CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
Workbook answers
1 Numbers and the number system
d
Exercise 1.1
Focus
1
a
b
2
28, 34
3
33 circled
4
2020, 2031, 2042, 2053, 2064
5
a
1, −2, −5, −8
c
990, 955, 920, 885
add 11
110
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
(multiply each counting number by itself –
square numbers)
Exercise 1.2
Focus
b
−3, −1, 1, 3
Practice
1
Arrow pointing to −5.
2
a
5° C
b
−3 ° C
3
a
−3
b
0
c
−2
d
−9
a
−2 circled
difference: 4
4
6
750 and 900 circled
b
–1 circled
difference: 2
7
No. All terms are 1 more than a multiple of 7,
and 77 is a multiple of 7.
c
4 circled
difference: 8
8
302
9
1001, 1006, 1011, 1016, 1021, 1026, 1031,
1036, 1041
Practice
5
−7 and 4
6
10 1 1 and 96
−10
−4 −1
0
−4 and 12
10
14
20
30
40 °C
2
Challenge
7
a
11 15
8
7 ° C (Do not accept 7)
Add 5 to previous term (you add one more
each time).
12 24 and 44
Challenge
13 alinear first term 5 term-to-term rule
‘add 4’ 21 and 25
b
c
–5
−10, 10 and 15
–3 –2 –1 0 1
10 9 ° C
non-linear first term 3 term-to-term
rule ‘add 8 then one less each time’ 29 and 33
11 19 ° C
non-linear first term 3 term-to-term
rule ‘double’ 48 and 96
13 No, together with an explanation that the
sequence continues −10, −7, −4, −1, 2 . . .,
and 0 is not included.
14 Examples (other answers are possible):
1
9
b
a
1, 3, 6, 10
(add one more each time)
b
6, 13, 20
(add 7)
c
3, 6, 9, 12, 15
(add 3)
12 −40 and 80
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
Exercise 1.3
Challenge
Focus
11 Nine hundred and seventy-five thousand
three hundred and ten
1
One thousand, four hundred and fifty
2
Circle 5005
3
April
4
305 469 = 300 000 + 5000 + 400 + 60 + 9
5
Fourteen thousand, three hundred and
fifty two, 14 352
6
6
12
600
D
2
I
T
H
× 10
3
E
I
I
G
4
T
5
R
G
× 10
60
× 100
1
S
E
V
H
Z
E
E
N
T
U
R
Y
R
32
6
× 10
320
× 100
3200
13 a
× 10
d
÷ 10
b
30
100
e
304 000
14
8000
80
100
35 × 10 = 350
Exercise 2.1
÷ 10
Focus
1
÷ 10
800
÷ 100
c
2 Time and timetables
140
÷ 100
O
35 800
14 350 ÷ 10
1400
F
2
÷ 10
3
Practice
7
Nine thousand, nine hundred and thirty
8
130 030
9
a
A
b
C
c
D
d
C
e
D
f
B
4
a
300
b
240
c
21
d
24
e
2
f
10
Half past four – 04:30
4 o’clock – 04:00
half past three – 03:30
a 3 weeks
b
8 years
c
21 months
9:15 circled
10 D
2
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
Exercise 2.2
5
eight fifty a.m.
or
ten to nine
11
10
12
1
Focus
2
9
3
8
three thirty p.m.
or
half past three
7
6
5
11 12 1
10
2
9
3
8
7 6 5
4
afternoon
eight thirty a.m.
or
half past eight in
the morning
6
11
10
12
1
2
9
3
8
7
6
5
4
Joe is wrong. He should add 12 to the hours,
not the minutes.
Practice
7
8
1
a
25 minutes
c
35 minutes
2
a
3
4
b
50 minutes
40 minutes
b
17 minutes
a
10 minutes
b
30 minutes
c
train 2 or 10.20 a.m. train
Practice
4
a
15 minutes
c
32 minutes
5
a
35 minutes
6
14:43
7
2 hours
b
20 minutes
b
3.55 p.m.
Challenge
8
8.35 a.m. or 25 minutes to nine
9
a
12:45
b
a
104
b
630
10 5 times
c
62
d
72
A
5.30 p.m.
B
3.25 a.m.
C
5.15 p.m.
D
10.20 a.m.
11 Missing times (from the top):
11.13 a.m.
10.35 a.m. 11.37 a.m.
10.53 a.m. 11.55 a.m.
9
quarter past 7 in the evening — 19:15
twenty past ten in the morning — 10:20
half past two in the afternoon — 14:30
quarter to eleven in the morning — 10:45
10 a 10:00
b 18:00
c
23:00
d
08:00
11 15:45 → 16:45 → 17:45 → 18:45 → 19:45
Challenge
15 minutes
3 Addition and
subtraction of whole
numbers
Exercise 3.1
Focus
12 16:10 07:15 21:45
13 a
3.10 p.m.
b
11.55 p.m.
c
11.10 a.m.
d
3.05 a.m.
