an egg timer to make sure she
boils the eggs for 5 minutes. This is so that Mathilda’s
eggs are just the way she likes them.
The egg timer measures a total of 7 minutes. The egg
timer shows how long it takes to boil eggs.
a) Mathilda’s mother boils Mathilda’s egg for 5 minutes. How does Mathilda
like her eggs cooked?
b) How long does it take to boil a soft-boiled egg?
c) How many seconds do each of the smaller lines on the timer represent?
d) Would you use this timer to measure the time you spend at school each
day? Why?
Word bank
a b
a.m.:
p.m.:
midday:
midnight:
24-hour time:
schedule:
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c
before midday
after midday
12 o’clock in the middle of the day
12 o’clock in the middle of the night
measuring time using 24 hours
a table or a list of times and events
Term
1
Unit 6 Data handling 1
In this unit you will:
collect data using tally marks and tables for recording
draw pictographs to display and interpret data.
Activity 1
Collecting and counting data
Elana wants to find out which sport is the most popular at her school. Elana watches
all the children on the playground. She wants to see which sport they are playing.
Netball
Soccer
Cricket
Tennis
Rugby
Hockey
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49
1. Which sport is played by the most children?
2. Which sport is played by the fewest children?
3. Which sports are played by the same number of children?
4. Were more children playing rugby than cricket?
5. How many more children were playing soccer than tennis?
You had to count the children in each sport to answer the questions. This is easy
to do if there are not too many children, but we need a better way to organise data
when there are too many to count.
Activity 2
Organising data
Elana organised the data. She used a tally table.
She drew this table:
Sport
netball
soccer
cricket
tennis
rugby
hockey
Total
Tally
Number
Can you help Elana?
Make a mark or tally to show one child who likes a sport: /
You make each fifth tally across the four tally marks before it.
So this shows that five children like a sport: / / / /
1. Count the number of children who are playing netball. Complete the tally table.
Do the same for the other sports.
2. Add the tallies for each sport. Complete the last column in the table.
3. Add the numbers in the last column to get a total. Check that the total is the
same as the number of children in the picture.
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Key ideas
Use a tally table to count things. You can count as you go along. You can find
the total when you are finished.
Activity 3
Representing data
A pictograph is a graph that you make up of pictures. Make all the pictures in the
pictograph the same size. This is so that you can compare the columns easily.
1. Elana used the data from the tally table. She made the following pictograph:
Sports played by children
10
9
8
7
6
Number
of
children
5
4
3
2
1
0
netball
soccer
cricket
tennis
rugby
hockey
a) Which sport is played by the most children?
b) Which sport is played by the fewest children?
c) Which sports are being played by the same number of children?
d) Were more children playing rugby or cricket?
e) How many more children were playing soccer than tennis?
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51
2. Is it easier to answer these questions from the picture on page 49, or from
Elana’s pictograph on page 51? Why do you say so?
3. Write a short story. Describe what the most popular and least popular sports at
Elana’s school are.
Activity 4
Lists of information
Here is a list of learners in Khetiwe’s class and their birthdays. Khetiwe guesses
that September has more birthdays than the other months.
Musfika
10 March
Songeza
21 June
Fred
2 August
Miriam
3 October
Imraan
19 September
Janet
15 January
Arnold
11 November
Elana
30 July
Adri
25 December
Thandeka
14 September
Bernard
18 June
1. In which months are there:
a) the most birthdays
b) no birthdays?
2. Did it take you long to answer these questions? Sometimes it is difficult to get
information from a long list like this.
In the next activity, we will look at ways of showing the information that make it
easier to read.
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Activity 5
Pictograph
Khetiwe’s class made a pictograph. They each drew a picture of themselves. They
then placed the pictures in columns to show their birthday months.
Grade 4 birthdays
9
8
7
6
Number
of
learners
5
4
3
2
1
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Months
1. In which month are there:
a) two birthdays
b) three birthdays
c) four birthdays?
2. What is the most common number of birthdays in a month?
This pictograph is useful. You can keep it for a long time. You can read it after many
days.
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53
Dec
Exercise 1
Class pictograph
Work with the other learners in your class. Make a birthday graph. Look at
Khetiwe’s class graph to help you.
