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Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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CAMBRIDGE
P
Primary Mathematics
Workbook 5
S
A
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Emma Low & Mary Wood
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
University Printing House, Cambridge CB2 8BS, United Kingdom
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Information on this title: www.cambridge.org/9781108746311
© Cambridge University Press 2021
First published 2014
Second edition 2021
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This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Printed in ‘country’ by ‘printer’
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A catalogue record for this publication is available from the British Library
ISBN 978-1-108-74631-1 Paperback
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A
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NOTICE TO TEACHERS IN THE UK
S
It is illegal to reproduce any part of this work in material form (including
photocopying and electronic storage) except under the following circumstances:
(i)
where you are abiding by a licence granted to your school or institution by the
Copyright Licensing Agency;
(ii)
where no such licence exists, or where you wish to exceed the terms of a licence,
and you have gained the written permission of Cambridge University Press;
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of Chapter 3 of the Copyright, Designs and Patents Act 1988, which covers, for
example, the reproduction of short passages within certain types of educational
anthology and reproduction for the purposes of setting examination questions.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Contents
5
Thinking and Working Mathematically
6
1
The number system
8
1.1
1.2
Understanding place value
Rounding decimal numbers
2
2D shape and pattern
2.1
2.2
Triangles
Symmetry
3
Numbers and sequences
31
3.1
3.2
3.3
Counting and sequences
Square and triangular numbers
Prime and composite numbers
31
36
40
4
Averages
44
4.1
Mode and median
44
5
Addition and subtraction
49
5.1
5.2
Addition and subtraction including decimal numbers
Addition and subtraction of positive and negative numbers
49
54
6
3D shapes
59
6.1
Nets of cubes and drawing 3D shapes
59
7
Fractions, decimals and percentages
66
7.1
7.2
7.3
Understanding fractions
Percentages, decimals and fractions
Equivalence and comparison
66
70
75
8
Probability
80
8.1
8.2
Likelihood
Experiments and simulations
80
85
8
13
17
P
17
24
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S
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How to use this book
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Contents
3
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Contents
9
Addition and subtraction of fractions
92
9.1
Addition and subtraction of fractions
92
10 Angles
97
10.1 Angles
97
102
11.1 Multiplication
11.2 Division
11.3 Tests of divisibility
102
107
110
12 Data
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11 Multiplication and division
113
113
125
13 Ratio and proportion
135
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12.1 Representing and interpreting data
12.2 Frequency diagrams and line graphs
135
14 Area and perimeter
143
14.1 Area and perimeter
143
M
13.1 Ratio and proportion
150
15.1 Multiplying and dividing fractions
15.2 Multiplying a decimal and a whole number
150
155
16 Time
159
16.1 Time intervals and time zones
159
17 Number and the laws of arithmetic
168
17.1 The laws of arithmetic
168
18 Position and direction
174
18.1 Coordinates and translation
174
Acknowledgements
181
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A
15 Multiplying and dividing fractions and decimals
4
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
How to use this book
How to use this book
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This workbook provides questions for you to practise what you have
learned in class. There is a unit to match each unit in your Learner’s Book.
Each exercise is divided into three parts:
•
Focus: these questions help you to master the basics
•
Practice: these questions help you to become more confident in
using what you have learned
•
1
The number
Challenge: these questions will make you think very hard.
system
Each exercise is divided into three parts. You might not need to work on
all of them. Your teacher will tell you which parts to do.
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1.1 Understanding place value
16
You will also find these features:
Worked example 1
decimal
Important words that
you
will
use.
Find the
missing
numbers.
a
0.9 ×
decimal place
decimal point
=9
M
Step-by-step examples
b 350 ÷
showing a way to solve
a
100s
a problem.
= 3.5
10s
1s
1
s
10
0
9
1
s
100
The time in Mai’s time zone is 15:07. What is the time for Yared and Susan?
10s
1s
3
5
0
A
100s
1
s
10
1
s
100
5
0
There are
often many different
ways to solve a
problem.