14 08:10
15 15:25
1
63
2
700
3
46 + 54 = 100
4
513
16 Sara (85 secs), Petra (88 secs), Ingrid (91 secs),
Milly (94 secs), Neve (100 secs)
3
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
5
30
40
14
10
30
10
50
20
40
60
20
20
Practice
6
13
7
1250
8
22
9
50
15
30
3
1
20
40
5
5
4
3
1
2
4
2
56
The numbers at the end of each line are
­interchangeable.
36
Exercise 3.2
Focus
63
+20
1
37 + 24 = 61
+3
37
57
100
+1
60
61
+40
37
10 Δ =
74 + 38 = 112
and
= 4, Δ = 1 and
= 3,
Δ = 2 and
= 2, Δ = 3 and
= 1,
Δ = 4 and
=0
11 16 + 24 or 14 + 26
74
–2
112
2
56 – 25 =
31
Challenge
–20
–5
31
–20
65 – 19 = 46
65
+1
45
4
56
36
12 8
13 7972
114
46
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3
749 =
700 +
40
+
9
568 =
500 +
60
+
8
1200 +
100
+
17
4
a
b
150
Exercise 3.3
Focus
= 1317
1
H
2
16 42 106 even
3
odd + odd =
14
even + even =
Practice
5
72
31
13
60
41
18
31
23
30
25
4
106
17
95
48
37
5
20
32
1
1
19
7
a
8
594
8
6
4
9
8
1
4
Add the ones
7
0
8
0
0
4
Add the tens
Add the hundreds
762
b
324
6
True
Not true
7

Leroy adds two odd numbers and an even
number. Odd + odd + even = even and 33 is odd.
odd − odd = even so the statement is never true.
Do not accept one numerical answer such
as 13 − 9 = 4 and 4 is even.
Challenge
9
16
41
90
248
511
1308
even, even, odd
10 true, false, true, false
11 The sum of three odd numbers is 22. ✗
Challenge
9
17 43 111 odd
8
7
1
1
2
5


+
Never true. Counter example: 1 + 3 + 5 = 9
which is odd (odd + odd = even,
then even + odd = odd)
Practice
47
28
odd
aAlways true, for example, 1 + 3 = 4,
25 + 13 = 38 (odd + odd = even)
b
46
29
67
6
even
odd + even =
150, 250 and 350 or 50, 250 and 450
10 74 + 26 or 76 + 24
12 Sometimes true.
4 + 6 + 8 + 10 = 28
2 + 4 + 8 + 12 = 26
28 ÷ 4 = 7
26 ÷ 4 = 6 remainder 2
11 891
5
12 a
61 − 34 = 27
b
13 a
Largest number 1395
b
smallest number 603
615 − 151 = 464
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
4 Probability
Exercise 4.1
5 Multiplication,
multiples and factors
Focus
Exercise 5.1
1
2
3
A dice lands on an even number.
No chance
You will change into a fish tomorrow.
Poor chance
You will breathe today.
Even chance
You will turn left today.
Good chance
You will become famous tomorrow.
Certain
Focus
1
Multiples of 10 are coloured twice because
they are multiples of 2 and multiples of 5.
2
×
3
4
5
There is a good chance of taking a black ball
from the bag.
2
6
8
10
There is a poor chance of taking a white ball
from the bag.
There is no chance of taking a red ball from
the bag.
Answer depends on the outcomes of the
learners’ investigations.
4
12
16
20
6
18
24
30
4
8
Any number except 1 to 6.
3
1
Practice
4
a
False
b
True
c
True
d
False
e
True
f
True
6
Table values depend on the outcomes of
learners’ investigations.
a
There is no chance of getting 11.
b
It is certain to be a number less than 11.
c
There is a poor chance of getting a 2.
Challenge
7
6
8
4
5
b
Example: It is certain they will take
a T-shirt from the suitcase.
c
Example: There is a poor chance of taking
a white T-shirt from the suitcase.
d
Example: There is a good chance of taking
a T-shirt that is not white from the suitcase.
e
Example: There is an even chance of
taking a black T-shirt.
8
EDBCA
9
Answers will vary from learner to learner.
9
7
9
0
1
2
4
1 and 18, 2 and 9, 3 and 6.
36
1
2
3
aExample: There is no chance of taking
a red T-shirt from the suitcase.
5
4
3
6
1
8
4
6
C
3
8
2
Learners’ own sentences.