1. Draw a picture of yourself. Everyone in the class must use the same
size paper.
2. Make columns for each month on the board or on a large piece of paper.
Make sure there is a space between each column.
3. Stick each learner’s picture in the column showing their birthday month.
4. In which month are the most birthdays?
5. In which month are the least birthdays?
Check what you know
1. Mantse asked 40 children what their favourite colour is. Here are their
answers:
red
blue
yellow
red
green green
orange green
blue
yellow
red
blue
red
red
green
green orange orange red
red
yellow green
red
blue orange
yellow
red
green yellow green
blue
green orange yellow
red
red
blue
green orange yellow
a) Organise this data. Use a tally table.
b) Which colour is the most popular?
c) Which colour is the least popular?
2. Zimkitha makes a pictograph. It shows the weather for each day of the month.
The weather this month
6
5
Number
of
days
4
3
2
1
sunny
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cloudy
rainy
a) What was the weather like for most of the month?
b) On how many days was it rainy?
c) On how many more days was it cloudy than rainy?
d) On how many more days was it sunny than cloudy?
3. Find out which fruit juice each learner in your class likes. Let your
classmates choose between orange, mango, grape, apple and strawberry.
a) Write down this data. It does not have to be in any order.
b) Make a tally table for this data.
c) Copy and complete the following pictograph to show your data:
Favourite fruit juice
9
8
7
6
Number
of
learners
5
4
3
2
1
orange
mango
grape
apple
strawberry
Type of fruit
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55
Word bank
a b
data:
tallies:
tally table:
frequency:
pictograph:
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c
information
marks you use to count data
a table you use to organise data using tallies
the total number of tallies in each row of a
tally table
a graph made of pictures of the same size and
shape, you arrange the pictures in columns or rows
Term
1
Unit 7 Data handling 2
In this unit you will:
draw bar graphs to display and interpret data
read and interpret data shown in bar graphs and pie charts
read and interpret data from stories.
Pictographs and bar graphs
Pictographs are useful. The pictures help you to know what the columns are about.
Sometimes it takes too long to draw a pictograph.
A bar graph is like a picture graph without the pictures. A bar graph has columns
instead.
When you draw a bar graph:
Give your graph a name. This is so that people know what the graph is about.
Explain what the bars or columns in the bar show. You do not have the pictures
to give you clues.
Always show numbers on the left side. This makes it clear how many there are
in each column.
Activity 1
Pictographs and bar graphs
In Unit 6, Activity 5, Khetiwe made a pictograph. It showed the birthdays of all the
children in her class.
Grade 4 birthdays
9
8
7
6
Number
of
learners
5
4
3
2
1
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Months
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57
Gavin is in the same class as Khetiwe. Gavin decides it is much easier to shade
squares on a graph than to draw all the faces for the pictograph.
Gavin’s graph started to look like this:
Grade 4 birthdays
9
8
7
6
Number
of
learners
5
4
3
2
1
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Months
1. Copy Gavin’s graph. Complete it for him.
2. Use your completed graph to answer the following questions:
a) How many birthdays are there in September?
b) How many birthdays are there in October?
c) How many birthdays are there in February?
d) How many more birthdays are there in November than in April?
Activity 2
More bar graphs
Jabu, Modupi and Lucas made bar graphs. They were about the kinds of cars that
passed their houses.
Modupi
5
4
3
3
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sp
am
Kinds of cars
s
Kinds of cars
bu
s
bu
la
ib
u
in
kk
m
ba
bu
s
in
i
kk
m
ba
Kinds of cars
ib
u
0
in
0
kk
0
m
1
nc
or e
ts
ca
r
1
s
1
ie
2
sp bus
or
ts
ca
r
2
ie
2
ie
Number
ca
r
Number
ba
Number
ts
3
4
tru
ck
4
Lucas
5
sp
or
Jabu
5
1. How many cars did each child see?
2. Who saw the most cars?
3. Who saw the most minibuses?
4. Who saw an ambulance?
5. Why do you think the children saw different cars and different numbers?
Collecting information can help you to compare how information is different at
different times and in different places. In this activity the children probably lived in
different places. They could have collected information at different times of the day.
