Solutions for all
Mathematics
Grade 5
Learner’s Book
Schools Development Unit
Kaashief Hassan
Toyer Nakidien
Kulsum Omar
Connie Skelton
Solutions for all Mathematics Grade 5 Learner’s Book
© Schools Development Unit 2012
© Illustrations and design Macmillan South Africa (Pty) Ltd, 2012
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted in any form
or by any means, electronic, photocopying, recording,
or otherwise, without the prior written permission of the
copyright holder or in accordance with the provisions
of the Copyright Act, 1978 (as amended).
Any person who commits any unauthorised act in relation to this
publication may be liable for criminal prosecution and
civil claims for damages.
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 Merrick James
Illustrations by Geoff Walton
Photographs by:
AAI: page 159
Gallo Images: page 185
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. The publishers would also
like to thank those organisations and individuals we have already approached
and from whom we are anticipating permission.
e-ISBN: 978 1 4310 2320 2
ISBN: 978 1 4310 0976 3
WIP: 4073M000
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
Whole numbers and number sentences ............................................................
Addition and subtraction of whole numbers.......................................................
Number patterns ................................................................................................
Multiplication and division of whole numbers ....................................................
Time ...................................................................................................................
Data handling 1 .................................................................................................
Data handling 2 .................................................................................................
2-dimensional shapes........................................................................................
Capacity and volume .........................................................................................
Revision .............................................................................................................
1
1
13
21
28
36
45
51
58
67
76
Term 2 .................................................................................................................. 86
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Whole numbers and addition and subtraction ..................................................
Common fractions..............................................................................................
Length ................................................................................................................
Multiplication of whole numbers ........................................................................
Properties of 3-D objects ..................................................................................
Geometric patterns ............................................................................................
Symmetry ..........................................................................................................
Division of whole numbers.................................................................................
More division of whole numbers .......................................................................
Revision .............................................................................................................
86
94
104
114
123
132
140
144
151
158
Term 3 .................................................................................................................. 168
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
Unit 11
Common fractions..............................................................................................
Mass ..................................................................................................................
Whole numbers and addition and subtraction ...................................................
Viewing objects ..................................................................................................
Properties of 2-D shapes ...................................................................................
Transformations .................................................................................................
Temperature ......................................................................................................
Data handling ....................................................................................................
Numeric patterns ...............................................................................................
Multiplication of whole numbers ........................................................................
Revision .............................................................................................................
168
176
183
194
198
205
212
217
228
237
247
Term 4 ........................................................................................................................... 256
Unit 1 Whole numbers and addition and subtraction ..................................................
Unit 2 Properties of 3-D objects ...................................................................................
Unit 3 Common fractions..............................................................................................
Unit 4 Division ..............................................................................................................
Unit 5 Perimeter, area and volume ..............................................................................
Unit 6 Position and movement .....................................................................................
Unit 7 Transformations .................................................................................................
Unit 8 Shape patterns ..................................................................................................
Unit 9 Number sentences ............................................................................................
Unit 10 Probability..........................................................................................................
Unit 11 Revision .............................................................................................................
Mental mathematics ......................................................................................................
256
263
269
276
284
294
298
302
306
310
315
322
Term
1
Unit 1 Whole numbers
and number
sentences
In this unit you will:
•
•
•
•
•
•
•
•
count forwards and backwards in 2s, 3s, 5s, 10s, 25s, 50s and 100s, up to at
least 1 000
count forwards and backwards in 100s up to at least 10 000
order, compare and represent numbers to at least 4-digit numbers
represent odd and even numbers to at least 1 000
recognise the place value of digits in whole numbers to at least 4-digit
numbers
round off to the nearest 5, 10, 100 and 1 000
write number sentences to describe problem situations
solve and complete number sentences by inspection, trial and improvement
and substitution.
Getting started
Counting forwards and backwards
1. Themba collected sticks. Count them. There are 10 sticks in each bundle.
Term 1 • Unit 1
1
2. Count the dots on all the ladybirds. The ladybirds have 5 dots on each wing.
3. Copy and complete the flow diagram.
4. Count backwards in 5s from 478 to 443
478; 473; _____ ; _____ ; _____ ; _____ ; _____ ; 443
5. Copy and complete the following counting patterns.
a) 655; 680; 705; _____ ; _____ ; _____ ; _____
b) 7 809; 7 807; 7 805; 7 803; _____ ; _____ ; _____ ; _____
c) 3 655; 3 705; 3 755; 3 805; _____ ; _____ ; _____ ; _____
d) 8 766; 8 866; 8 966; _____ ; _____ ; _____ ; _____ ; _____
2
Term 1 • Unit 1
Activity 1
Ordering, comparing, representing and
recognising whole numbers
There are:
•
•
•
•
1 352 learners at Thandeswa Primary
922 learners at Sunnyhill Primary
1 025 learners at J.S. Spies Primary
1 253 learners at Turfloop Primary.
1. a) Which school has the most learners?
b) Arrange the number of learners at each school from the least to
the most.
2. Look at the number 5 428.
a) What is the value of the 5?
b) What is value of the 4?
c) Write the number 5 428 in words.
d) Round off 5 428 to the nearest 100.
3. Write the following numbers in words.
a) 3 489
b) 4 805
4. Write the following as numbers:
a) three thousand and fifty
b) seven thousand, six hundred and twenty-nine.
5. Fill in > or < to make the following statements true.
a) 3 829 _____ 3 289
b) 9 238 _____ 9 823
6. Write down the number for 3 tens, 4 hundreds, 5 ones and 2 thousands.
7. Round off 3 282 to the nearest:
a) 100
b) 10
c) 1 000
Term 1 • Unit 1
3
Activity 2
Odds and evens
The Grade 5E class at Marble Arch Primary School designed a pamphlet about odd
and even numbers.
There are two mistakes in the pamphlet. Find them and rewrite the statements
correctly.
The learners forgot to include examples of their statements. Design your own
pamphlet. Copy the correct statements, and add your own examples.
Grade 5E Marble Arch Primary School
Hey, we know our odd and even numbers!
1. The last digit of an even number is 2; 4; 6; 8; or 0.
2. The last digit of an odd number is 1; 3; 5; 7 or 9.
3. An odd number is two more than an even number.
4. The numbers smaller and bigger than an odd number are even.
5. After 2, every second number is odd.
6. If you add two odd numbers, the answer is always even.
Key ideas
Remember that each part of a number is called a digit.
Exercise 1
More odds and evens
1. Copy and compare these even number and odd number addition tables.
+
50
52
54
56
20
22
24
26
28
+
61
63
65
67
2. Are the answers in the tables odd or even?
4
Term 1 • Unit 1
41
43
45
47
49
3. Complete the sentences.
a) When we add two even numbers the answer is _____ .
b) When we add two odd numbers the answer is _____ .
4. What will an odd number added to an even number give? Give your own
example.
5. Copy and complete these sums. Look carefully at the numbers you have
added and at your answers.
a) 2 + 4 + 6 =
b) 24 + 2 + 10 =
c) 36 + 4 + 12 =
d) 1 + 3 + 5 =
e) 9 + 11 + 3 =
f) 13 + 3 + 1 =
6. Do you notice anything interesting? Now write a statement about adding
odd and even numbers.
Activity 3
Inverse operations
1. a) If 38 + 15 =
, then 53 – 15 =
b) If 69 ÷ 3 = 23, then 23 × 3 =
and 53 – 38 =
and 69 ÷ 23 =
, then 32 ÷ 4 =
and 32 ÷ 8 +
.
d) If 6 × 9 = 54, then 54 ÷ 6 =
and 54 ÷ 9 =
.
c) If 4 × 8 =
.
.
2. Use the pattern to complete the number sentences. Do not use long calculations.
a) If 2 345 + 128 = 2 473, then 2 473 –
b) If 3 812 ÷ 4 = 953, then 953 ÷ 4 =
= 128 and 2 473 – 128 =
and 3 812 ÷ 953 =
.
.
3. a) Explain how adding and subtracting work together, no matter what numbers
you use. Write one sentence. Use your own words.
b) Explain how multiplying and dividing work together, no matter what numbers
you use. Write one sentence. Use your own words.
Key ideas
•
•
If we know the sum of two numbers, we can make a subtraction number
sentence as well.
Example: If 3 214 + 455 = 3 669, then 3 669 – 3 214 = 455
and 3 669 – 455 = 3 214.
If we know the subtraction number sentence, we can make an addition
number sentence as well.
Example: If 3 669 – 3 214 = 455, then 3 214 + 455 = 3 669 and
455 + 3 214 = 3 669.
Term 1 • Unit 1
5
Activity 4
Number sentences about problems
1. Write a number sentence and the answer for each of the following problems.
a) Themba lives in Cape Town. He takes 18 hours to drive to Johannesburg.
He takes 7 hours to drive to Port Elizabeth. How many more hours does
Themba take to drive to Johannesburg than to Port Elizabeth?
b) My Maths book has 231 pages. My English book has 318 pages. How
many more pages are there in my English book than in my Maths book?
c) We use 4 eggs to bake a chocolate cake. How many eggs do we need to
bake 6 chocolate cakes?
2. Write number sentences for each of the following.
a) Add 5 to 17. Subtract 5 from your answer.
b) Subtract 22 from 53. Add 22 to your answer.
c) Multiply 4 by 5. Divide your answer by 5.
d) Divide 30 by 6. Multiply your answer by 6.
Activity 5
Patterns in number sentences
Complete the following number sentences. Use the pattern to help you.