3
S
8
These questions will help
you develop your skills of
thinking and working
mathematically.
tenth
16.1 Time intervals and time zones
The time on Susan’s clock is 3 hours behind the time on Mai’s clock.
0.9 × 10 = 9
350 ÷ 100 = 3.5
hundredth
place value
Worked example 1
Use a place value grid to help you.
Mai, Yared and Susan live in different time zones.
To move digits one column to the left you
multiplyThe
by time
10. on Yared’s clock is 2 hours ahead of the time on
Mai’s clock.
9
b
Time
Yared’s time is 2 hours ahead of Mai’s.
To move digits two columns to the right you
The100.
time for Yared is 17:07.
divide by
Susan’s time is 3 hours behind Mai’s.
Add 2 hours to 15:07.
Subtract 3 hours from 15:07.
The time for Susan is 12:07.
Exercise 16.1
time interval
Focus
time zone
1
Universal Time (UT)
Circle the amount of time to correctly
complete each sentence.
a
0.5 minutes is the same as:
30 seconds
b
5 seconds
50 seconds
1.1 Understanding place value
0.5 hours is the same as:
11
Draw a ring around
the odd one out.
5 minutes
30 seconds
30 minutes
c
1.5 days is368.4
the same
tenthsas:
1 day and 5 hours
36.84
368.4
3684 hundredths
1 day and 12 hours
1 day and 15 hours
368 tenths and 4 hundredths
Explain your answer.
159
Challenge
12 Write down the value of the digit 3 in each of these numbers.
a
72.3
5
eighty-four point zero three
Original material © Cambridge University Press 2020. This material isb not
final and is subject to further changes prior to publication.
5 Additionand
and Working
subtraction
Thinking
Mathematically
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Thinking and Working
Mathematically
There are some important skills that you will develop as you learn
mathematics.
P
Specialising
is when I test
examples to see if
they fit a rule
or pattern.
M
Characterising
is when I explain how
a group of things are
the same.
S
A
Generalising
is when I can explain
and use a rule or
pattern to find more
examples.
6
Classifying
is when I put
things into groups and
can say what rule
I have used.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
Thinking and Working Mathematically
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Critiquing
is when I think about
what is good and what
could be better in my
work or someone
else’s work.
P
Improving
is when I try to
make my maths
better.
S
A
M
Conjecturing is
when I think of an idea
or question linked to
my maths.
Convincing
is when I explain my
thinking to someone else,
to help them
understand.
7
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
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1
The number
system
1.1 Understanding place value
Worked example 1
Find the missing numbers.
b
350 ÷
a
=9
100s
= 3.5
10s
hundredth
decimal place
place value
decimal point
tenth
P
0.9 ×
M
a
decimal
1s
1
s
10
0
9
1
s
100
Use a place value grid to help you.
To move digits one column to the left you
multiply by 10.
A
9
0.9 × 10 = 9
100s
10s
1s
3
5
0
S
b
3
1
s
10
1
s
100
5
0
To move digits two columns to the right you
divide by 100.
350 ÷ 100 = 3.5
8
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.1 Understanding place value
Exercise 1.1
Focus
Write the missing numbers in this sequence.
1900
÷ 10
19
÷ 10
190
a
fifteen point three seven
b
one hundred and five point zero five
c
thirty four point three four
P
3
Write these numbers in digits.
÷ 10
You may find a
place value grid
helpful for these
questions.
Write the missing numbers.
a
75
×
M
2
÷ 10
Tip
LE
1
×100
A
×10
b
25 000
×10
S
÷
÷100
9
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
4
Complete the table to show what the digits in the number
47.56 stand for.
4
tens
5
LE
6
7
5
Write the missing number.
6.58 = 6 +
+ 0.08
Practice
Draw a ring around the number equivalent to five hundredths.
P
6
500 5.00 0.50 0.05
Divide 3.6 by 10.
8
Write the missing numbers.
M
7
38.14 = 30 + 8 +
Here are four number cards.