Exercise 1
Your own bar graph
1. Count the number of cars that pass your home in 15 minutes.
a) First make a list of about four to six kinds of cars that you think will
go past.
b) Then make a tally on your list for each kind of car that goes past.
c) Organise your data in a table. Show the kinds and numbers of cars.
d) Make a bar graph. Name your graph. Name each column of the graph.
Number the left side of the graph. Leave spaces between the columns.
e) Write down some questions about the number of cars.
2. Compare your graph with those of some friends. Talk about how your
graphs are the same. Talk about how they are different. Talk about why
your graphs are the same or different.
Activity 3
Data represented in words
Read the story that follows.
The lion’s spring feast
Shumba the lion invited all the animals to the spring feast. Tutwa, the giraffe, was
the first to arrive. Tutwa moved fast. It was easy for her to travel the 15 km from
home. Then Lwobo, the mongoose, who lived only about 1 km away, arrived. Next
Tlou, the elephant, who easily travelled the 6 km in an afternoon, arrived. The
fourth to arrive was Bulume, the ostrich, who travelled about 10 km.
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59
Pela, the dassie, was fifth to arrive. Pela had only about 3 km to travel. The
music was already playing when Humba, the snail, and Lelobo, the chameleon,
arrived. Humba and Lelobo had left three days before, although they lived very
near Lwobo, the mongoose. ‘I know that Ufundu, the tortoise, is still coming. We
all passed him on the way. I never understand why Ufundu takes a week to travel
4 km. But where is Thlware, the python?’ asked Pela, the dassie. ‘I didn’t invite
him,’ roared Shumba. There was a silence. All the animals wondered what Thlware
would do about not being invited to the feast.
1. Who travelled the furthest?
2. Who spent the most time travelling?
3. Which animals travelled the same distance?
4. Copy this table. Use the story to fill in the distances.
Animal
elephant
tortoise
giraffe
dassie
snail
ostrich
mongoose
chameleon
Distance
a) Who travelled 3 km more than Pela, the dassie?
b) Who travelled the shortest distance?
5. If the giraffe travelled 6 km more, how far would she travel in total?
6. Look back at questions 1 to 5. Is it easier to answer them from the table or
the story?
7. Make a bar graph. Show how far the animals travelled. Number the left side of
the graph up to 16 km. Use a column for each animal. Remember to give your
graph a name.
8. Which do you like best: the story, the table, or the graph? Say why.
Key ideas
Using a table or a graph to show written information
60
Use a table to write information in a short way.
You can usually see information better in a table than in a story.
Sometimes you can see the information better in a graph than in a table.
Draw a table first. This helps you to draw a graph.
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Exercise 2
Reading a graph
1. What information does the following graph give you?
Favourite programmes
10
9
8
Number
of
children
7
6
5
4
3
2
1
0
ilie
ak
uz
d
M
s
nd
an
m
Fa
ie
Fr
ur
s
ia
an
M
f
al
rH
ro
or
H
n
ar
Ho
e
to
m
Ti
er
es
pl
Le
g
in
ov
u
Co
L
rn
n
itio
Co
t
pe
m
Co
2. Fill in the missing words:
The programme most children like best is ___ a) ___. The programme
children like second best is ___ b) ___. ___ c) ___ children like Friends
and Families best. Only one child likes ___ d) ___ best. If ___ e) ___
more child had liked Horror Half Hour best, this would have been the
same number as children who liked Friends and Families best. Only
___ f) ___ children liked Competition Corner best.
Activity 4
Pie charts
Look at the pie chart. It shows the favourite subjects
of learners in a Grade 4 class.
1. What fraction of the learners prefers Mathematics?
2. What fraction of the learners prefers Languages?
3. What fraction of the learners prefers Social
Sciences?
Favourite subjects of learners in
a Grade 4 class
Life Skills
Social
Sciences
Mathematics
Languages
4. There are 32 learners in the class.
a) How many learners prefer Mathematics?
b) How many learners prefer Social Sciences?
5. Which two fractions (or slices of the pie chart) together are the same size as the
fraction for learners who prefer Languages?