1. 3 + 5 = 8
30 + 50 =
300 + 500 =
3 000 + 5 000 =
2. 4 + 7 = 11
40 + 70 =
400 + 700 =
4 000 + 7 000 =
3. 5 + 9 = 14 and 9 + 5 = 14.
15 +
= 24 and
+ 15 = 24.
25 + 9 =
and 9 + 25 =
.
35 + 5 =
and 5 + 35 =
.
4. True or false?
a) 14 – 9 = 5, so 9 – 14 = 5.
b) 237 – 193 = 44, so 193 – 237 = 44.
c) 1 238 + 62 = 1 300, so 62 + 1 238 = 1 300.
5. Copy and complete the sentences:
a) It does not matter what _____ we use to add numbers.
b) The _____ does matter when we subtract numbers.
6
Term 1 • Unit 1
Key ideas
•
•
When we add numbers, we can add in any order.
When we subtract numbers, the order matters.
Activity 6
Properties of 1 and 0
1. Complete the following number sentences.
a) 12 × 1 =
, so 12 ÷ 12 =
.
b) 35 × 1 =
c) 77 ÷ 1 =
, so 77 ÷ 77 =
.
d) 100 ÷ 1 =
, so 35 ÷ 35 =
.
, so 100 ÷ 100 =
.
2. Gerrit works out these examples.
When you add and
subtract the same number, it doesn’t
change the sum. It is like adding zero. When you
multiply and divide by the same number,
it doesn’t change the sum. It is
like multiplying...
15 + 8 – 8 = 15
64 – 28 + 28 = 64
36 x 22 ÷ 22 = 36
47 ÷ 9 × 9 = 47
Copy and complete the sentences.
a) Any number that we multiply or divide by 1 will stay _____ .
b) Any number that we divide by itself is always equal to _____ .
3. Make the number sentences true. Fill in the missing numbers.
a) 3 × 0 = , so ÷ 3 = 0.
c) 55 + 0 = , so – 55 = 0.
b) 5 × = 0, so 0 ÷ 5 = .
d)
+ 100 = 100, so 100 – 100 =
.
4. Copy and complete the sentences.
a)
b)
c)
d)
Any number that we multiply by 0 equals .
0 divided by any number is always equal to .
Any number that we add to 0 will stay _____ .
Any number minus 0 will stay _____ .
Term 1 • Unit 1
7
Activity 7
Associative property of multiplication
and addition
1. Copy and complete the table below:
a)
b)
c)
d)
7×5×3=
2×9×6=
4×8×5=
2×3×5=
7×3×5=
2×6×9=
4×5×8=
2×5×3=
(7 × 5) × 3 =
(2 × 9) × 6 =
(4 × 8) × 5 =
(2 × 3) × 5 =
7 × (5 × 3) =
2 × (9 × 6) =
4 × (8 × 5) =
2 × (3 × 5) =
e) What do you notice about your answers in each of the rows in the
table?
f) Make up three more similar examples (like the ones in the table) to see
if you get the same result.
Key ideas
When we multiply three or more numbers, it does not matter how we group the
numbers. The answer will always be the same.
2. Copy and compete the table below:
a)
b)
c)
d)
7+9+3=
4+8+6=
13 + 5 + 2 =
12 + 9 + 6 =
7+3+9=
4+6+8=
13 + 2 + 5 =
12 + 6 + 9 =
7 + (9 + 3) =
4 + (8 + 6) =
13 + (5 + 2) =
12 + (9 + 6) =
(7 + 9) + 3 =
(4 + 8) + 6 =
(13 + 5) + 2 =
(12 + 9) + 6 =
e) What do you notice about your answers in each of the rows
above?
f) Make up three more similar examples (like the ones in the table) to see
if you get the same result.
8
Term 1 • Unit 1
Key ideas
When we add three or more numbers, it does not matter how we group our
numbers. The answers will always be the same.
3. Copy and complete the table below:
a)
b)
c)
d)
27 – 8 – 4 =
36 – 7 – 5 =
40 – 20 – 10 =
57 – 9 – 6 =
27 – 4 – 8 =
36 – 5 – 7 =
40 – 10 – 20 =
57 – 6 – 9 =
(27 – 8) – 4 =
(36 – 7) – 5 =
(40 – 20) – 10 =
(57 – 9) – 6 =
27 – (8 – 4) =
36 – (7 – 5) =
40 – (20 – 10) =
57 – (9 – 6) =
e) What do you notice about your answers in each of the rows above?
Why do you think this is happening?
f) Use three more of your own examples to see if you get the same type
of results as you found when working with the table.
Key ideas
When we subtract two numbers from a third number, we cannot group the last
two numbers.
4. Copy and complete the table below:
a)
b)
c)
d)
36 ÷ 9 ÷ 2 =
56 ÷ 4 ÷ 7 =
48 ÷ 6 ÷ 2 =
54 ÷ 6 ÷ 3 =
e)
What do you notice about your answers in each of the rows above?
Why do you think this is happening?
f)
Use three more of your own examples to see if you get the same type
of results as you found when working with the table.
36 ÷ 2 ÷ 9 =
56 ÷ 7 ÷ 4 =
48 ÷ 2 ÷ 6 =
54 ÷ 3 ÷ 6 =
(36 ÷ 9) ÷ 2 =
(56 ÷ 4) ÷ 7 =
(48 ÷ 6) ÷ 2 =
(54 ÷ 6) ÷ 3 =
36 ÷ (9 ÷ 2) =
56 ÷ (4 ÷ 7) =
48 ÷ (6 ÷ 2) =
54 ÷ (6 ÷ 3) =
Term 1 • Unit 1
9
Key ideas
When we calculate a division number-sentence that has three or more numbers,
we can only group the first two numbers. We cannot group the last two
numbers.
Exercise 2
1. Copy and complete the number sentences.
a) 3 523 = 3000 +
b) 83 428 =
+
+3
+ 3000 +
+ 20 +
c) 200 + 50 + 1000 + 5 =
2. Arrange these numbers from biggest to smallest.
7 231
2 371
3 271
7 321
2 713
3. Copy and complete the number sentences.
a) 234 ÷ 234 =
b) 257 × 0 =
c) 1 × 770 =
d) If 837 ÷ 3 = 279, then 279 × 3 =
and 837 ÷
e) If 738 + 199 = 937, then 199 + 738 =
= 3.
.
4. a) Copy and complete the flow diagram.
b) Complete the instructions for this flow diagram.
Add
to 50. Halve your answer. _____ 9.
Now _____ your answer by
.
c) Complete the number sentences. Use your flow chart.
÷2= ¤
–9= ¤
×3=
50 + = ¤
10
Term 1 • Unit 1
Check what you know
1. Copy and complete the following number sequences.
a) 39; 42; 45; _____ ; _____ ; _____ ; _____
b) 377; 372; 367; _____ ; _____ ; _____ ; _____
2. For each number, write if it is even or odd.
a) 2 331
b) 5 328
c) 7 779
d) 328
e) 121
f) 775
g) 1 354
h) 9 756
i)
999
3. Complete the following sentences.
a) 31 + 53 = . When we add two odd numbers, is the answer odd or
even? Explain why.
b) 32 + 54 = . When we add two even numbers, is the answer odd or
even? Explain why.
c) 31 + 54 = . When we add an odd number to an even number, is the
answer odd or even? Explain why.
4. Use the digits 7, 1, 8 and 4 for the following.
a) Make as many odd numbers as you can. Use up to 4 digits in a number.
b) What is the largest number that you can make?
c) Make as many even numbers as you can. Use up to 4 digits in
a number.
5. Count backwards in 50s from 3 238 to 2 988. Write down the numbers.
6. What is the value of 9 in each of the following numbers?
a) 3 928
b) 9 238
c) 2 389
d) 8 392
7. Arrange the following numbers from smallest to biggest.
9 238 3 298 3 928 3 289
8. What number is:
a) 2 more than 999?
b) 50 less than 1 380?
9. What number is represented by 5 tens, 3 thousands, 2 hundreds and
6 ones?
10. Which is less:
a) 5 tens or 4 hundreds?
b) 3 thousands or 4 hundreds?
Term 1 • Unit 1
11
11. Complete the following number sentences.
If 7 + 8 = 15 then 70 +
= 150 and 700 +
= 1 500.
12. Copy and complete:
a) 57 + 83 = 83 +
b) 62 – 57 = 62 – 50 –
+7
c) 532 + 77 = 532 +
d) 99 × 5 = (100 × 5) – (
× 5)
e) 184 + 182 = double 182 +
Word bank
a b
even number:
odd number:
number sentence:
flow diagram:
12
Term 1 • Unit 1
c
a number that you can divide by 2 without a
remainder. Even numbers end with 0, 2, 4, 6 or 8
a number that has a remainder of 1 when you
divide by 2. Odd numbers end with 1, 3, 5, 7 or 9
a number sentence that uses numbers and
symbols
a diagram that shows input values and output
values in a number sentence
Term
1
Unit 2 Addition and
subtraction of
whole numbers
In this unit you will:
•
•
•
•
•
add and subtract numbers up to 4 digits using different strategies
estimate answers by rounding off numbers to the nearest 10 or 100
check solutions
judge the reasonableness of solutions
solve problems involving whole numbers.
Getting started Tens, hundreds and thousands
Remember that: 10
100
1 000
=
=
=
1 ten
1 hundred
1 thousand
=
=
=
10 ones
10 tens
10 hundreds
1. Copy and complete.
a) 33 tens =
hundreds +
b) 28 hundreds =
tens = 330
thousands +
hundreds =
c) 76 tens = 7 _____ + 6 _____ =
2. Copy and complete the table.
a)
b)
c)
d)
2 934
75
506
9 013
5 132
Thousands
2
Hundreds
9
Tens
3
Ones
4
Term 1 • Unit 2
13
Key ideas
•
You can break down a number into its place value parts.