5
2
4
18
12
9
36
45
1
6
3
15
45
5
9
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Practice
13
×
3
7
9
4
2
5
15
35
45
20
10
6
18
42
54
24
12
3
9
21
27
12
6
8
24
56
72
32
16
4
12
28
36
16
8
×
3
5
7
6
10
3
9
15
21
18
30
5
15
25
35
30
50
7
21
35
49
42
70
6
18
30
42
36
60
10
30
50
70
60
100
6
15
5
6
30
3
63
7
2
a
c
<
>
8
7
17
9
49
6
36
27
5
7
42
9
7
35
4
37
56
6
47
57
7
b
d
=
=
67
77
8
87
97
10
1
5
25
11
2
10
16
13
Start
9
4
6
17
14
18
20
3
15
7
14 24 + 39 or 29 + 34
15
11 1, 2, 3, 4, 6 and 12 circled
Challenge
12
5
30
6
24
35
4
7
7
9
5
12
21
45
63
4
7
2
4
8
5
6
2
3
7
7
1
3
2
6
3
9
5
20
28
1
20
3
4
Exercise 5.2
Focus
45
36
16 2 and 6
1
30
9
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
2
13
39
3
6 2D shapes
34
65
15
68
5
2
238
Exercise 6.1
7
14
Focus
1
14
42
3
Enter
5
56
12
105
4
21
15
63
3
3
156
4
522
5
1 × 36 = 36 2 × 18 = 36 3 × 12 = 36
Practice
6
a
left-hand side: 9 × 2 × 5 = 18 × 5 = 90
right-hand side: 9 × 2 × 5 = 9 × 10 = 90
right-hand side is better
b
left-hand side: 2 × 5 × 7 = 10 × 7 = 70
right-hand side: 2 × 5 × 7 = 2 × 35 = 70
2
a
left-hand side is better
7
a
b
8
300 × 8, 600 × 4, 400 × 6 and 800 × 3 circled
9
120 and 441
200
10 250 × 3
150 × 5
c
414
375 × 2
684
125 × 6
b
Challenge
11 Either girl with an appropriate explanation.
for example:
Amy because I prefer to find factors of the
larger number
6 × 15 = 15 + 15 + 15 + 15 + 15 + 15 = 90
12 a
636
b
1278
c
3584
13 702
14 9 (396 × 9 = 3564)
15 763 × 8 = 6104
8
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
•
•
•
c
7
is a parallelogram
is a rectangle
has 2 lines of symmetry.
Completed tessellating pattern
Exercise 6.2
Focus
1
3
Drawing showing tessellating triangles.
14 triangles tessellate in the space.
Four lines of symmetry drawn: vertical line
down the centre, horizontal line through the
centre and two diagonal lines corner to corner.
2
Practice
4
a
The shapes are:
Triangle, square, triangle, quadrilateral
­(parallelogram)
The new shape has 4 sides and 4 vertices.
It has one pair of parallel sides.
It is a quadrilateral (trapezium).
b
c
5
3
The shapes are:
Practice
Triangle, triangle, triangle, square
4
The new shape has 6 sides and 6 vertices.
It has one pair of parallel sides. It is a
hexagon.
Two diagonal lines of symmetry drawn on
the tile.
5
Octagon
Number of lines of symmetry
The shapes are:
A
8
Triangle, triangle, quadrilateral
(parallelogram)
B
4
C
0
The new shape has 6 sides and 6 vertices.
It has two right angles. It is a hexagon.
D
2
Completed tessellating pattern.
6
The horizontal line circled.
Challenge
Octagons and squares.
7
Challenge
6
8
Any four from:
• has 4 sides
• has 4 vertices
• has two pairs of parallel sides
• has 4 right angles
• is a quadrilateral
9
Four lines of symmetry drawn: horizontal,
vertical and two diagonal lines.
9
a
Diagonal lines of symmetry drawn on.
b
4
c
No, for example, a rectangular pattern can
have a horizontal line of symmetry and
a vertical line of symmetry, but it cannot
have a diagonal line of symmetry.
a
No more lines of symmetry drawn.
b
2
a
No lines of symmetry drawn.
b
0
10 a
Octagon. 8 lines of symmetry drawn.
b
Pentagon. 5 lines of symmetry drawn.
c
Decagon. 10 lines of symmetry drawn.
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CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
7 Fractions
5
Exercise 7.1
6
12 cards
Focus
7
7 cm
1
8
8
9
1
of 15
5
2
3
4
3
2
is greater than 2
4
6
Practice
This gives the answer 3, but all the other
calculations give the answer 2.
10 6 squares, 3 squares, 2 squares and 1 square.
Challenge
2
is less than 2
4
3
In order: 2
6
11 15 balloons
2
4
12 10 beads are blue. There are 20 beads
2
3
1
altogether. 2 of 20 = 10
Practice
4
B and E
5
a
6
1
>1> 1
4
6
12
13 1 of 16 = 4
b
1
litre
4
15 Show that 1 of $36 = $12 and 1 of $60 = $15
3
2
> 2
3 12
1
is the smaller fraction but it is a quarter of a
4
larger amount of money.
Same amount of space covered (equivalent).
8
4
3
and
5
10
8 Angles
9
Sometimes. If a shape is split into four equal
parts it is split into quarters.
Exercise 8.1
Exercise 7.2
Focus
1
Ring around any 3 counters.
2
4
3
1
of 20 – Answer equal to 10
2
Focus
1
2
a
Angle B circled.
b
Angle A circled.
c
Angle B circled.
d
Angle A circled.
e
Angle A circled.
f
Angle B circled.
a
B circled.
b
D circled.
c
C circled.
1
of 60 – Answer more than 10
5
Practice
1
of 32 – Answer less than 10
4
3
1
of 30 – Answer equal to 10
3
4
so it is better to have $15.