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61
Key ideas
Can you see that the pie chart on page 61 looks like a pie that somebody
has sliced up?
This is a special graph called a pie chart.
Use a pie chart when you want to see how a whole is divided up into parts.
You can show the parts as fractions.
Activity 5
More about pie charts
How learners travel
to school
The pie chart shows the transport that learners at
Thandeka’s school use to travel to school each
day. There are 480 learners at Thandeka’s school.
1. What is the most common way that learners
travel to school?
train
car
bus
2. How many learners travel by taxi?
walk
3. What fraction of the learners travel by bus?
4. What fraction of the learners travel by car?
taxi
5. How many learners travel by train?
6. Thandeka says that the number of learners
who travel by bus is the same as the number
of learners who travel by car and by train added together. Use the pie chart to
explain why she is right. You do not need to calculate anything.
Exercise 3
Reading a pie chart
Look at the pie chart. It shows the most
popular sandwiches in a Grade 4 class.
Favourite sandwiches in
a Grade 4 class
1. What is the most popular sandwich?
2. Which two sandwiches are the least
popular?
3. There were 40 learners in the class.
How many learners liked peanut butter
sandwiches?
4. How many learners liked polony
sandwiches?
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jam
peanut
butter
polony
cheese
Check what you know
The weather this month
12
11
10
9
8
7
6
5
4
3
2
1
0
1. Bertha draws a bar graph. It shows the
weather for each day of the month.
a) What was the most common
type of weather in that month? Number
b) On how many days was it rainy? of days
c) On how many more days was it
cloudy than rainy?
2. Compare Bertha’s bar graph with Zimkitha’s
sunny
cloudy
rainy
pictograph (Unit 6, Check What you
Type of weather
know, Question 2 on page 54).
a) Do the graphs show the same types of weather?
b) The graphs do not show the same number of days for each type of
weather. Explain why.
c) How do Bertha’s and Zimkitha’s graphs look different from each other?
3. Here is what Tano’s class likes to do on the weekend:
There are 14 children who like to go to parties. Five children like to play
soccer. Three like to watch soccer. Eight like to watch TV. Six like to go
swimming. Five like to visit friends. Ten like to go shopping.
What children like to do
Number of children
a) Copy this table. You need seven empty rows in your table. Use the
information given to complete it.
b) Now make a bar graph. Use the information.
c) Write questions about what the children like to do.
d) Now write a story about the information in the graph.
4. Of all the learners at a school, half have a tap inside their home. A quarter
only have a tap outside in the yard. A quarter do not have a tap in their
home or outside. Draw a pie chart to show this information.
Word bank
bar graph:
pie chart:
a b
c
a graph that uses separate columns to show information
a circle-shaped graph which shows information in ‘slices’
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63
Term
1
Unit 8 Properties of 2-D
shapes
In this unit you will:
sort and compare shapes according to whether they have curved or straight
sides
know and name different closed, straight-sided shapes (polygons) and
circles
sort and compare straight-sided shapes according to the number of sides
they have
draw different 2-D shapes on grid paper
make a design with shapes with no gaps between shapes.
Getting started
Counting shapes
1. Count the circles.
2. Count the triangles.
3. Count the squares.
4. Count the rectangles.
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Activity 1
What is a polygon?
Marlene, John and Thembeka look at the following shapes:
Their teacher asks them to group the shapes in as many ways as they can.
1. Marlene puts the shapes into two groups: open shapes and closed shapes.
She says shapes 3 and 7 are open. The rest are closed. Explain what Marlene
means by ‘open shapes’.
2. John put the ‘closed shapes’ into another two groups. He says shapes 5 and 9
have lines that cross each other. The other closed shapes do not. Explain what
John means by lines that cross each other.
3. Thembeka puts the shapes with ‘no crossing lines’ into three groups. Copy and
complete Thembeka’s table. Use shapes 2, 4, 6, 8 and 10.
Group
Curved sides
Straight and curved sides
Straight sides
Shape number
1
4. Name a shape that is not a polygon.
5. Draw any polygon.
Key ideas
A polygon is a closed shape. It has straight sides that do not cross over each
other. Triangles, squares and rectangles are all examples of polygons.
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