Example: 4 503 is made up of 4 thousands, 5 hundreds and 3 ones.
4 503 = 4 000 + 500 + 3
Each part of a number is called a digit.
Example: the digits of 4 503 are 4, 5, 0 and 3.
•
Activity 1
Breaking down numbers to add and subtract
1. Gertrude Mayisela sold 1 646 cooldrinks before a Soccer World Cup match
at the Moses Mabhida Stadium in 2010. After the match, soccer fans bought
1 227 more cooldrinks from Ms Mayisela. How many cooldrinks did she sell
altogether?
2. Compare the way you solved your problem with the way Siyabonga and
Nomfundo solved theirs.
Siyabonga
This is easy. I learnt how to do this last year.
First I split the numbers into parts.
1 646 = 1 000 + 600 + 40 + 6
1 227 = 1 000 + 200 + 20 + 7
Then I added like this.
First I added the 1 000s
1 000 + 1 000 = 2 000
Then the 100s
600 + 200 = 800
Then the 10s
40 + 20 = 60
And then the ones
6 + 7 = 13
Then I put it all back together again 2 000 + 800 + 60 + 13 = 2 000 + 800 + 70 + 3
= 2 873
14
Term 1 • Unit 2
Nomfundo
I broke up the numbers into parts.
I then wrote the parts underneath each other.
1 646
=
1 000 + 600 + 40 + 6
1 227
=
1 000 + 200 + 20 + 7
2 000 + 800 + 60 + 13
Then I split up the answer into parts again.
2 000 + 800 + 60 + 10 + 3 =
2 000 + 800 + 70 + 3 = 2 873
3. Add 2 834 + 3 157. Break both numbers into parts.
4. Calculate 1 874 + 6 987. Break both numbers into parts.
5. Check that 2 873 is the correct answer to 1 646 + 1 227. Use subtraction.
6. Compare the way you solved your problem with the way Mpho and
Neo solved theirs.
Mpho and Neo use subtraction and work out 2 873 – 1 227 =
.
Mpho
First I broke up the numbers into their parts.
2 873 = 2 000 + 800 + 70 + 3
1 227 = 1 000 + 200 + 20 + 7
First I subtracted the thousands.
2 000 – 1 000 = 1 000
Then the hundreds.
800 – 200 = 600
Then the tens.
70 – 20 = 50
And then the ones. But 7 is more than 3.
3–7
So I joined the tens and ones again.
53 – 7 = 46
I added to get my answer.
1 000 + 600 + 46 = 1 646
My way shows that 2 873 – 1 227 = 1 646.
Term 1 • Unit 2
15
Neo
First I split the numbers into their parts. Then I wrote the parts underneath
each other.
2 873 = 2 000 + 800 + 70 + 3
1 227 = 1 000 + 200 + 20 + 7
Then I subtracted the parts.
When I try to subtract 7 from 3, I see that 3 is less than 7.
So I take 1 ten from the tens column. 2 000 + 800 + 60 + 13
This leaves 60 in the tens column and 10 + 3 in the ones column.
2 000 + 800 + 60 + 13
Then I subtract it all.
– 1 000 + 200 + 20 + 7
1 000 + 600 + 40 + 6 = 1 646
My way shows that 2 873 – 1 227 = 1 646. So, Siyabonga and Nomfundo did their
addition sums correctly.
7. Calculate the following:
a) 6 974 – 5 361 =
b) 9 487 – 6 517 =
c) 3 875 – 1 543 =
8. Check your answers in Question 7. Use addition.
Key ideas
•
When you add or subtract large numbers, first break down the numbers into
their place value parts.
Use subtraction to check your addition. Use addition to check your
subtraction.
•
Activity 2
Filling up tens and hundreds to add
1. Add or subtract to get to the closest hundred. Work quickly to find answers.
a) 387 +
= 400
b) 429 –
= 400
c) 768 +
= 800
d) 837 –
= 800
16
Term 1 • Unit 2
2. Calculate 387 + 137 =
. Use your answer to Question 1 a).
3. Look at how Musa worked this out.
387 + 13 = 400. So I can add 13 to 387 to get 400. I will have to subtract 13 again
from 137 to keep the sum the same.
387 + 13 + 137 – 13
= 400 + 124
= 524
Calculate the following. Use Musa’s method.
a) 712 + 579 =
b) 5 362 + 1 998 =
c) 7 522 + 796 =
Activity 3
Using making up to subtract
What happens if you need to subtract a number like 792 from 2 974?
Look at what Ntsako does.
2 974 – 792 = (2 000 + 900 + 70 + 4) – 700 – 90 – 2
= 2 000 + 900 – 700 + 70 – 90 + 4 – 2
But I cannot subtract 90 from 70!
So I will make up for this by breaking down 2 974 to 2 000 + 800 + 170 + 4
2 974 – 792 = (2 000 + 800 + 170 + 4) – 700 – 90 – 2
= 2 000 + 800 – 700 + 170 – 90 + 4 – 2
= 2 000 + 100 + 80 + 2
= 2 182
Use Ntsako’s method to subtract.
1. 5 392 – 3 480
2. 7 216 – 6 300
3. 4 306 – 3 290
4. 9 021 – 8 903
Term 1 • Unit 2
17
Exercise 1
Adding and subtracting
1. Complete the number pyramids.
a)
b)
2. The Ndzumeka family keeps a record of how far they have cycled.
Albert:
2 316 m
Sikumbuzo:
3 472 m
Mathinzi:
5 329 m
a) Who cycled the furthest distance?
b) Who cycled the shortest distance?
c) How many metres did the Ndzumeka family cycle altogether?
Activity 4
Using number sentences to solve problems
Write number sentences. Answer the following questions.
1. Four candidates stood for election as ward councillor during the South African
elections. The following results were recorded after the votes were counted:
Candidate A: 2 381 votes
Candidate B: 1 976 votes
Candidate C: 5 424 votes
Candidate D: 4 702 votes
a) Which candidate won the election in this area?
b) Which candidate got the least votes?
c) How many people voted in this area?
d) Only half of the potential voters actually voted. How many voters live in this
area?
18
Term 1 • Unit 2
2. The sum of two numbers is 7 351. One number is 1 489. What is the other
number?
3.
Nomsa has made a beautiful mat using
2 876 yellow beads, 1 425 blue beads and
976 green beads. How many beads did
Nomsa use in her mat altogether?
Check what you know
1. Copy and complete the following. You will need at least two steps of
working out.
a) 8 000 + 3 000 + 200 + 900 + 10 + 7 + 5 =
+
+
+
=
b) 72 tens + 15 hundreds =
2. Do the following sums. Use any method. Show all your working out.
a) 5 917 + 3 574
b) 9 576 – 2 897
c) 4 962 + 2 307
d) 8 013 – 5 467
3.
a) Samuel helped his mother to carry her three packets of shopping home.
How many grams did Samuel carry altogether?
b) Samuel’s mother’s shopping costs R154. She paid with a R200 note.
How much change did Samuel’s mother get?
Term 1 • Unit 2
19
Word bank
a b
difference:
sum:
number pyramids:
20
Term 1 • Unit 2
c
the amount left after you subtract one number from
another number
the amount after you add two or more numbers
together
numbers arranged so that each brick is the sum of
the two numbers below it
Term
1
Unit 3 Number patterns
In this unit you will:
•
•
•
complete given number patterns and find the rule
find the input values, output values and rules for patterns using flow
diagrams
work out the relationship between different rules used in flow diagrams.
Getting started
Input and output values in flow diagrams
1. Copy and complete the following number patterns.
a) 7; 14; 21; _____ ; _____ ; _____ ; _____
b) 10; 20; 30; _____ ; _____ ; _____ ; _____
c) 8; 16; 24; 32; _____ ; _____ ; _____ ; _____
2. What is the rule for each number pattern in Question 1?
3. a) Copy and complete the following flow diagram.
2
rule
4
input
×3
–1
output
7
9
b) Complete this sentence to describe the flow diagram.
and then subtract
I take each input value and multiply by
gives me the _____ value.
. That
c) Write a number sentence to show the flow diagram when the input is 2.
d) Write a number sentence to show the flow diagram for any input value.
Use empty blocks to show the input and output values.
4. Work out the input values. Complete the flow diagram. Write each answer as
a number sentence.
a
3
rule
b
×4
input
6
–2
output
c
7
d
10
Term 1 • Unit 3
21
5. a) Work out the rule for the following flow diagram.
b) Find the output produced by the rule with an input of 3. Write a number
sentence.
1
2
rule
2
input
14 output
–4
×
3
8
4
5
Key ideas
•
•
•
We can use words to describe how a pattern works.
We can use a table or a number pattern to find out how a pattern works.
We can use a flow diagram to find out how a pattern works.
Activity 1
Investigating number patterns
1. Copy and complete the following table
1
×
×
×
×
2
3
3
30
300
3 000
4
5
6
9
90
900
9 000
2. Complete the sentences.
a) When you multiply by 30, it is the same as multiplying by 3 and then
by .
b) When you multiply by 4 000, it is the same as multiplying by 4 and
then by .
3. Complete the following.
=
a) 83 × 200 = 83 × 2 ×
b) 8 × 600 = 8 ×
× 100 =
c) 25 × 3 000 = 25 ×
× 1 000 =
d) 57 × 40 = 57 × 2 × 2 ×
22
Term 1 • Unit 3
× 100 =
× 1 000 =
= 114 × 2 ×
=
×
=
Key ideas
We can multiply numbers by breaking down multiples of 10, 100 and 1 000 into
easier numbers.