7
4
1
of 24 = 6
4
14 20
Challenge
10
1
of 20 = 5
4
4
3
litre 4
2
<2
12
6
7 and 8
a
Angle A circled.
b
Angle A circled.
c
Angle B circled.
d
Angle B circled.
e
Angle A circled.
f
Angle A circled.
$8
Cambridge Primary Mathematics 4 – Wood & Low © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
4
Learners’ answers and explanations.
Challenge
5
aAngle of between 70 and
110 degrees drawn.
b Angle of between 20 and
60 degrees drawn.
c Angle of between 120 and
150 degrees drawn.
6
7
Challenge
Any acute-angled triangle.
b
Any right-angled triangle.
c
Any obtuse-angled triangle.
d
Angles in parts a to c labelled.
a
obtuse
b
acute
d
obtuse
e
acute
c
acute
6
B, D, A, E, C
Exercise 8.3
7
C, E, A, B, D
Focus
8
Learners’ explanations.
1
90 degrees
2
a
45 degrees
b
130 degrees
c
95 degrees
d
30 degrees
e
160 degrees
Exercise 8.2
Focus
1
2
f p m e o b
w z q s m a
t v c t o a
s w o i f r
u e m m e i
d x p a q g
z a a t k h
k g r e a t
g d e g r e
v j a n g l
t u s
l l e
c u t
a w d
c k v
c v z
a j v
e r h
e s i
e b h
e
r
e
a
v
n
h
g
g
n
acute
angle
compare
degrees
estimate
greater
obtuse
right
smaller
3
Obtuse
4
5
Acute
Acute
Obtuse
6
Practice
4
A – 92 degrees, B – 169 degrees, C – 14
degrees, D – 47 degrees, E – 132 degrees
Practice
a, b and d circled.
3
All angles in ‘Acute angles’ box are less than
90 degrees.
All angles in ‘Obtuse angles’ box are less than
180 degrees, but more than 90 degrees.
start
120
45
60
10
50
80
100
130
165
35
65
20
50
10
100
70
80
150
100
170
175
130
145
160
60
30
70
40
20
70
20
40
20
160
70
150
110
135
150
110
50
120
40
70
165
10
60
100
160
110
30
155
125
105
170
60
30
70
60
30
40
80
145
end
120
a
4 right angles
b
360 degrees
c
3 turns
d
270 degrees
a
Estimate between 5° and 25°.
b
Estimate between 91° and 110°.
c
Estimate between 150° and 170°.
d
Estimate between 35° and 55°.
e
Estimate between 70° and 85°.
f
Estimate between 125° and 145°.
Learners’ answers and explanations.
Challenge
7
a
8
For every right angle there is 90 degrees of
turn.
9
a
Angle between 85° and 95° drawn.
b
Angle between 37° and 53° drawn.
c
Angle between 10° and 30° drawn.
d
Angle between 127° and 143° drawn.
e
Angle between 95° and 110° drawn.
f
Angle between 150° and 170° drawn.
5
11
a
3 right angles
b
90 degrees
Cambridge Primary Mathematics 4 – Wood & Low © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 4: TEACHER’S RESOURCE
9 Comparing, rounding
and dividing
Exercise 9.2
Focus
1
24 divided by 2 3 4 5 6 7 8 9 10
Remainder
Exercise 9.1
4
1
a
2
85 94 86
3
a
5650
5656
6505
6550
6555
2
There is no remainder when 24 is divided by 2,
3, 4, 6 and 8.
There is the same remainder when 24 is
divided by 5 and 10 or any other relevant
observation.
13 jugs
b
1234
1432
2134
2341
2413
3
a
4
a
8216 > 8126
6031 > 6013
4
16 packs
5
6162, 6164, 6166, 6168
5
16 and 8
Focus
b
3510
c
3490
b
4660
Practice
6
a
b
7
Number Rounded
to the
nearest
thousand
Rounded
to the
nearest
hundred
Rounded
to the
nearest
ten
4155
4000
4200
4160
4505
5000
4500
4510
5455
5000
5500
5460
3500
c
3000
5000
b
13
Practice
6
7 children
7
8 boxes
8
4 photos
9
85
Challenge
8
3170 and 3180
11 10
9
Learners’ own numbers.
12 Mercury
11 a
4000
13
b
30 000
c
500 000
7
12
21
Challenge
12 a
D A B C
17
E
1500 1600 1700 1800 1900 2000 2100
b
12
10 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6
(numbers in any order)
10 8800 metres
855 900 < 897 910
98 150 > 91 899
500 779 < 686 400
259 420 > 100 192
36
51
18
45
CE
Isaac Newton Carl Gauss Leonhard
Euler Ada Lovelace Alan Turing
13 455 119 > 455 110
12
0 0 0 4 0 3 0 6
15
6
30
10
The number in the outer circle is the number
in the inner circle divided by 3.
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3
3
9
15
15
45
75
35
85
7
60
17
12
0
The number in the outer circle is the number
in the inner circle divided by 5
14
4
Coconuts cost $2 each.
How many coconuts
can be bought for $15?
A minibus holds 12
people. 50 people go on
an outing. How many
minibuses are needed?
2
3
4
5
6
7
8
Question: How many seeds are there in
a packet?