A
9
+
Draw a ring round the card that shows the number that is
100 times bigger than 33.3
S
33.300
3330
333.00
33300
10 Find the missing numbers.
10
a
7.2 × 100 =
b
0.75 × 100 =
c
4.28 × 10 =
d
270 ÷ 100 =
e
151 ÷ 100 =
f
6.6 ÷ 10 =
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.1 Understanding place value
11 Draw a ring around the odd one out.
368.4 tenths 368.4 3684 hundredths
36.84 368 tenths and 4 hundredths
LE
Explain your answer.
Challenge
12 Write down the value of the digit 3 in each of these numbers.
72.3
b
eighty-four point zero three
M
13 Arun has these cards.
P
a
2
3
5
A
Write all the numbers he can make between 0 and 40 using
all four cards.
S
14 Write the missing numbers.
a
× 0.6 = 6
b
103 ÷
c
× 0.13 = 13
d
76 ÷
e
× 4.1 = 410
f
0.09 ×
= 1.03
= 7.6
=9
11
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
15 Look at this number line.
Write the number that goes in the box.
4
16 Heidi makes cakes for a snack bar.
a
5
LE
3
It costs $1.50 to make one chocolate cake.
How much does it cost to make 100 chocolate cakes?
b
It costs $19.00 to make 100 small cakes.
c
P
How much does it cost to make 10 small cakes?
It costs $0.75 to make a sponge cake.
M
How much does it cost to make 100 sponge cakes?
17 Arun and Marcus each write a decimal number between zero
and one.
A
Arun says, ‘My number has 9 hundredths and Marcus’s
number has only 7 hundredths so my number must be bigger.’
S
Arun is not correct. Explain why.
12
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Rounding decimal numbers
1.2 Rounding decimal numbers
Worked example 2
nearest
A number with 1 decimal is rounded to the nearest whole number.
What is the smallest number that rounds to 10?
b
What is the largest number that rounds to 20?
You can use a number line to help you.
10
11
19
20
21
P
9
LE
a
round
If the tenths digit is 5, 6, 7, 8 or 9 the number
rounds up to the nearest whole number.
9.5
b
20.4
If the tenths digit is 0, 1, 2, 3 or 4 the
number rounds down to the nearest
whole number.
M
a
Exercise 1.2
A
Focus
Here is part of a number line. The arrow shows the position
of a number.
S
1
33
34
35
Complete the sentence for this number.
rounded to the nearest whole number is
.
13
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
2
Zara has four number cards.
36.5
36.4
35.4
35.1
She rounds each number to the nearest whole number.
3
LE
Which of her numbers rounds to 36?
Draw an arrow to match each number to the nearest
whole number.
9.9
10.1
8.5
4
8
9.4
9
10
11.5
M
7
8.2
P
7.4
10.7
11
12
Write a number with 1 decimal place to complete each
number sentence.
A
rounds to 1
rounds to 10
Practice
Round these lengths to the nearest whole centimetre.
S
5
14
a
4.1 cm
c
10.1 cm
cm
cm
b
6.6 cm
cm
d
8.5 cm
cm
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1.2 Rounding decimal numbers
6
Here are three number cards.
9
1
5
A number with 1 decimal place is rounded to the nearest
whole number
a
What is the smallest number that rounds to 100?
b
What is the largest number that rounds to 100?
P
7
LE
Use each card once to make a number that rounds to 20 to
the nearest whole number.
Challenge
Write the letters of all the numbers that round to 10 to the
nearest whole number. What word is spelt out?
A
B
C
D
E
F
G
H
I
J
K
L
M
10.1
9.3
11.1
10.4
7.8
8.8
9.3
19.8
1.9
10.7
9.6
99.9
A
10.8
M
8
O
P
Q
R
S
T
U
V
W
X
Y
Z
1.8
9.2
10.6
9.1
10.5
7.9
9.5
19.9
16.2
10.9
20.3
8.9
9.4
S
N
15
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
1 The number system
9
Here are eight numbers.
