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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Learner’s Book answers
Unit 1 The number system
Getting started
1
a
5271
b
109 090
2
a
6 thousands
b
6 tens
c
6 ten thousands
a
800 000 + 5000 + 400 + 60 + 9
b
600 000 + 80 000 + 9000 + 500 + 60 + 7
3
6
20
7
a
b
345
8
c
1.68
580
58.0
5800
0.58
× 10
÷ 100
× 100
58
4
C
5
C
6
a
640
b
10
c
80
d
100
9
b
500 005.9
Think like a mathematician
÷ 10
Exercise 1.1
1
2
3
4
a
1001.01
c
403 034.66
a
Three hundred and forty-five point
zero nine
b
Five thousand, three hundred and
seventy-eight point one two
One hundred and fifty-eight thousand,
and thirty-five point four
d
Three thousand and thirty point zero three
a
7 hundreds
b
7 ten thousands
c
7 tenths
d
7 hundredths
a
Two hundred and six thousand, three
hundred and two point one
5.8
C because in C □ = 3.03 but in all the other
statements □ = 3.3.
1
A 2.6, rounds to 3
B 5.5, rounds to 6
C 8.1, rounds to 8
a
66
b
101
c
44
d
56
a
3 cm
b
9 cm
c
7m
d
0m
4
a
4.5
b
5.4
5
No, 0.5 rounds up to the next whole number
so 74.5 rounds to 75.
6
230.6 + 231.4 or 230.7 + 231.3 or
230.8 + 231.2 or 230.9 + 231.1
990 909.9
7
9.9
One hundred and twenty-five thousand,
six hundred and twenty-five point four
three
Think like a mathematician
Nine hundred and ninety thousand, nine
hundred and nine point nine
125 625.43
5
5800 58 000
Exercise 1.2
2
3
206 302.1
c
× 1000
0.37
c
b
65
a
35 800
b
100
c
5.6
d
456 000
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6,
3.1, 3.2, 3.3, 3.4, 3.5, 3.6
4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6,
6.1, 6.2, 6.3, 6.4, 6.5, 6.6 (36 different numbers)
1
1
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Numbers round to 1, 2, 3, 4, 5, 6 and 7
(7 different numbers).
2
a
3 ones
c
3 tenths
a
103 507.9
One hundred and three thousand,
five hundred and seven point nine
b
b
B
Think like a mathematician
Check your progress
1
4
3 hundredths
660 606.06
Six hundred and sixty thousand,
six hundred and six point zero six
a
Isosceles or scalene.
b
No triangle can have two right angles.
c
No triangle can have three right angles.
d
Sentences describing the possible types of
angles in different types of triangles.
5
a
equilateral
c
scalene
6
a
0.3
b
5.55
4
a
5m
b
17 cm
Exercise 2.2
c
10 m
d
11 cm
1
G
6
a
7
10
8
Sofia 0.35
Marcus 35
b
20 000
5430
Arun 3.5
Zara 0.53
Unit 2 2D shape and
pattern
2
3
4
Getting started
1
A, D and E
2
3
3
Any pattern of tessellating rectangles.
4
4
isosceles
No, it is not possible.
3
5
b
a
1
b
0
c
0
d
1
e
0
f
3
a
1
b
1
c
1
d
1
e
5
a
Any colour except black.
b
Black
c
Impossible, the pattern cannot have more
than two lines of symmetry.
A
orange
B
C
red
D purple
E
blue
F
blue
red
G green
5
Exercise 2.1
1
B, D and E
2
a
equilateral triangle
b
isosceles triangle
c
equilateral triangle
d
scalene triangle
e
isosceles triangle
a
A triangle with two lines the same length.
b
A triangle with no lines the same length.
c
Learner’s own answer.
3
2
2
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Think like a mathematician
There are 12 different patterns with at least one
line of symmetry.
b
4
36 or 96
Exercise 3.1
1
Check your progress
square numbers
a
b
5
c
Add 3
d
32 sticks
2
a
1, 12, 23, 34
3
−5 and −14
4
No. The numbers in the sequence are multiples
of 8 so Pierre will count back to 8, then 0.
5
No, together with an explanation:
8
Drawing of an isosceles triangle with one side
longer than the other two sides.
2
A and D
3
All triangles tessellate (equilateral, isosceles
and scalene).
4
3
5
a
6
b
0
a
Pattern with 0 lines of symmetry.
b
Pattern with exactly 1 line of symmetry.
c
Pattern with exactly 2 lines of symmetry.
A
1, 5, 9, 13, 17
d
Pattern with exactly 4 lines of symmetry.
B
20, 17, 14, 11, 8
C
−15, −4, 7, 18, 29
Unit 3 Numbers and
sequences
Getting started
1
−2
2
a
Add 100
b
916 and 1016
3
a
14
b
155
Sofia could keep subtracting 7 but it would
take a very long time and she is quite likely to
make errors.