Activity 2
Multiplication and division together
1. Look at the flow diagrams. Fill in the missing numbers.
a)
4
32
rule
×8
input
output
56
6
48
24
rule
×6
input
output
÷6
42
6
36
36
rule
output
rule
81
9
×9
input
rule
input
7
4
output
54
9
c)
÷8
input
7
4
b)
rule
72
9
output
÷9
input
7
63
6
54
output
2. a) Compare the input numbers of flow diagram a) with the output numbers of
flow diagram b). What do you notice?
b) Write a sentence about how multiplication and division work together.
3. Copy and complete the following. Do not do any calculations.
a) If 115 × 25 = 2 875, then 2 875 ÷ 25 =
b) If 371 ÷ 7 = 53, then 53 × 7 =
.
.
.
c) If 1 075 × 105 = 112 875, then 112 875 ÷ 105 =
d) If 993 744 ÷ 27 604 = 36, then 36 × 27 604 =
.
Term 1 • Unit 3
23
Key ideas
You can check multiplication by division. You can check division by
multiplication.
Activity 3
Breaking down the rule in a flow diagram
1. Copy and complete the following flow diagrams. Write a number sentence for
each input value.
a)
5
rule
6
×2
input
×7
output
4
3
b)
5
rule
6
output
× 14
input
4
3
2. Compare your number sentences. Complete the sentence.
Multiplying by 2 and then by 7 is the same as _____ .
3. Complete the following flow diagrams. Write down a number sentence for each
input value.
a)
8
rule
6
output
× 25
input
3
4
8
b)
rule
6
× 100
input
3
4
24
Term 1 • Unit 3
÷4
output
4. Compare your number sentences. Complete the sentence.
Multiplying by
and then dividing by
is the same as _____ .
5. Complete the output values. Break the following flow diagrams into two parts
(use two rules). This makes the calculations easier.
a)
12
input
8
rule
output
× 16
7
b)
8
input
6
rule
output
× 35
3
Activity 4
Order of multiplication and addition
1. a) These two flow diagrams have the same input numbers. But, the rules are in
a different order. Will the two flow diagrams have the same output values?
8
rule
5
×3
input
×4
output
×3
output
6
2
8
rule
5
×4
input
6
2
b) Write number sentences for each input value on each flow diagram.
c) Compare the answers. Do you get the same answers for the same input
values?
d) Write a rule about the order of multiplication by two numbers.
Term 1 • Unit 3
25
2. a) These two flow diagrams have the same input numbers. But, the rules are
in a different order. Will these two flow diagrams have the same output
values?
3
rule
5
+3
input
×4
output
+3
output
6
2
3
rule
5
×4
input
6
2
b) Write number sentences for each input value on each flow diagram.
c) Compare the answers. Do you get the same answers for the same input
values?
d) Write a rule about the order of multiplying and adding in a number sentence.
Key ideas
•
•
26
The order of multiplying by two numbers does not change the output value.
Example: 5 × 4 × 3 = 20 × 3 = 60 and 5 × 3 × 4 = 15 × 4 = 60.
The order of multiplying and adding together gives different output values. So
you cannot change the order of the operations.
Example: 5 × 4 + 3 = 23 but 3 + 5 = 8 and 8 × 4 = 32.
Term 1 • Unit 3
Check what you know
1. Copy and complete the number patterns.
a) 2; 4; 6; 8; _____ ; _____ ; _____ ; _____ .
b) 13; 26; 39; _____ ; _____ ; _____ ; _____ .
c) 36; 33; 30; _____ ; _____ ; _____ ; _____ .
2. a) Draw a flow diagram. Draw the rules ‘divide by 3’ and ‘then add 7’. Use
the input values 12, 54, 27 and 18.
b) Complete the output values for the flow diagram.
c) Write a number sentence. Show each input value and its output value.
Word bank
flow diagram:
input value:
output value:
a b
c
a diagram that shows the rule that works on input
values to produce output values
the independent value that you put into a flow
diagram to produce an output value
the number that is produced by using the rule on
the input values in a flow diagram
Term 1 • Unit 3
27
Term
1
Unit 4 Multiplication and
division of whole
numbers
In this unit you will:
•
•
•
•
multiply at least 2-digit by 2-digit whole numbers
divide at least 3-digit by 1-digit whole numbers
break down numbers into factors to make multiplication easier
check the reasonableness of your answer by rounding off.
Getting started
Quick mental multiplication
Lena practises her mental calculations during aftercare. Lena’s friend Felicity
helps her.
What is
4 × 35?
Um …
I don’t know. Why do
you ask me such a
difficult question?
Felicity helps Lena. Felicity rewrites the sum like this:
4 × 35 =
4×5×7=
Felicity helps Lena to multiply quickly. Felicity breaks down the number 35.
I know that
4 × 5 = 20.
And I know
that 20 × 7 = 140.
So 4 × 35 = 140!
28
Term 1 • Unit 4
Let’s see how
fast you can do
the next sum:
7 x 18
Easy. I just break
up 18 into 9 × 2 first. Then I’ll
have 7 × 9 × 2. And 7 × 9 = 63
and 63 × 2 is the same as
63 + 63 = 126.
So 7 × 18 = 126.
Multiply these sums. Use Felicity’s way.
1. 3 × 28
2. 4 × 18
3. 7 × 25
Activity 1
Multiplication of whole numbers
1. State whether the following number sentences are true or false.
a) 7 × 22 = 7 × 11 × 2
b) 231 ÷ 7 = 7 ÷ 231
c) 15 × 2 + 3 = 15 + 3 × 2
d) 83 × 7 = 80 × 7 + 3 × 7
e) 72 × 8 = 70 × 8 + 2 × 8
2. Estimate the following answers. First round each number to the nearest 10.
a) 28 × 6
b) 32 × 4
c) 19 × 8
d) 237 ÷ 3
3. Calculate the answers to Question 2.
4. 282 × 12 = 3 384
Write down and complete the number sentences. Do not calculate.
a) 3 384 ÷ 12 =
b) 3 384 ÷ 282
5. Calculate:
a) 35 × 200 =
b) 7 × 7 000 =
c) 8 × 30 =
d) 24 × 100 =
Term 1 • Unit 4
29
6. Complete the following table quickly.
×
Multiply by
5
4
6
2
9
7
8
Activity 2
2
8
6
3
1
10
56
Using your multiplication facts
1. a) Complete:
8×6=
80 × 6 =
and
8 × 60 =
800 × 6 =
and
80 × 60 =
8 000 × 6 =
and
800 × 60 =
b) Write a sentence about the number of noughts at the end of each answer.
2. Complete the following.
a) 5 × 500 = 5 × 5 ×
=
b) 13 × 7 = 10 × 7 + 3 × 7 =
c) 26 × 4 =
d) 315 × 3 =
×4+
×3+
×4=
×3+
+
=
+
=
×3=
+
+
=
3. Calculate these multiplication sums. Show your working.
a) 27 × 3 =
b) 36 × 5 =
c) 176 × 8 =
d) 215 × 7 =
30
Term 1 • Unit 4
Activity 3
Multiplication problems
1. There are 30 eggs in a tray. How many eggs are there in 7 trays?
2. Lerato packs 500 T-shirts in a box. How many T-shirts does Lerato pack
in 5 boxes?
3. A litre juice bottle can hold 1 000 ml. How many millilitres can six 200 ml juice
bottles hold altogether?
4. There are 300 vitamin tablets in a bottle of Plentivite. How many vitamin
tablets are there in 5 bottles of Plentivite?
5. A pocket of potatoes has a mass of 12 kg. What is the mass of 200 pockets
of potatoes?
Term 1 • Unit 4
31
Activity 4
Different ways of multiplying
1. Calculate 29 × 16.
Thabo found the answer like this.
Faith worked it out like this.
I noticed that 29 = 30 – 1. So I wrote:
I can work with doubling 2s.
29 × 16
16 = 2 × 2 × 2 × 2
= (30 – 1) × 16
So 29 × 16
= 30 × 16 – 1 × 16
= 29 × 2 × 2 × 2 × 2
= 3 × 16 × 10 – 16
= 58 × 2 × 2 × 2
= 480 – 16
= 116 × 2 × 2
= 464
= 232 × 2
= 464
Answer the following. Use Thabo’s method or Faith’s method.
a) 62 × 12 =
b) 87 × 19 =
c) 13 × 45 =
2. There are 15 jars on the shelf in a toy shop. Each jar contains 25 marbles.
How many marbles are there altogether?
3. a) One pencil costs 75 cents. What will 23 pencils cost?
b) I buy 23 pencils. How much change will I get from R20?
4. Estimate the answers. Round off to the nearest 10.
a) 67 × 36
b) 99 × 17
5. Calculate the answers to Question 4.
32
Term 1 • Unit 4
Activity 5
Breaking up numbers to multiply
1. Calculate 69 × 22.
Phumzile worked it out like this:
69 × 22
= 69 × (20 + 2)
= (69 × 20) + (69 × 2)
= (69 × 2 × 10) + (69 × 2)
= 138 × 10 + 138
= 1 380 + 138
= 1 518
2. Work out the following. Use Phumzile’s way.
a) 35 × 14
Exercise 1
b) 436 × 28
c) 769 × 53
Remembering division facts
1. Arrange the following dominoes so that the answer to the sum at the
bottom of one tile is the number at the top of the next tile. You can start
with any tile.