19.4 19.9 21.1 20.4 20.3 19.7 21.4 10.1
Draw a ring round the number that these clues are describing.
The number rounds to 20 to the nearest whole number.
•
The tenths digit is odd.
•
The sum of the digits is less than 18.
•
The tens digit is even.
10 Rashid has these number cards.
1.4
2.4
3.4
4.4
P
He chooses two cards.
LE
•
He adds the numbers on the cards together.
He rounds the result to the nearest whole number.
M
His answer is 7.
Which two cards did he choose?
and
.
11 Arun rounds these numbers to the nearest whole number.
A
3.3 3.5 3.7 3.9 4.4 4.5 4.9
He sorts them into 3 groups and places them in a table.
Complete the table.
S
Rounds to . . .
16
Rounds to . . .
Rounds to . . .
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
Worked example 1
LE
2
2D shape and
pattern
equilateral triangle
Is this triangle isosceles?
scalene triangle
M
P
isosceles triangle
A
4 cm
5 cm
Measure the length of each side of the
triangle.
In an isosceles triangle, two sides have
the same length.
S
6 cm
The sides are all different lengths.
Answer: No, the triangle is not isosceles.
17
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
Exercise 2.1
Focus
2
M
How do you know?
LE
Is this triangle isosceles?
P
1
Draw a ring around the scalene triangles.
S
A
A
18
E
B
C
F
D
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
Label the angle at each vertex of these triangles ‘acute’,
‘obtuse’ or ‘right-angle’.
A
LE
3
P
B
A
Practice
M
C
Draw a scalene triangle using a ruler and pencil.
S
4
19
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
5
On each of these isosceles triangles, circle the angles that are the same
size. You could use tracing paper to compare the sizes of the angles.
B
D
A
M
C
P
LE
A
a
Write a sentence about the sides of an equilateral triangle.
S
6
b
20
Write a sentence about the angles of an equilateral triangle.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
Challenge
aDraw an isosceles triangle with two sides 6 cm long and the
other side shorter than 6 cm.
M
Draw an isosceles triangle with two sides 6 cm long and the
other side longer than 6 cm.
S
A
b
P
LE
7
21
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
Trace the triangles in this tessellating pattern.
Make templates of the triangles and complete the pattern.
S
A
M
P
LE
8
22
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.1 Triangles
This is a crossword is filled in with words about triangles.
Write the clues for the crossword.
1
4
t
e
s
2
i
3
a
s
s
n
i
o
g
d
s
e
l
a
e
c
LE
9
5
t
e
s
r
e
i
l
a
e
s
P
n
g
s
c
a
l
e
n
e
M
6
e
Across
A
4
6
Down
S
1
2
3
5
23
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
2.2 Symmetry
Worked example 2
line of symmetry
symmetrical
LE
Colour the squares to make a symmetrical pattern where
the dashed line is a line of symmetry.
M
P
Place a small mirror along the mirror line to
see what the complete symmetrical pattern
will look like.
A
Reflect the shaded squares across the
mirror line.
Squares that are next to the mirror line are
reflected to squares that are next to the
mirror line on the other side.
Squares that are one square away from the
mirror line are reflected to squares that are
one square away from the mirror line on the
other side.
S
Answer:
24
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.2 Symmetry
Exercise 2.2
Tip
Focus
Place a small mirror on the mirror line.
1
Check that the picture on the right
looks the same as the image in
the mirror.
LE
Spot the difference.
Draw shapes on the right side of the
picture to make it a reflection of
the picture on the left.
Zara says that she is thinking of a triangle with three lines
of symmetry. Draw a ring around the name of the triangle
that Zara is thinking of.
A
2
M
P
mirror line
scalene isosceles equilateral right-angled
Shade squares to make a pattern with one line of symmetry.
S
3
mirror line
25
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
4
Predict where the reflection of the triangle will be after it is
reflected over each of the mirror lines. Draw your predictions
using a ruler.
mirror line
LE
mirror line
mirror line
P
mirror line
Practice
Use a ruler to draw all of the lines of symmetry on these triangles.