I will count how many seeds are in
each packet.
I will record the number of seeds in a table or
dot plot.
Round up
14 peaches are put in
bags. Each bag holds
4 peaches. How many
full bags are there?
1
Number of green sweets in the packets
Practice
5
a
Round down
15 1 and 60, 2 and 30, 3 and 20, 4 and 15, 5 and
12, 6 and 10 (numbers in any order).
Number of cars
How many hours?
10
3
11
2
12
0
13
5
14
2
b
10 Collecting and
recording data
Exercise 10.1
Focus
1
2
13
Number of birds
How many days?
3
2
4
3
5
4
6
2
7
2
8
1
a
1
b
6
10
11
12
13
14
Number of cars each hour
6
7
c
6
a
0
b
d
Individual answers.
14
c
5
How many cubes can my friends hold in
one hand?
People I will use: names of friends.
Table completed individually.
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Challenge
8
a
b
3 6 9 12 15 18 21 24 27 30
= = = = = = = = =
4 8 12 16 20 24 28 32 36 40
c
2 4 6 8 10 12 14 16 18 20
= = = = = = = = =
3 6 9 12 15 18 21 24 27 30
2
a
1 5 2 3
, , ,
3 8 3 4
b
1 2 5 7
, , ,
2 3 6 8
3
a
<
b
<
Number of seeds Number of packets
21
1
22
3
23
4
24
3
25
0
26
1
Practice
4
b
5
H and P
1
2
0
1
4
21
22
23
24
25
0
d
f
Answers could include:
e
7
>3
8
4
Challenge
People I will use: Names of friends.
Equipment I will need: Cubes, stopwatch (or
other device for measuring one minute).
Plots will vary. Axis should be labelled
‘Number of cubes in the line’.
11 Fractions and
percentages
Exercise 11.1
Focus
14
c
1
2
3
> 1 4 > 1 5 > 1 6 > 1 7 > 1
8
4
8
4
8
4
8
4
8
4
8
1 2 3 4 5
= = = = = 6 = 7 = 8 = 9 = 10
2 4 6 8 10 12 14 16 18 20
3 6 9
= =
4 8 12
2 4 6
= =
3 6 9
3
= 6 = 30
10 20 100
Question: How many cubes can my friends
connect together in a line in one minute?
a
5
6
7
4
It is easier in a dot plot to see which
categories have the most and least
number. It is easier in a dot plot to count
the number that is more or less.
1
b
5
> 2 6 > 2 7 > 2
8
4
8
4
8
4
Dot plot
9
2
3
a
26
21
2
5
6
Number of packets
c
3
4
1
2 4 10
= =
5 10 25
5 10 20
= =
6 12 24
9
2
and 10 are equivalent so 9 is the odd
3
15
12
2
10
one out. Or and have even numbers as
3
15
numerators so 9 is the odd one out.
12
Other answers are possible.
10 Answers such as:
= 20 and
= 30
= 40 and
= 60
= 60 and
= 90
= 80 and
= 120
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11 5 circled
8
12 Yes. Sevenths are greater than ninths because
the whole is divided into a smaller number of
parts.
Exercise 11.2
1
1
34% and 25%
2
Shade: a 50 squares b 75 squares c 10
squares
3
a
35%
b
36%
d
14%
e
67%
c
Practice
Shade: a 55 squares b 48 squares
c 1 square
5
67%
80 %
75%
25%
20%
50%
33%
50%
6
Exercise 12.1
Focus
Focus
4
12 Investigating
3D shapes and nets
20%
Challenge
7
50% 25% 75% 50%
8
80 learners
9
15%
10 a
Shade 10 squares
b
Shade 10 squares
72%
Arrow from ‘face’ to any flat surface on
the shape.
2
Arrow from ‘edge’ to any line on the shape.
Arrow from ‘vertex’ to any point where three
lines meet on the shape.
a 12
b 8
c 6
3
a
4
Pentagon, pentagon, rectangle, rectangle,
rectangle, rectangle, rectangle
b
Triangle
Rectangle
Practice
5
A tetrahedron has: 4 faces, 6 edges and
4 vertices.
6
B, D and E ticked
7
Any pyramid
8
Cone or cylinder
Challenge
9
Shape
Number
of faces
Number
of
edges
Number
of
vertices
Cuboid
6
12
8
Triangular
prism
5
9
6
Pentagonbased
pyramid
6
10
6
Hexagonal 8
prism
18
12
Squarebased
pyramid
8
5
5
10 Ticks beside triangular prism, tetrahedron and
square-based pyramid.
11 For example, triangular prisms and trianglebased pyramids both have some faces that are
triangles. They are different because a triangular
prism has 5 faces and a triangle-based pyramid
has 4 faces.