2. Complete the following number sentences.
a) 69 ÷ 3 = (60 ÷ 3) + (
b) 735 ÷ 5 = (
÷ 5) + (
÷ 3) =
÷ 5) + (
+
=
÷ 5) =
+
+
=
3. Complete the patterns.
a) 72 ÷ 8 =
720 ÷ 8 =
7 200 ÷ 8 =
b) 720 ÷ 80 =
7 200 ÷ 80 =
72 000 ÷ 80 =
Term 1 • Unit 4
33
Activity 6
Multiplication and division with remainders
1. There are 3 packets of sweets. There are 8 sweets in each packet. 2 sweets are
lying next to the packets.
a) How many sweets are there altogether?
Nelisa wrote this.
Nozi wrote this.
(8 × 3) + 2
26 ÷ 3 = 8 remainder 2
= 24 + 2
= 26
b) Compare what Nelisa and Nozi wrote. Explain why they are both right.
2. Calculate and write equivalent number sentences. Here is an example.
48 ÷ 5 = 9 remainder 3, so (9 × 5) + 3 = 48
a) 72 ÷ 7 =
, so 72 = (7 ×
)+
.
b) 34 ÷ 5 =
, so 34 = (5 ×
)+
.
c) 85 ÷ 6 =
, so 85 = (6 ×
)+
.
3. Six learners share R385 equally between them. They decide to use the money
left to buy sweets.
a) How much money did each learner get?
b) How much did they have to spend on sweets?
Activity 7
Using a clue board to divide
1. Calculate 297 ÷ 7. Follow these steps.
a) Draw a clue board on your page. Write down some facts about
multiplication by 7 on your clue board. Use numbers that you think will help
you with dividing 297 by 7.
b) Break 297 into parts. Use what you found on the clue board.
2. Calculate the following. Use a clue board to help you.
a) 325 ÷ 6
b) 287 ÷ 5
34
Term 1 • Unit 4
Check what you know
1. Copy and complete the number sentences.
a) 63 ÷ 7 = 9, so 65 ÷ 7 =
rem
.
b) 81 ÷ 9 = 9, so 87 ÷ 9 =
rem
.
c) 56 ÷ 8 =
, so 59 ÷ 8 = rem .
2. Copy the following number square.
a) Find the numbers that give a remainder of 1 when
you divide them by 8. Colour them green.
73
35
93
79
33
27
75
41
b) Find the numbers that give a remainder of 3 when
you divide them by 8. Colour them yellow.
51
43
81
25
c) There are two remaining numbers that are not
green or yellow. Write them down.
65
19
49
11
3. There are 6 eggs in a box. I need 750 eggs. How many boxes do I need?
4. Spring onions are tied in bundles of 6. Leeks are tied in bundles of 3.
Spinach leaves are tied in bundles of 5. There are 744 spring onions,
837 leeks and 950 spinach leaves. How many bundles of each can you make?
5. Find the answers to the following. Use a clue board.
a) 477 ÷ 8
b) 232 ÷ 6
6. A shopkeeper sells 516 oranges in packets of 6. How many packets of
oranges does he sell?
7. Mr Matomela’s car uses 1 litre of petrol for every 9 kilometres that he drives.
Mr Matomela drives 873 kilometres from Kimberley to Durban. How many
litres of petrol does he use?
8. If 785 ÷ 7 = 112 remainder 1, then (112 × 7) + 1 =
Word bank
clue board:
remainder:
a b
.
c
a set of multiplication facts that you use to find the
answer to a division sum
the amount left after you divide a number by
another number
Term 1 • Unit 4
35
Term
1
Unit 5 Time
In this unit you will:
•
•
•
•
•
•
read, tell and write time in 12-hour and 24-hour formats
read clocks, watches and stopwatches, analogue and digital
use calendars
calculate length of time in seconds, minutes, hours, days, weeks, months,
years and decades
convert between different units of time
solve time problems.
Getting started Telling the time
Each clock shows a different time. Write down the time in words for each clock.
A
B
C
D
E
F
G
H
I
J
Activity 1
A time before calendars and clocks
Early people who walked the Earth hunted animals and collected berries, nuts,
roots and fruits. They did not live in towns or villages but moved to where they
could find food. They needed to know about seasons so that they could know
when to expect certain fruits to be ripe. They needed to know directions so that
they could find their way back to places where fruits could be found. People slowly
learned about seasons and directions by trying things out and making mistakes.
36
Term 1 • Unit 5
Remember, there were no books, magazines or newspapers, no radios, television,
movies or computers.
1. How do you think people kept time before there were calendars and clocks?
2. How did knowledge about time change over the years?
People learned how to use the sun, moon and stars to find their way around
and to keep track of time. People counted passing days to keep track of time.
They watched how the moon changed from being full and round to being a thin
curved line.
People needed to be able to remember how many days or full moons had passed.
They kept a record of how much time had passed by tying knots in string or by
cutting lines in bone or wood.
When people started farming, they needed to predict seasons more accurately.
This helped them to plant and pick their crops at the right time. They wanted to
know when to expect new animals to be born. They needed to develop better
ways of keeping track of time. At first, people measured the time of day by
looking at where the sun was in the sky. They also looked at how long or short
shadows were.
Activity 2
Make your own time-keeping device
1. At what times of the day:
a) are shadows short?
b) are shadows long?
2. Make one of the following models of time-keeping instruments. You can get
help from your teacher or from a book. When you have made your model,
show the class how it works and explain how it keeps track of time.
Term 1 • Unit 5
37
Shadow sticks and sundials
As society changed, people needed to know about the
time of day in more detail. People
Model 1
developed fixed clocks based on shadow
lengths. These were called sundials.
A shadow stick is a simple sundial.
Sundials work well in the day in sunny
places like Africa. But sundials cannot help
you to tell time at night or when the sun is
morning shadow
midday shadow
not shining. In some places, the sun only
shines for a few hours in winter. People
developed other ways of telling the time.
A candle clock
Model 2
People noticed how many candles would burn through
a night. Then they marked candles into equal parts.
Does it take the same amount of time to burn each equal
part? Light your candle clock at the beginning of the day.
Watch for when it burns past each mark. One problem
with candle clocks is that a candle burns faster when it
is in a breeze.
Sand and water clocks
Model 3
People also developed clocks based on how long it
takes for sand or water to pour from one part of a
container to another. These were called hourglasses.
Watch how the sand runs to the bottom of a sand clock.
When the sand has run through, turn the sand clock
the other way around. Have you ever seen the 5-minute
timers that use this design?
38
Term 1 • Unit 5
Activity 3
Different instruments to measure time
The following are instruments to measure time that have been used over the years.
Find out who invented them. Find out when and how they were used.
A
grandfather clock
Activity 4
B
sundial
C
water clock
D
wristwatch
Time in seconds, minutes and hours
1. Copy the following table. Guess how long each event will take to
complete. Then measure the exact time that each activity takes.
Use a stopwatch.
a)
b)
c)
d)
e)
Activity
Count in threes to 99
Blink 20 times
Say the first names of
everybody in your class
Jump on the spot 40
times
Write down the numbers
from 2 340 to 2 400
Time in seconds
My estimation
2. How many seconds are there in:
1
a) half a minute?
b) __ of a minute?
4
1
1
d) 1__ minutes?
e) 2__ minutes?
2
2
Actual time
c) 2 minutes?
f) 5 minutes?
Term 1 • Unit 5
39
3. The times shown on these watches are fast. Write down the correct time for
each watch.
A
B
C
D
E
a) Watch A is fast by 27 minutes.
b) Watch B is fast by 55 minutes.
c) Watch C is fast by 1 hour and 40 minutes.
d) Watch D is fast by 6 minutes and 58 seconds.
e) Watch E is fast by 95 minutes and 60 seconds.
4. The times shown on these watches are slow. Write down the correct time for
each watch.
A
B
C
D
a) Watch A is slow by 17 minutes.
b) Watch B is slow by 49 minutes.
c) Watch C is slow by 2 hours and 15 seconds.
d) Watch D is slow by 22 minutes and 40 seconds.
e) Watch E is slow by 120 minutes and 60 seconds.
Key ideas
•
•
40
We use a stopwatch when we need to time ourselves. We also use a
stopwatch for short activities.
There are 60 seconds in one minute. There are 60 minutes in one hour.
Term 1 • Unit 5
E
Activity 5
24-hour time
1. The table compares 12-hour time with 24-hour time.
Midnight:
12-hour
12:00 a.m.
2:00 a.m.
4:00 a.m.
6:00 a.m.
8:00 a.m.
10:00 a.m.
11:00 a.m.
24-hour
00:00
02:00
04:00
06:00
08:00
10:00
11:00
Noon:
12-hour
12:00 p.m.
1:00 p.m.
3:00 p.m.
5:00 p.m.
7:00 p.m.
9:00 p.m.
11:00 p.m.
24-hour
12:00
13:00
15:00
17:00
19:00
21:00
23:00
Copy and complete the following table.
17:47
24-hour 13:00 15:25
12:37
12-hour 1:00
p.m.
a.m.
19:40
8:56
p.m.
11:00
10:20
p.m.
6:00
11:45
p.m.
2. a) Write the time on each clock in words and as digital time.
A
B
C
afternoon
morning
morning
b) It is a normal school week. Write down what you would be doing at home or
school at these times.
Key ideas
•
•
•
We write 12-hour time using a.m. or p.m. We use a dot between the hours
and the minutes of the time. For example, we write 3:45 p.m.
We write 24-hour time like this:
{
03h45 or 03:45 for quarter to 4 in the morning
{
15h45 or 15:45 for quarter to 4 in the afternoon.
After midday or noon, the time on the 24-hour clock continues with 13:00.
The 12-hour time starts with 1:00 p.m.