A
5
M
Check your predictions by placing a mirror along each of the
mirror lines in turn. Look at how the triangle is reflected.
Tick the predicted reflections that are correct. Use a different
colour pencil to correct the predictions that are wrong.
S
A
C
26
B
D
E
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.2 Symmetry
6
Shade 5 squares in each of the empty quadrants to make a
pattern with two lines of symmetry.
LE
mirror line
Reflect the square, triangle, rectangle and pentagon over both
the horizontal and vertical mirror lines until you make a pattern
with reflective symmetry.
M
7
P
mirror line
S
A
mirror line
mirror line
27
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
Challenge
8
Choose four colours. Use coloured pencils or pens to shade in the
squares and half squares marked with a star (*).
Reflect the pattern over the mirror lines and colour all the squares
to make a pattern with two lines of symmetry.
LE
mirror line
Tip
9
M
P
You could rotate the
pattern so that the
mirror lines appear
vertical and horizontal.
mirror line
Sofia says that a right-angled triangle cannot have a line of symmetry.
Draw a triangle to show that Sofia is wrong.
S
A
a
b
28
rite the name of the triangle you have drawn and draw
W
the line of symmetry onto it.
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2.2 Symmetry
10 This is a chessboard.
aHow many lines of symmetry does a
chessboard have?
LE
bWhere could you place a counter on the
chessboard so that the chessboard still has
two lines of symmetry? Mark the place with a
blue circle.
cWhere could you place a counter on the
chessboard so that the chessboard has no
lines of symmetry? Mark the place with a
red circle.
P
dWhere could you place a counter on the chessboard
so that the chessboard has only one line of symmetry?
Mark the place with a green circle.
S
A
M
11 aColour two more squares so that this pattern has exactly
1 line of symmetry.
29
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
2 2D shape and pattern
P
LE
bColour two more squares so that this pattern has exactly
2 lines of symmetry.
M
cWhat is the fewest number of squares that have to be shaded
to make this pattern have exactly 4 lines of symmetry?
S
A
Shade the grid to show your solution.
30
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
LE
3
Numbers and
sequences
3.1 Counting and sequences
Worked example 1
linear sequence
Marcus counts back in eights starting at 50:
sequence term
P
50 42 34 ….
term-to-term rule
What is the first negative number Marcus says?
How do you know?
Another way to think about this question is:
M
Six jumps of 8 is 48 so after counting
back six lots of 8 Marcus says the
number 2.
10 is 2 more than a multiple of 8 and if you
count back in 8s you get to 10, then 2 and
then −6.
A
The next number Marcus says is −6.
Each term is 2 more than a multiple of 8.
Answer: −6
S
Exercise 3.1
Focus
1
What is the next number in this sequence?
8, 6, 4, 2, 0, …
How do you know?
31
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3 Numbers and sequences
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
P
LE
1
a
Colour the multiples of 7.
b
What do you notice?
c
If you continued the sequence would 100 be in it?
This pattern makes a sequence.
A
3
This is an 8 by 8 number grid.
M
2
S
You count the squares in each row of the staircase.
The sequence starts 1, 3, 5, …
a
32
Complete the table.
Row number
1
2
3
Number of squares in row
1
3
5
4
5
6
7
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3.1 Counting and sequences
Continue the sequence to show your results.
1, 3, 5,
c
,
,
,
,
What is the term-to-term rule for the sequence?
Practice
4
,
LE
b
A sequence starts at 19.
9 is subtracted each time.
What is the first number in the sequence that is less than zero?
Zara counts back in steps of equal size.
P
5
Write the missing numbers in her sequence.
,
, 34
aHere are some patterns made from sticks.
Draw the next pattern in the sequence.
M
6
, 61, 52,
1
3
Complete the table.
A
b
2
Pattern number
Number of sticks
1
S
2
3
4
c
Find the term-to-term rule.
33
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3 Numbers and sequences
d
7
How many sticks are in the 10th pattern?