15
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Exercise 12.2
7
445 + 55 or 455 + 45
Focus
8
1
1
Net B circled
Challenge
2
Net C circled
9
3
Pentagon-based pyramid circled
+
Practice
4
Square-based pyramid
5
Net C circled
6
A – cone
B – cube
C – cylinder
7
9
1
9
3
7
4
2
12 13 more girls
A – tetrahedron
B – square-based pyramid
C – cuboid
D – heptagonal prism
Possible answers include:
•
9
11 605 + 197 = 802
Octagon-based pyramid
•
4
10 Possible solutions: 987 − 654 = 300 and
975 − 864 = 111
Challenge
8
5
13 545 + 355 = 900
86 + 814 = 900
791 + 109 = 900
437 + 463 = 900
Exercise 13.2
Focus
1
The net has only 5 faces, but a
pentagon-based pyramid has 6 faces.
1
4
2
2
5
The net is missing one triangular face.
10 Octagonal prism
5
6
3
5
13 Addition and
subtraction
2
8
4
5
Exercise 13.1
Focus
1
474 boys and girls
2
a
3
943 − 349 = 594
4
47 children
66
b
Practice
5
6
16
a
127 + 212 = 339 km
b
188 + 334 = 522 km
c
6
8
3
4
1
6
1
5
a
8
6
b
4
8
c
8
12
d
2
12
4
a
6
8
b
5
8
5
3
8
3
104
1
4
156
101
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Practice
6
14 8
9
Accept correctly simplified answers or
mixed numbers.
15
21
20
8
6 12
7
4
9
9
20
4
13 7
3
8
6
2
20
3
3 3
5
9
7
8
3 5
10
9
8
7
7
9
Focus
1
5
9
5
9
6
9
1 3
+ and 2 + 2
3 3
3 3
5
9
b
5
7
11 4 2 5
4
9
4
a
5 cm2
7 cm2
c
12 cm2
b
18 cm
c
16 cm
a
6
65 m
7
Four shapes drawn – each with an area of
9 cm2.
8
a
16 cm
6 cm2
Challenge
9
b
8 cm2
c
14 cm2
146 mm (allow 144 mm to 148 mm)
10 16 cm2
11 Four shapes with curved sides – each with
estimated area 6 cm2.
1 6
+ 2 + 5 3 + 4
3 3
3 3
3 3
12 82 m
13 aAny pair of fractions with a sum of 7 ,
8
for example 1 and 6
8
b
b
5
4
3 9
9
9
12
Accept equivalents.
8
Any pair of fractions with a difference of
3
, for example 4 and 1
8
8
8
17
Three shapes added to the grid – each 8 cm2.
3
1 4
3
8
6
3
6 7
5
7
9
12
3
Practice
Challenge
7
2
Line 1 = 4 cm
Line 2 = 2 cm
Line 3 = 4 cm
Line 4 = 2 cm
Perimeter = 12 cm
52 m
3
9
4
9
10 a
5
20
Exercise 14.1
2
9
8
9
9
7
20
14 Area and perimeter
7
5
8
12
20
Exercise 14.2
Focus
1
a
b
c
Rectangle
Correctly labelled sides of 2 cm and 7 cm.
18 cm
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2
3
a
3
b
12, 15, 18
c
1 cm
d
18 cm2 circled
a
c
e
5
b 5 cm
4
d 4 cm
The length of the rectangle is the same as
the number of squares in a row.
15 Special numbers
Exercise 15.1
Focus
1
Practice
4
Rectangle drawn with sides 8 cm and 5 cm.
5
Perimeter = 26 cm
a 8
6
7
b
2
32 cm2 circled
There are 7 squares in each row and 3 squares
in each column.
The rectangle is 7 cm long and 3 cm wide.
3 rows of 7 makes 21 squares altogether.
The area of the rectangle is 3 multiplied by 7.
The area of the rectangle is 21 cm2.
a Area = 24 m2 , perimeter = 22 m
Area = 80 mm2, perimeter = 36 mm
d Area = 49 cm2, perimeter = 28 cm
Perimeter = 18 cm
9
a
Missing sides are 3 m and 1 m
Perimeter = 8 m
b
Missing sides are 9 km and 6 km
Perimeter = 30 km
c
Area = 20 cm
b
−8 ° C, −4 °C, 3 °C, 7 ° C
c
−10 ° C, −2 ° C, 2 ° C, 7 ° C
a
−15, −10, −5, 0, 5, 10
b
The numbers go up by 5 each time.
c
No. The numbers in the pattern end in 5
or 0, and 71 ends in 1.
−1
4
−6 or −5
Practice
5
a
−8 ° C, −4 ° C, −2 ° C, 1 ° C, 3 ° C
b
−13 ° C, −7 ° C, −2 ° C, 4 ° C, 13 ° C
c
−7 ° C, −6 ° C, −4 ° C, 0 ° C, 6 ° C
6
6 > −17
7
There are many solutions, two of which are:
8
–17 < –13 < –4 < –3, 12 > 7 > 5
–3 < 5 < 7 < 12, –4 > –13 > –17
−4 and 0 circled
Challenge
8
−9 ° C, −2 ° C, 0 ° C, 3 ° C
3
b Area = 10 km2, perimeter = 14 km
c
a
2
−16 < −13
0 > −2
Challenge
9
Missing sides are 72 mm and 6 mm
−15, −8, −1
6 > −1 > −8 > −15 > −22
10 a Ulaanbaatar
Perimeter = 156 mm
b
Karachi
c
−20 ° C, −8 ° C, −3 ° C, 1 ° C, 5 ° C, 14 ° C,
18 ° C
10 The area of a rectangle can be calculated by
multiplying the length of the rectangle by its
width.