Term 1 • Unit 5
41
Exercise 1
Time and converting time
1. a) Write 22:40 in 12-hour format.
b) Draw a clock face to show 22:40.
2. How many hours and minutes are there from 8:15 a.m. to 2 p.m.?
3. Convert between different units of time.
a) 2 minutes are
c) 72 hours are
Activity 6
seconds.
days.
b) 63 days are
d) 10 years are
weeks.
months.
Reading calendars
1. a) On what day of the week is 29 February?
b) How do you know that the year 2012 is a leap year?
2. a) How many days are there from 15 February to the first public holiday?
b) How many weeks are there from 15 February to the first public holiday?
c) Find out why we commemorate this day. Write a short paragraph on what
you have found.
3. a) What do we celebrate on 27 April?
b) What is the date 3 weeks before 27 April?
Key ideas
•
•
42
February has 28 days. In a leap year, there are 29 days in February. A leap
year happens every 4th year.
We can count days, weeks and months on a calendar. A calendar shows the
day of the week for each date.
Term 1 • Unit 5
Check what you know
1. Write the following times. Use 24-hour time.
a) Quarter to ten in the evening
b) 9.45 a.m.
c) 3.30 p.m.
d) 6.15 p.m.
e) Eight o’clock in the morning
2. Match the times in the first column with the times in the second column.
a)
b)
c)
d)
e)
f)
g)
37 years
5 weeks
two centuries
72 seconds
New Year’s Day
24 hours
Freedom Day
1
h) 1__ hours
2
A)
B.
C.
D.
E.
F.
G.
1 January
200 years
one day
27th April
35 days
90 minutes
3 decades and 7 years
H. 1 minute 12 seconds
3. Calculate how many hours you spend at school on a Monday.
4. An athlete runs a 100 m race. Which instrument would you use to measure
how fast the athlete ran?
5. Edward Machakela makes a family tree. The family tree includes his
grandparents. He finds out that Mr Njemla was born in 1950, Mrs Njemla
was born in 1952 and Mr Machakela was born in 1948.
a) How many years ago was Mr Machakela born?
b) About how many decades ago was Mrs Njemla born?
c) Write down the ages of the three grandparents in order, from the
youngest to the oldest.
6. Sandra takes 136 minutes to walk 6 kilometres.
a) Sandra walks at the same speed all the time. How long does she take
to walk 1 kilometre?
b) At this speed, how long will Sandra take to walk 15 kilometres?
7. What unit of time would you use to measure each of the following? You can
choose to use seconds, minutes, hours, days, weeks, years or decades.
a) The time it takes you to travel between your house and your school.
b) The time it takes you to grow 10 cm taller than you are now.
Term 1 • Unit 5
43
c) The difference between your age and your mother’s age.
d) The time it takes you to cook an egg.
e) The time it takes a bean seed to grow into a bean plant.
8. There are 10 years in 1 decade. Uncle James has lived for 5 decades and
3 years. How old is he?
9. Rock and roll music was popular in the 1960s. About how many decades
have passed since then?
10. Mrs Fry took 5 years to pay off her car. She paid in monthly instalments.
How many payments did Mrs Fry make?
Word bank
a b
24-hour clock:
analogue clock:
digital clock:
leap year:
44
Term 1 • Unit 5
c
a clock that shows the hours in the afternoon and
evening as numbers between 12 and 24
a clock with the numbers 1 to 12. It has moving
hands to show the time
a clock that shows the time using only digits. It
shows how many minutes have passed since the
last hour
a year that has 366 days. It has an extra day in
February
Term
1
Unit 6 Data handling 1
In this unit you will:
•
•
•
•
collect and record data using tally marks and tables
order data from the smallest to the largest group of data
organise and represent data in tables and bar graphs
interpret and analyse data.
Getting started
Organising and reading information
Mendi’s class collected these shells on the beach. The class put the shells in
the following groups:
ear shells
bivalves
cowries
limpets
winkles
whelks
1. Do the following. Just look at the picture. Do not count.
a) Say which kind of shell Mendi’s class collected the most of.
b) Say what kind of shell they collected the least of.
c) Order the groups of shells from the least to the most.
d) Estimate how many shells they collected altogether.
2. Now check whether you estimated correctly. Count the shells.
Term 1 • Unit 6
45
3. Mendi’s class made a tally table to show the number of each shell type.
Type of shell
Ear shells
Ear-shaped shells.
They have a wide
opening.
Limpets
Flat, cone-shaped
shells. They have a
wide opening.
Bivalves
Shells that have
two similar parts.
The two parts hold
together tightly
when an animal
lives in the shell.
Winkles
Coiled shells.
They have a round
opening.
Cowries
Shiny egg-shaped
shells. They have
a long narrow
opening.
Whelks
Pointed or spiralled
shells. They have
an oval opening
with a notch
or groove.
Tally
Number
2
//
7
//// //
//// /
////
////
//// ///
a) Read off the table what / / / / stands for. Then copy and complete
the table.
46
Term 1 • Unit 6
b) Use the table. Work out how many of the following Mendi’s class
collected.
i)
Bivalves
ii)
Whelks
iii)
Cowries
c) Now use the table to answer Question 1 a), b) and c) again. Is the
information easier to see from the table or from the picture?
4. Copy and complete the bar graph.
8
7
6
5
Number
of
shells
4
3
2
1
0
lls
ar
e
e
sh
es
s
lim
t
pe
v
al
v
bi
es
l
nk
wi
s
ie
c
r
ow
s
lk
e
wh
Type of shells
5. How many more whelks than cowries did Mendi’s class collect?
6. How many fewer ear shells did Mendi’s class collect than bivalves?
Key ideas
•
•
•
•
•
Data is information we read or collect.
You can show data in different ways. You can write data in paragraphs, in
lists, in tables or show it as a graph.
Tables and graphs make it easier to read and understand information.
A tally is a way of counting and showing how many of something you have.
Often, tallies have things grouped in fives. This is shown like this: / / / / .
The mode of the data is the data group that has most objects in it.
Term 1 • Unit 6
47
Activity 1
Drawing and naming bar graphs
Mendi has a friend, Katriena. Katriena also collected shells with her class.
Katriena’s class collected 5 ear shells, 9 limpets, 8 bivalves, 4 winkles, no cowries
and 10 whelks.
1. Make a tally table. Show the numbers of shells that Katriena’s class collected.
2. a) Now make a bar graph. Show the numbers of shells the two classes
collected. Give your graph a name.
b) Name each bar. Explain what the bars show altogether.
c) Write numbers down the side of the graph to show how long the bars are.
Also explain what these numbers mean.
3. Compare the shells collected by Mendi’s class and Katriena’s class.
a) Which class collected the most limpets?
b) Which class collected the most bivalves?
c) Which class collected the most whelks?
d) Which class collected the most cowries?
e) Which class collected the most shells altogether?
4. Why do you think the two classes collected different numbers of different types
of shells?
5. Do you prefer comparing data in a paragraph, a table or a graph? Explain your
answer.
Key ideas
•
•
•
•
48
If you collect information at different times and places, you often get different
data.
Put your data into a table. This helps you to make a graph.
Give your graph a name or title. This helps people know what the information
is about.
You can read information off the graph. Look at what is shown along the
bottom of the graph and down the side of the graph.
Term 1 • Unit 6
Exercise 1
Making a class nature graph
Work as a whole class. Collect and group things.
1. a) Collect things from nature such as shells, leaves or seeds.
b) Put your collection into groups of similar things. They could have the
same shape, size or colour. They could have the same number of
branches.
c) Organise your data with a tally table. Then make a bar graph.
2. Present and explain your bar graph to your class.
3. Ask the class questions about your bar graph that they must answer.
Check what you know
1. Nuhar’s class made a graph of the seeds they collected. The class
organised the seeds according to how the seeds move away from the
parent plant.
How seeds find a home
10
9
8
Number
of
seeds
collected
7
6
5
4
3
2
1
0
s
al
ic
ks
st
to
nd
m
ni
a
n
b
w
lo
by
n
s
en
by
bi
o
st
r
t
ea
s
d
po
t
ha
bu
t
r
te
pe
rd
wi
d
e
rri
by
wa
ca
Ways that seeds move
a) What is the most common way for these seeds to move?
b) What is the least common way for these seeds to move?
c) How many more seeds are eaten by birds than are blown by the wind?
d) Nuhar found 10 more wind-blown seeds, 5 more that stick to animals,
9 more that are eaten by birds and 6 more that are shot away by pods.
Draw what her new graph will look like.
e) Now answer Questions 1 a), b) and c) again. Use the new graph.
Term 1 • Unit 6
49
Word bank
a b
bar graph:
data:
tally:
50
Term 1 • Unit 6
c
a chart with bars to show or compare data
a collection of information. We usually collect data
by observing, questioning or measuring
marks that you use to record counting. Tallies are
usually in bundles of 5
Term
1
Unit 7 Data handling 2
In this unit you will:
•
•
•
•
•
collect and record data using tally marks and tables
order and organise data
represent data on pictographs, bar graphs and pie charts
interpret and analyse data
find the mode of ungrouped numerical data.
Getting started
Using pictographs and bar graphs
Silaelo recorded the people’s hairstyles in his neighbourhood. He made a table
and two graphs.
Style
Bob
Number of
people
93
Baby
dreads
79
Freeze
wave
70
Braids
Number 1
Other
87
35
51
Hairstyles
Hairstyles
90
90
80
80
Number of children
100
Number of children
100
70
60
50
40
30
20
10
= 10 children
70
60
50
40
30
20
10
0
0
s
ad
b
bo
by
ba
e
dr
e
av
e
w
ze
fre
s
br
d
ai
b
m
nu
1
er
ot
r
he
s
b
by
ba
Types of hairstyles
e
av
ad
bo
e
dr
e
w
ze
fre
r1
ds
ai
br
be
m
nu
r
he
ot
Types of hairstyles
1. Compare the picture graph and the bar graph:
a) How are the two graphs different? How are they the same?
b) What does each face show on the pictograph? Where on the graph does
it tell you this?