A sequence starts at 400 and 90 is added each time.
400, 490, 580, 670, …
LE
What is the first number in the sequence that is greater than 1000?
Challenge
a
1
2
3
Complete the table.
M
b
Draw the next pattern in the sequence.
P
8
Pattern number
Number of hexagons
1
2
A
3
4
Find the term-to-term rule.
S
c
d
34
How many hexagons are in the 8th pattern?
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3.1 Counting and sequences
9
Sofia counts in threes starting at 3.
3, 6, 9, 12, ….
Zara counts in fives starting at 5.
5, 10, 15, 20, ….
LE
They both count on.
What is the first number greater than 100 that both Sofia and Zara say?
P
Explain your answer.
10 Zara writes a sequence of five numbers.
The first number is 2.
M
The last number is 18.
Her rule is to add the same amount each time.
Write the missing numbers.
2,
,
,
, 18
A
11 Arun writes a sequence of numbers.
His rule is to add the same amount each time.
Write the missing numbers.
,
, 14
S
−1,
35
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3 Numbers and sequences
3.2 Square and triangular numbers
Worked example 2
spatial pattern
square number
The sequence starts 1, 3, 6 …
triangular number
LE
Look at these patterns made from squares.
a
Draw the next term in the sequence.
b
Write the next three numbers in the sequence.
a
P
10, 15, 21
M
b
Each term has an extra column that is one
square taller.
The sequence 1, 3, 6, 10, 15, 21 … is the
sequence of triangular numbers
Exercise 3.2
A
Focus
Draw the next term in this sequence.
S
1
What is the mathematical name for these numbers?
36
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3.2 Square and triangular numbers
2
Draw the next term in this sequence.
3
Write the next two terms in these sequences.
a
1, 4, 9, 16, 25,
b
1, 3, 6, 10,
,
,
P
Practice
This pattern is made by adding two consecutive
triangular numbers.
M
4
LE
What is the mathematical name for these numbers?
1
a
1+3=4
3+6=9
6 + 10 = 16
A
numbers.
What are the next two numbers in the sequence?
2
Find the value of 8 .
S
5
Remember that
consecutive
means next to
each other.
Look at the total in each term and complete this sentence.
The terms in the sequence are the
b
Tip
37
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3 Numbers and sequences
Solve these number riddles.
b
c
The number is:
•
a square number
•
a multiple of 3
•
less than 25
LE
a
The number is:
•
a square number
•
an even number
•
a single digit number
The number is:
•
a square number
•
a 2-digit number
P
6
the sum of the digits is 13
7
Zara has a lot of small squares all equal in size.
M
She uses the small squares to make big squares.
She can use 9 small squares to make a big square.
Which of these numbers of squares could Zara use to
make a big square?
46
64
14
4
24
100
60
66
18
81
9
90
S
A
a
b
Can Zara make a big square using 49 small squares?
Explain how you know.
38
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3.2 Square and triangular numbers
Challenge
Write the missing numbers in the table.
Product of
two numbers
1 more than
the product
1×3=3
4
2×4=8
9
3 × 5 = 15
×
2
3 =9
2
=
2
=
2
=
=
Find two square numbers to make each of these calculations correct.
a
c
+
= 10
b
+
= 20
+
= 40
d
+
= 50
+
= 80
f
+
= 90
+
= 100
A
e
M
9
2
2 =4
P
4×6=
Equivalent
square number
LE
8
g
S
10 Find the 10th term in this sequence.
1, 3, 6, 10, 15,
39
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3 Numbers and sequences
3.3 Prime and composite numbers
Worked example 3
composite number
Here are four digit cards.
9
2
multiple
LE
3
factor
1
prime number
Use each card once to make two 2-digit prime numbers.
and
The prime numbers are:
Start by writing a list of prime numbers
Answer: 13 and 29
Choose two of these numbers that satisfy
the criteria.
P
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, …
There is more than one correct answer.
M
You could also have chosen
31 and 29
or
19 and 23
S
A
You are specialising when you choose a number and
check whether it satisfies the criteria.