11 −3 > −4 −19 < 11 0 > −1
11 a
60 km
12 −6 and −14
c
64 cm
d
7 m2
2
2
b
99 mm
2
Exercise 15.2
Focus
1
12
2
63, 70 and 77
3
3 and 7 are factors of 21 because 3 × 7 = 21
21 is a multiple of 3 and 7 because 21÷ 3 = 7
and 21÷ 7 = 3
18
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4
50 should be in the same part of the diagram as 45.
5
1 × 24, 2 × 12, 3 × 8, 4 × 6
6
A square number is a number multiplied by the same number, 3 × 3 = 9.
Practice
7
45
8
All multiples of 4 are even and 5 is odd.
9
64 25 24 65
10 a
b
1, 2, 4, 5, 10, 20
20, 40, 60, 80
11 1 + 4 in either order 9 + 16 in either order
Challenge
12 49. It is a square number.
13 36 and 54 or 34 and 56
45 and 63 or 43 and 65
14 a8 is the odd one out because all the other numbers have 2 digits.
b
12 is the odd one out because it is the only one that has 3 as a factor.
c
25 is the odd one out because it is the only odd number.
d
40 is the odd one out because it is the only one divisible by 10.
15
Is it a negative number?
Yes
Is the number even?
Yes
Is the number
less than –20?
Yes
–24
No
–14
No
Is the number even?
No
Yes
Is the number
less than –20?
Yes
–21
No
–5
No
Is the number a
multiple of 9?
Yes
18
No
Is the number a
multiple of 9?
Yes
14
27
No
19
Exercise 15.3
Focus
1
19
232, 234
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16 Data display and
interpretation
2
divisible by 2
divisible by 5
302
400
52
25
205
Exercise 16.1
502
203
3
Divisible by 2 – ones digit is 0, 2, 4, 6 or 8
Divisible by 5 – ones digit is 0 or 5
Divisible by 10 – ones digit is 0
Divisible by 100 – tens and ones digits are 0
Focus
1
2
a
2
b
5, 10
Pictogram
b
Dot plot
c
Carroll diagram
d
Frequency table
aCarroll diagram, because it is a sorting
diagram.
bBar chart, because it shows numbers of
things so that they can be compared.
Practice
4
a
3
10 12
5
Divisible
by 5
Divisible by Divisible by 5,
5 and 10
10 and 100
25
310
500
105
690
1000
6
1 70 20 80 3 13 61 17 43 52 54 90 31
27 4 63 32 69 39 44 19 29 75 9 14 59
67 62 46 10 53 22 70 25 7 12 28 55 73
14
18
4
20
41 30 38 34 73 33 51 51 69 53 57 105 87
18
Number of people
63 8 17 34 29 77 32 71 43 59 49 62 79
Challenge
7
No, 15 553 does not end in 5 or 0.
8
205 is odd. Numbers divisible by 2 and 10
must be even.
9
a
300 and 600
b
50, 300, 350, 600, 650
c
50, 75, 300, 350, 600, 650, 675
2
16
4
6
8
Odd
1
5
3
7
9
11
15
13
17
19
20
Correctly completed Carroll diagram with
learners’ categories.
5
17
Less
than 10
Bar chart showing how many pets
each person has
16
14
12
10
8
6
4
2
0
0
1
2
3
Number of pets
4
10 17
a
9
b
4
b
Bar chart
Practice
20
6
a
Venn diagram
7
a
b
Venn diagram, Carroll diagram
Two from bar chart, pictogram and
dot plot
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23
21
27
7 1 3
6 11 9 19 5
13
8 4 17
15
2
16
12
14 18
10
Less
than 20
9
13 a
Odd
28 22 24
26
29
25
b
There are no factors of 12 that are odd
and not less than 10.
15
Time for Anna to get to school
Multiple
of 5
28
20
30
Clara should have curly hair and no glasses.
10 Answer depends on the data collected by
learners.
Learners should choose to represent the data
in a bar chart, dot plot or pictogram. They
should give the reason that the graph or chart
they have chosen to represent their data shows
the number of names in each group so each
group can be easily compared.
Number of birds Basil saw on each day
11
Numbers 6, 10, 11, 14, 19, 20 circled.
14 Correctly completed Carroll diagram.
Number of minutes to get to school
8
26
24
22
20
18
16
14
12
10
8
6
4
2
10
21
2
3
Day
4
5
6
Time for Carlos to get to school
4
2
0
1
2
3
Day
4
5
a
Both Daisy and Basil saw 10 birds
on day 1.
b
Daisy saw many more birds than Basil.
In total Daisy saw 64 birds, but Basil only
saw 31 birds.
c
Learners might refer to Daisy and Basil
being in different places, in different
seasons, or experiencing different weather
that might affect the number of birds.