1
6
11
Encourage learners to think about multiples
of 7 (7, 14, 21, 28, …). If the sequence ended
at 0 it would have to include multiples of 7.
6
3, 5. Learner’s own answer.
7
1, 6, 11, 16, 21
Think like a mathematician
The sequences are:
D 100, 74, 48, 22, −4
E
−40, −25, −10, 5, 20
Exercise 3.2
1
a
2
Learner’s own answers.
b
100
3
3
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
3
4
a
b
15 and 21
triangular numbers
4, 7, 10
4
No, 77 is a multiple of 7 and Zara’s numbers
are all 1 more than a multiple of 7.
5
17
a
1
1
5
3
5
6
10
15
10
5
20
1
15
6
b
c
1, 2, 4, 8, 16, 32, 64, 128
The numbers double each time.
a
36
b
c
64
1
Unit 4 Averages
Getting started
81
1
Green pencil / 5th pencil from left.
2
a
1, 3, 4, 5, 7, 8, 9
b
14, 41, 104, 114, 144, 401, 414
Think like a mathematician
The smallest number is 10.
3
Sphere, because there are more spheres than
any other shape.
4
25
The largest number is 31.
Exercise 3.3
1
Exercise 4.1
11, 31, 41, 61
1
They have exactly two factors.
2
49 is the only square number.
19 is the only prime number.
3
composite
4
Prime
numbers
Square
numbers
Even numbers
16
18
15
1
b
29
c
9
d
1
3
4
2
5 bananas
3
a
3
b
8
c
308
4
a
5
b
13
c
453
5
789 g
6
a
The mode is 6 and the median is 5.
b
The mode is 11 and the median is 11.
c
The mode is 3 and the median is 4.
d
The mode is 2 and the median is 3.
17
19
a
Think like a mathematician
Possible answers include:
5
23
6
a
c
3, 3, 3, 3, 3
19, 29 or 59
25
b
d
12, 21, 15 or 51
12
Think like a mathematician
5, 23, 67, 89 or 2, 59, 67, 83 or 5, 29, 67, 83
C
2
a
b
7, 13, 19, 25, 31, 37
2, 9, 16, 23, 30, 37
2, 3, 3, 4, 5
Reflection: I check that the mode is 3 by counting
how many times each number occurs to see if 3
occurs the most.
I check that the median is 3 by putting the numbers
in order and checking that 3 is in the middle.
7
Check your progress
1
1, 3, 3, 3, 5
8
a
4
b
c
The shopkeeper should use the mode
because that is the size that is sold the most.
a
0 mm
b
3
4 mm
4
4
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
c
The median describes the average rainfall
in a month better because the mode
is 0 mm. Eight of the 11 months have
more than 0 mm of rain so 0 mm is not
typical. The median is 4 mm which is the
middle value.
1
$18.50
2
3m
3
a
The mode is 106, the median is 104.
b
The mode is 7, the median is 5.
c
The mode is 32, the median is 30.
d
The mode is 2, the median is 2.
a
The mode is $9.
b
The median is $7.
c
The median best describes the average
because only two people raised $9;
everyone else raised less than that amount.
$7 represents the data better.
5
2
a
41.6
b
13.77
c
17.8
d
14.4
e
75.8
f
26.88
a
4
c
It would be best to use the mode
because that represents the size that is
needed the most and Maryam wants to
know which size table is most useful.
Although the median is 3, only one
group had 3 people.
b
4
$22.75
5
a
A $4.40
b
$38.20
a
□ = 14
○=9
b
∆=9
○=4
7
□ = 15
8
3
1
a
63
2
a
6708; six thousand, seven hundred
and eight.
b
One example is 6000 + 700 + 8.
b
C $13.25
○=6
D $6.45
∆=7
□ in kg
∆ in kg
0.1
1
0.2
0.7
0.3
0.4
0.4
0.1
Think like a mathematician
This is a version of a magic square but using
decimals instead of whole numbers. Accept different
orientations. 0.5 will always be in the middle cell.
59
Subtraction: Answer should be 224. It was
incorrect to subtract the smaller digit from the
larger digit in the ones column.
B $14.10
Accept other answers that use more than
1 decimal place.
Addition: Answer should be 614. In the ones
column, 7 + 7 = 14, but the 1 ten has not been
added in.
−5 or −4
3.4 + 1.8 = 5.2. The 1 should be carried to the
ones column and added to the other ones.
Make sure to estimate before calculating and
check your answer against the estimate.
6
Getting started
4
78.31
6.5 − 2.7 = 3.8. It was incorrect to subtract
the smaller digit from the larger digit in the
tenths column.