40
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3.3 Prime and composite numbers
Exercise 3.3
Focus
1
Here is a grid of numbers.
13
5
8
15
3
1
11
15
1
11
19
7
6
9
17
9
15
12
12
5
16
4
14
P
2
Write each number in the correct place on the diagram.
M
2
14
LE
Shade all the prime numbers. What letter is revealed?
Composite
numbers
S
A
Prime
numbers
3
2, 3, 4, 5, 6
Complete this sentence.
A number with only two factors is called a
number.
41
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3 Numbers and sequences
Practice
4
Here is a grid of numbers.
Draw a path between the two shaded numbers that passes
only through prime numbers.
a
4
6
8
13
3
23
29
71
65
1
51
45
7
5
15
92
25
1
2
31
37
16
14
11
P
5
2
LE
You must not move diagonally.
Find two different prime numbers that total 9.
b
=9
M
+
Find two different prime numbers that total 50.
+
Show that 15 is a composite number.
A
6
= 50
Challenge
Use the clues to find two prime numbers less than 20.
S
7
Prime number 1: Subtracting 4 from this prime number gives
a multiple of 5.
Prime number 2: This prime number is one more than a multiple
of 4, but not 1 less than a multiple of 3.
Prime number 1 is
42
Prime number 2 is
Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
3.3 Prime and composite numbers
Multiples of 6 are shaded on this grid.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
LE
8
Ingrid looks at the grid and says, ‘One more than any multiple
of 6 is always a prime number.’
Ingrid is wrong.
9
P
Explain how you know.
Arun chooses a prime number.
He rounds it to the nearest 10 and his answer is 70.
M
Write all the possible prime numbers Arun could choose.
A
10 Write each whole number from 1 to 20 in the correct place on
this Venn diagram.
S
Triangular
numbers
Prime
numbers
Even
numbers
43
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4
Averages
average
Worked example 1
median
What is the mode of these areas?
2
LE
4.1 Mode and median
2
2
2
2
2
mode
2
45 cm , 36 cm , 18 cm , 36 cm , 21 cm , 45 cm , 36 cm
2
One area is 18 cm
Count how many there are of each area.
2
2
Three areas are 36 cm
2
Two areas are 45 cm
The mode is the area that appears the
most often.
P
One area is 21 cm
2
M
Answer: The mode is 36 cm .
Exercise 4.1
Focus
This box contains some numbers.
A
1
a
How many 3s are in the box?
How many 4s are in the box?
c
What is the mode of the
numbers in the box?
S
b
44
3
4
343
4
3
4
3
4
3
3
4
3
4
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4.1 Mode and median
2
a
Write these numbers in order from smallest to greatest.
117 109
b
120
118
121
Draw a rind around the middle number.
3
LE
What is the median of the numbers?
Complete the sentences about this set of numbers.
20 21 22 23 24 24 25
The mode (most frequent) is
b
The median (middle) is
.
.
P
This is how many sweets Tom found in each packet.
M
4
a
11
11
11
12
13
14
14
A
Complete the sentences about the average number of sweets
in a packet.
a
The mode is
b
The median is
.
.
S
Practice
5
Explain in words how to find the median of a set of data.
First
Then
45
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4 Averages
6
Tick the sets of numbers that have a mode of 8 and a
median of 9.
A 10, 7, 9, 8, 11, 8, 12
LE
B 8, 9, 8, 10, 8, 12, 8
C 10, 8, 8, 9, 10, 9, 10
D 11, 8, 8, 7, 9, 10, 7, 10, 10, 8, 8, 11, 11
Write your own set of numbers that has a mode of 8 and a
median of 9.
8
P
7
Seven children reviewed a book about dinosaurs.
They gave the book a score out of 5.
M
These are the scores.
Dinosaurs
4 1 3 5 5 1 1
What is the mode of the scores?
A
a
What is the median of the scores?
c
Would you use the mode or the median to describe the
scores? Why?
S
b
46
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