Term 1 • Unit 7
51
c) Look at the numbers on the vertical axis of the bar graph. In groups of
how many are they?
2. Answer the following questions by reading off the graphs.
a) Use the bar graph. How many people have their hair in a freeze wave?
b) Use the pictograph. How many people have their hair in baby dreads?
1
c) There are 3__ faces in the ‘Number 1’ column in the pictograph.
2
How many people does this show?
d) What is the least common hairstyle?
e) What is the most common hairstyle?
f) Which graph gives you a better idea of the exact numbers?
g) Which graph do you like best? Why?
3. Now answer questions 2 a), b) and c). Read the data in the table.
4. What do you notice about your answers to Question 2 and Question 3?
5. a) Why do you think the last group is called ‘other’?
b) Name some possible hairstyles in this group.
Key ideas
•
•
•
Sometimes you have too much data to let each space or picture stand for
1 piece of information. You have to show the information in larger groups.
The bar graph for hairstyles is numbered in groups of 10. Each space on the
side of the graph stands for 10 people.
In the picture graph for hairstyles, each face stands for 10 people. This is
shown in the key at the bottom of the graph.
•
To show about 5 children, you can show half a face.
•
The table shows you the exact number of people with each hairstyle. The
graphs tell you more or less how many people have each hairstyle. The
graph is easier for comparing different groups with each other.
Sometimes you have lots of small and different bits of information or data
that do not fit into your groups. You can group these bits of information
together. You can call this group ‘other’.
93 people had a bob. The bob is the most common hairstyle. The mode is
the most common item of data.
•
•
52
Term 1 • Unit 7
Exercise 1
Yusrah does a survey about how learners get to school each day. Yusrah
found that of the 100 Grade 5 learners, 15 learners travelled by train,
25 travelled by car, 45 travelled by taxi and the rest walked to school.
1. How many learners walked to school?
2. Use a table to organise the data that Yusrah has collected.
3. Show the data on a bar graph. Draw the bar graph neatly. Label the bar
graph fully.
Activity 1
The complete data cycle (project)
1. Choose a topic that you can ask your class about to find out what is most
popular. Here are some examples:
sport
films
music or film stars
TV programmes
food
fruits
colours
cooldrinks
a) Write down a question to ask the class about that topic.
b) Write down about five possible answers they can choose from.
c) Do a survey in your class. Ask at least 20 children to answer your question.
Write down their answers.
What fruit do you like best?
grapes
apples
oranges
strawberries
bananas
2. Organise and show the data that you collected in a table. Use a column for the
possible answers. Use a column for the tally and a column for the number of
children.
Term 1 • Unit 7
53
What fruit do you like best?
Fruit
Tally
Number
grapes
apples
oranges
strawberries
bananas
3. Use the data from your table to make a bar graph or a pictograph. Give the
graph a heading. Label each column. Show the numbers on the side of the
graph.
What fruit do you like best?
6
5
4
3
2
1
0
s
pe
a
gr
s
es
le
p
ap
or
g
an
s
rie
r
be
as
n
na
ba
aw
st
The favourite fruit of the class
4. a) Write about 3 questions about your graph. You could ask about:
• the most popular and the least popular thing
• two things compared with each other
• reasons why one thing is more popular.
b) Ask at least three children to answer your questions.
5. Report to the class. Present your survey, your graph and your questions to the
class on a poster. Draw a conclusion about your research.
54
Term 1 • Unit 7
Key ideas
In this activity, you do the following steps in the complete data handling cycle:
•
•
•
•
•
•
Choose a question to ask and make a questionnaire.
Collect the data by doing a survey.
Organise the data into a table.
Represent the data with a bar graph.
Analyse the data by answering questions about it.
Present your findings to the class.
Activity 2
Pie graphs or pie charts
A survey was done in 2011 to see where South Africans get their water. The
following pie graph shows the results of the survey.
tap inside house
tap in yard
collect from beyond yard
Source: AMPS 2011 Household Survey taken from http://www.eighty20.co.za/
1. Where does the data in the pie chart come from?
2. In 2011, what fraction of South Africans got their water from a tap inside the
house?
3. Is the fraction of people that collect their water from the yard more or less than
one quarter?
4. Is the fraction of people that collect their water outside their yard more or less
than one quarter?
5. What does it mean to be able to get water? The law says all South Africans
should be able to get 25 litres of water a day from a distance of less than 2 km.
But what if you cannot afford to pay for the water? Two-thirds of South Africans
think that this water should be free to people who cannot afford to pay for it.
What do you think?
Term 1 • Unit 7
55
Key ideas
•
•
•
•
•
A pie graph or pie chart is a graph or chart that shows data as parts of a
circle. You call it this because the parts look like pieces of a pie.
The pie graph or pie chart on the previous page uses fractions of a circle to
show where South Africans get their water.
1
Example: About __ of all South Africans get their water from an inside tap.
2
You always get 1 whole if you add the fractions of a pie graph.
1 1 1
Example: __ + __ + __ = 1. The circle shows all of the information collected.
2 4 4
If there are many different pieces in a pie graph, sometimes the actual
number that each piece shows is written alongside it.
Each piece of the pie graph is labelled. In this example, the labels are in a
key next to the pie graph.
Activity 3
Another pie graph
Look at the following pie graph.
Toilets in South African homes
Inside flush toilet
Outside flush toilets
Non-flush toilet
Source: AMPS 2011 Household Survey taken from http://www.eighty20.co.za/
1. In what year was the data collected?
2. The source of data is http://www.eighty20.co.za/. Where do you find this type of
information?
1
3. What type of toilet is in about __ of South African homes?
2
1
4. What type of toilet do about __ of South African homes have?
3
5. What is the least common type of toilet in South African homes?
1
6. Do more or less than __ of South African homes use outside flush toilets?
8
56
Term 1 • Unit 7
Check what you know
Compare the bar graph and pie graph of how many people live in each province
in South Africa.
Population of the provinces
10
Population in millions
9
8 million
8
KwaZulu-Natal
9 __12 million
A
7
6
Eastern Cape
7 million
5
4
D
3
Northern Cape 1 million
2
B
3 __12 million
1
Free State 2 __12 million
0
l
o
op
t
e
es ap
t
p
a
C
S
C
l
W
C
N
u
m
a
n
i
e Ga
n
h
n
u
r
r
t
l
r
L
e
r
e
u
e
um the
Fr
st
No est
aZ Mp
Ea
No
W
Kw
e
ap
e
t
ta
g
en
a
at
a
ng
e
ap
4 __21 million
C
3 million
Limpopo 5 __12 million
Provinces
1. a) Which province has the most people in it? From which graph did you
read your answer?
b) About how many million people live in this province?
1
1
c) Is this more than __ or less than __ of the total population of South Africa?
4
4
d) Which graph gives you the answer to Question 1 c)?
2. Fill in the missing bits of information A, B, C and D on the pie graph.
3. Which four provinces have almost the same fraction of the total population?
4. a) About how many million people live in Mpumalanga?
b) About how many million people live in the Eastern Cape?
c) About how many more people live in the Eastern Cape than in
Mpumalanga?
Word bank
a b
data source:
pictograph:
tally table:
pie chart or pie graph:
c
where you collect data from
a chart with pictures to show the data that you
collected
a table that you use to record a tally of scores. You
often use a tally when you do a survey
a graph that shows data as parts of a whole circle
Term 1 • Unit 7
57
Term
1
Unit 8 2-dimensional
shapes
In this unit you will:
•
•
•
•
•
recognise and name triangles, quadrilaterals, pentagons, hexagons and
heptagons
distinguish between squares and rectangles
describe, sort and compare shapes according to
{
number of sides and angles
{
length of sides
{
sizes of angles
draw 2-dimensional shapes on grid paper
draw and identify angles (only right angles, angles smaller than right angles,
angles greater than right angles).
Getting started
Making and using your own ‘turner’
You will need: thin cardboard to make strips, 2 split pins, ruler and scissors.
1. Make a cardboard turner. Follow the instructions.
a) Cut two pairs of cardboard strips. Make your strips 15 mm wide. Make
one pair 15 cm long. Make the other pair 20 cm long.
b) Put each pair of strips on top of each other. Join each pair of strips with a
split pin.
c) Now you can use your turner like the hands of a clock. Keep the one
arm of the turner still. This arm will show where you started from.
58
Term 1 • Unit 8
2. Zuhri made a quarter-turn clockwise. This is the picture he drew of it:
Now use your turners to make the following turns.
Remember to keep the one arm still to show the
starting place of your turn.
Zuhri
1
Draw the corner it makes when you show the direction
turn
4
of your turn on your drawing.
1
a) Make __ of a full turn clockwise.
2
3
__
b) Make of a full turn clockwise.
4
c) Make a full turn clockwise.
1
d) Make __ of a full turn clockwise.
4
e) Does the length of the arms of the turner affect or change the amount
you turn?
Key ideas
•
•
•
•
•
•
•
•
When you stop moving your turner, it will show a
corner. We call this corner an angle.
We call the moving parts of the turner its arms.
The sides of an angle are also called the arms of
the angle.
We can use an arrow to show how the arm of
the turner was moved to make an angle.
We call a quarter turn a right angle.
We see angles all around us. Angles are made
where the sides of shapes and objects make
corners.