Challenge
a
12 aA Carroll diagram can be used to sort
numbers, shapes or other items according
to their properties.
b
b
1
8
Number of minutes to get to school
Number of birds
0
A pictogram is used to display data so
that it can be more easily interpreted and
­compared.
c
20
18
16
14
12
10
8
6
4
2
0
1
2
3
Day
4
5
The same scale makes the data in the bar
charts easier to compare.
Anna and Carlos both took the longest
time to get to school on day 5.
Anna took longer to get to school than
­Carlos on every day.
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d
Learners might refer to Anna and Carlos
living different distances from school or
using different forms of transportation,
for example walking or catching a bus.
17 Multiplication and
division
9
Paula has 2 × 8 = 16 balloons and Milly has
4 × 16 = 64 balloons.
10 30 × 5 or 50 × 3
Challenge
11 821 × 9 = 7389 (921 × 8 = 7368)
12 40 × 5 = 200 but learners have recorded this
as 20, which may indicate a place value error.
Exercise 17.1
The correct answer is 3705.
13 80 × 4 = 320 or 40 × 8 = 320
Focus
14 7 (476 × 7 = 3332)
1
24 comics
2
78 tins
3
The 4 tens should be carried.
The correct answer is 282.
Yes, because 300 × 8 = 2400
Exercise 17.2
4
5
144
1
29
2
16
Practice
3
5 pencils; 7 cents
6
290
4
No.
7
a
5
50 ÷ 6 = 8 r2 so Conrad needs 9 boxes to hold
all the eggs.
15 trays
15 Yes and three examples, such as:
Using 12, 13 and 14: 12 + 13 + 14 = 39
and 13 × 3 = 39
Focus
Either: 48 × 4 = 192 → 192 − 48 = 144
or 48 × 3 = 144
19
133
7
28
b
Practice
76
6
2 photos
7
1 and 24, 2 and 12, 3 and 8, 4 and 6
(numbers in either order).
8
True
False
70 ÷ 7 = 10
63 ÷ 7 = 9
63 ÷ 9 = 7
45 ÷ 5 = 9
25 ÷ 4 = 5
76 ÷ 9 = 8
84 ÷ 8 = 11
29 ÷ 3 = 9
76 ÷ 9 = 8
4
17
51
136
9
3
8
24
No, the teacher needs 16 more pens.
24 × 6 = 144 160 – 144 = 16 or
25 × 6 = 150 which is less than 160 or any
other valid explanation.
10 9
8
Ollie is correct.
Erik has forgotten to add in the 1 hundred
that has been carried.
22
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Challenge
3
11 1 and 48, 2 and 24, 3 and 16, 4 and 12, 6 and 8
(numbers in either order).
y-axis
12 75 ÷ 5 = 15 but all the other answers are 12.
Accept any other valid choice provided it is
clearly explained.
5
13 < < <
3
14
2
4
(1, 2)
(5, 3)
1
12
2
0
(3, 0)
0
3
4
5
6 x-axis
6
5
18 Position, direction
and movement
4
3
Exercise 18.1
2
Focus
1
N
NW
0
0
1
2
3
4
5
6
x-axis
NE
W
Pentagon
E
SW
SE
Practice
5
2
2
y-axis
4
1
1
6
15 28 rhombuses. (She makes 56 ÷ 4 = 14 fish
and each fish uses 2 rhombuses.)
23
(4, 4)
4
96
8
(2, 6)
6
i
S (South)
S
ii
SW (South-west)
1.
North-east
iii
NE (North-east)
2.
East
b
NW (North-west)
3.
South
c
SE (South-east)
4.
South-west
5.
South-east
6
a
quadrant
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7
a
10 y-axis
y-axis
6
6
5
5
4
4
3
3
2
2
1
0
0
2
1
3
4
5
6
1
x-axis
0
b
Rectangle
0
1
2
3
4
5
6
x-axis
(5, 4)
Exercise 18.2
Challenge
8
Focus
N
0 degrees
NE 45 degrees
NW 315 degrees
W 270 degrees
1
E 90 degrees
SW 225 degrees
SE 135 degrees
S
180 degrees
9
y-axis
(5, 6)
6
5
(4, 5)
4
(5, 4)
3
2
(2, 2)
1
0
24
2
(1, 0)
0
1
2
3
4
5
6 x-axis
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3
a
(1, 4) (3, 6) (5, 4) in any order.
b
y-axis
5
6
5
4
3
2
1
0
1
2
3
4
5
c
(1, 4) (3, 2) (5, 4) in any order.
d
Square
Practice
4
0
6
x-axis
6
7
a
(2, 3) (2, 6) (5, 3) (5, 6) in any order.
b
Rectangle
c
Shape reflected to give a rectangle.
More than one solution. One possible
solution is:
y-axis
6
5
4
3
2
1
0
25
0
1
2
3
4
5
6 x-axis
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Challenge
c
y-axis
8
6
5
4
3
2
1
0
0
1
2
3
4
6 x-axis
5
11 More than one solution. One possible
solution is:
y-axis
9
6
5
4
3
2
1
0
10 a
b
26
0
1
2
3
4
5
6
x-axis
Octagon
(3, 4) (5, 4) (6, 3) (4, 2) (1, 3) in any order.
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