Think about angles at the corners of
triangles, squares, stars, boxes, doors
and pages.
Angles can have different sizes. We
look at angles that are right angles,
greater than right angles and smaller than right angles.
The lengths of the
arms do not affect
the size of the
angle.
angle
1
turn = right angle
4
Term 1 • Unit 8
59
Activity 1
Estimating the size of angles
Look at the sizes of the angles in the following drawings. Use the drawings to help
you answer the following questions.
A
B
less than
a right angle
C
a right
angle
bigger than a
right angle but smaller
than a sraight angle
1. For each angle, say if it is a right angle, or greater than or smaller than a
right angle.
a)
b)
c)
d)
e)
f)
2. Draw the following angles. Use a ruler and the corner of a page to measure the
right angle.
a) A right angle
b) An angle greater than a right angle
c) An angle smaller than a right angle
Activity 2
Curved and straight sides
1. Look at the shapes. Sort them into the following groups. For each group, write a
list of the letters of the shapes in that group.
Group 1: Shapes with straight sides only
Group 2: Shapes with curved sides only
Group 3: Shapes with both curved sides and straight sides
60
Term 1 • Unit 8
2. Write a list of the shapes that have one or more right angles.
Activity 3
Squares and rectangles
Use squared paper, dotted paper or geoboards for this activity.
A
D
C
B
E
1. Use the given line on each geoboard as one side of a square. Complete the
square. The first square is done for you.
2. Now make rectangles. Use the same lines as one side. How many different
rectangles can you make from each line?
3. a) What is the same about squares and rectangles?
b) What is different about squares and rectangles?
4. Which of Mogadi’s shapes are:
a) rectangles?
b) squares?
A
B
C
D
E
F
G
H
Term 1 • Unit 8
61
5. Copy and complete.
a) All closed shapes with four straight sides are called _____ .
b) Rectangles and squares are types of _____ .
c) The corners of a rectangle are all _____ .
d) The opposite _____ of a rectangle have the same length.
e) The corners of a square are all _____ .
f) The sides of a square are all _____ .
Key ideas
•
•
•
•
•
A quadrilateral is any closed four-sided shape.
You can only make one square from each line. You can make many different
rectangles from each line.
A rectangle is a four-sided shape. All corners of a rectangle are right angles.
A rectangle’s opposite sides are the same length.
A square is also a four-sided shape. All corners of a square are also right
angles. All four of a square’s sides have the same length.
Squares and rectangles are all four-sided. So, squares and rectangles are
types of quadrilaterals.
Activity 4
Number of sides and angles
1. Copy and complete the following table.
a)
Shape
triangle
Number of sides
Number of angles
3
b)
quadrilateral
4
62
Term 1 • Unit 8
c) pentagon
d) hexagon
e) heptagon
2. What do you notice about the number of sides and the number of angles for
each kind of shape?
Key ideas
•
•
•
•
•
A triangle has three sides and three angles.
A quadrilateral has four sides and four angles.
A pentagon has five sides and five angles.
A hexagon has six sides and six angles.
A heptagon has seven sides and seven angles.
Activity 5
Name and describe 2-D shapes
Copy and complete the following table.
Shape
Name of
shape
Number of sides
and angles
Length of
sides
Sizes of
angles
square
4
all equal
all right angles
Term 1 • Unit 8
63
Shape
Name of
shape
triangle
64
Term 1 • Unit 8
Number of sides
and angles
3
Length of
sides
Sizes of
angles
different
lengths
1 right angle
2 angles
smaller than a
right angle
Exercise 1
More naming of 2-D shapes
1. Look at the following shapes.
11
4
5
6
1
2
10
3
7
8
9
a) Write the name of each shape next to the number of the shape.
b) Which of these shapes are quadrilaterals?
2. Explain these shapes to a blind person. Write a sentence to describe each
of them.
a) A square
b) A rectangle
c) A triangle
d) A circle
3. Draw two different shapes for each of the following. Use squared paper
and a ruler.
a) Pentagons
b) Hexagons
c) Heptagons
Check what you know
97
15
15
12
23
45
79
7
54
3
42
1. Add all the numbers that are in the square together.
2. Add all the numbers that are in the circle together.
Term 1 • Unit 8
65
3. List all the numbers that are in the:
a) heptagon
b) pentagon.
4. Subtract the total of the numbers in the circle from the total of the numbers
in the square.
5. Which number is in the pentagon and in the heptagon?
6. Which number is in the heptagon and in the square?
7. Which shapes have four right angles?
8. Which shapes have angles that are greater than right angles?
9. Which shape has angles that are smaller than right angles?
Word bank
a b
2-dimensional shape:
angle:
arms of an angle:
right angle:
quadrilateral:
pentagon:
hexagon:
heptagon:
square:
rectangle:
66
Term 1 • Unit 8
c
a flat shape that you can draw on paper
the amount of turning between two lines that meet
at the same point
the two lines that meet to make the angle
a quarter-turn between two arms of the angle
any closed shape with 4 straight sides
any closed shape with 5 straight sides
any closed shape with 6 straight sides
any closed shape with 7 straight sides
a quadrilateral. All four sides of a square are equal.
All angles in a square are right angles
a quadrilateral. Opposite sides of a rectangle are
equal. All angles in a rectangle are right angles
Term
1
Unit 9 Capacity and
volume
In this unit you will:
•
•
•
•
estimate, measure, record and order the capacity of containers and the
volume of liquids
use the correct units (ml or ℓ) and measuring instruments for different
amounts of liquids
calculate and solve problems involving capacity and volume
convert between litres and millilitres.
Getting started
Litres and millilitres
You will need:
1 ℓ measuring jug
water
250 ml
measuring
cup
5 ml measuring
spoon
1 ml syringe
1. a) Fill the syringe. Carefully empty the syringe into the measuring spoon.
This is 1 ml of water.
b) The measuring spoon can hold 5 ml. You want to fill the measuring
spoon. How many times must you fill the syringe and empty it into the
measuring spoon?
c) Check that you are right. Fill the measuring spoon using the syringe.
How many times did you empty the syringe into the measuring spoon?
d) Empty the measuring spoon into the measuring cup.
Term 1 • Unit 9
67
e) Empty the measuring spoon into the measuring cup until the measuring
cup is full. How many measuring spoonfuls fill the measuring cup?
Write 1 measuring cup =
measuring spoonful.
f) 1 measuring cup = 250 ml. Copy and complete: 1 measuring cup =
× 5 ml.
g) Now fill the 1 ℓ measuring jug using the measuring cup. How many
measuring cupfuls to fill the measuring jug?
h) Copy and complete:
250 ml ×
i)
measuring cups =
ml
The measuring jug holds 1 000 ml of water. Therefore 1 ℓ =
ml.
2. Look at the following containers. For each container, decide if you will
measure the container’s capacity in millilitres or in litres.
bucket
petrol tank in a car
baby’s
milk bottle
soup bowl
a) bucket
b) petrol tank in a car
c) baby’s milk bottle
d) soup bowl
Key ideas
•
•
•
•
•
•
•
•
•
68
Capacity is the amount that a container can hold.
The volume of the liquid is the amount of liquid that is in the container.
We use litres and millilitres to measure
the capacity of containers.
1 litre = 1 000 millilitres
1
2__ ℓ = 2,5 ℓ = 2 500 ml
2
2,5 ℓ = 2 ℓ and 500 ml
A standard measuring cup holds 250 ml.
Ordinary teacups hold about 200 ml.
Ordinary mugs hold about 250 ml.
Term 1 • Unit 9
Activity 1
Measuring liquids
You will need:
1 ℓ measuring jug and water
1. Look carefully at the measuring jug.
a) What measurement does it show at
the top of the measuring jug?
b) There are lines on the measuring
jug. Only some lines have a
measurement written next to them.
How many millilitres does each line
represent?
2. a) Pour water into the measuring jug until it is about half full.
b) Put the measuring jug on a table or desk. Read off exactly how much water
you poured into the measuring jug. Your eyes must be in line with the level
of the water.
3. a) Empty some of the water out until there is about a quarter of the measuring
jug of water left.
b) Put the measuring jug on a table. Read off exactly how much water is in the
measuring jug.
4. Fill the measuring jug to about 600 ml. Put the measuring jug on the table.
Check if there is exactly 600 ml of water in the measuring jug. Add a little water
or pour a little water out until the level is exact.
Key ideas
•
•
Keep your eyes in line with the level of
the water when you read a measuring
jug.
Read the lines on the measuring jug
the way you read a number line.
Term 1 • Unit 9
69
Activity 2
Markings on measuring jugs
1. a) How much milk is in measuring jug A?
measuring jug A
b) What do the numbers 100, 200, 300, 400 and
500 on the measuring jug show?
c) What does each small line in between these
numbers show?
2. a) About how much milk is in measuring jug B?
1
Is it more or less than __ ℓ?
4
b) Now write exactly how much milk is in the
measuring jug.
measuring jug B
c) You pour 100 ml of milk out of the measuring
jug. How much milk is left in the measuring jug?
d) How much more milk do you need to make
500 ml?
e) How much more milk do you need to make
1 ℓ?
Key ideas
•
•
•
•
•
70
Look at the measuring jugs above. Every 10 ml is marked off, but only every
100 ml is labelled.
The measuring jugs can hold 500 ml. The amount of milk in measuring jug B
1
is 210 ml. 210 ml is less than __ litre.
4
1
500 ml = __ ℓ = 0,5 ℓ
2
1
__
ℓ = 250 ml
4
Few measuring containers have every millilitre marked off and labelled.
Check what the markings on a measuring container show.
Term 1 • Unit 9