Unit 5 Addition and
subtraction
3
1
3
Check your progress
4
Exercise 5.1
0.2
0.7
0.6
0.9
0.5
0.1
0.4
0.3
0.8
Exercise 5.2
1
−10 and 2
2
a
−3
b
1
c
395
d
−29
5
5
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
3
a
b
4
−3 °C
5
a
6
One possible answer is:
−2
5 °C
13 °C
−4
c
−4 °C
−2 °C
b
4
Complete net of a cube drawn.
0 °C
5
a
Cone and cylinder (other possible answers
include hemisphere and truncated cone).
Learners may also give ‘sphere’ as an
answer because spheres are projected onto
2D surfaces as circles.
b
Both of the shapes have a circular face.
Cones, cylinders and hemispheres have at
least one circular face. Spheres appear to
have a circular face when they are drawn as
2D images.
c
Learner’s answers could be:
−12 °C
Positive numbers: 4 + 0 = 4
−4 + 5 = 1
Negative numbers: −2 − 2 = −4
5 − 7 = −2
−3 − 1 = −4
Zero: −4 + 4 = 0
2
4 − 5= −1
6–6=0
Accept any other valid choice provided it is
clearly explained.
7
a
−78
b
−105
c
−100
d
66
e
310
f
350
Check your progress
1
0.3
2
20 cents
3
1.2 metres
4
a
−5
b
−4
5
a
98.73
b
7.55
cone
6
c
203
7
cylinder
sphere
a
0 or 1 depending on learner’s drawing.
b
0, 1 or 2 depending on learner’s drawing.
a
Unit 6 3D shapes
Getting started
1
a
triangular prism
b
cylinder
c
cone
d
cuboid
e
square-based pyramid
2
2 pentagons and 5 rectangles
3
9
b
c
Exercise 6.1
1
a
6
b
The faces are all squares.
2
An open cube.
3
B, C and E
6
6
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
d
Unit 7 Fractions,
decimals and
percentages
Getting started
e
1
a
2
$9
3
a
True
b
False
c
False
d
True
4
b
1
c
4
4
50% and 75%
Exercise 7.1
1
1÷5
2
8
or
Learner’s cuboid should match shape b, c or d
in a different orientation.
1
Think like a mathematician
Nets of a cube that can be made with the two
pieces are:
4
3
of a pizza (or
2
8
of a pizza)
3
4
4
a
5
Arun has confused multiplication and
division. He should divide by 10 and multiply
by 3. The answer is 6.
Check your progress
6
500 ml
1
Learner’s own answer.
7
Here are some possibilities. There are others.
2
C
3
Learners make a model that matches the
drawing using 12 cubes.
8
32
9
100
4
10
b
c
18
36
d
72
Think like a mathematician
There are several possible answers, but everyone
must have the equivalent of
3
5
of a cake.
7
7
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Exercise 7.2
1
5
1
2
is the odd one out because all the other three
a
40%
b
1%
c
10%
d
70%
e
25%
f
60%
6
a
2
a
30%
b
70%
c
25%
7
0.2, 0.3, 2.3, 2.4, 3.2
3
10% is the odd one out because it is the only
one that can be expressed in tenths as well as
in hundredths.
8
a
>
b
d
<
e
10% is the odd one out because it is the only
even number.
9
a
0.1
numbers are equivalent.
a
b
5
a
6
10
7
20% = 0.2
50%
6
10
8
or
c
25%
60
b
100
2
75%
Percentage
0.5
50%
2
9
6
or
4
b
75%
c
Fraction
Decimal
Percentage
0.3
30%
0.1
10%
0.2
20%
0.23
23%
0.25
25%
0.7
70%
3
0.1
10%
0.9
90%
1
10
10
12
1
4
7
30 are yellow, 10 red, 5 blue and 15 green.
10
Exercise 7.3
4
12
5
5
5
1
a
1 =
b
2 =
2
a
2
3
3 is the odd one out because it does not have
1
10
or
100
20
or
100
1
5
7
c
5
1
3
4
an improper fraction to pair with.
4
10
and
100
or
70
100
1
4
0.3
3
70%
4
Unit 8 Probability
d
3
7
Getting started
10
1
40
25
or
30%
2
1
4
0.2
(accept 1 )
b
4
5
44%
100
4
2
4
75%
a
Think like a mathematician
1
70%
3
6
6
3
5
4
2
2
=
3
23
3
f
6
(or equivalent)
10
<
2
1
9
<
0.7
10
10
c
Yes. The number is four quarters which
is four times bigger than one quarter.
The number is 6 × 4 = 24.
4
Decimal
1
=
1
60%
40% = 5 = 10 = 0.4
Fraction
25
50%
65%
5
c
8
Check your progress
Other answers are possible.
4
2
5
3
b
10% is the odd one out because it is the only
composite (not prime) number.
b
12
a
False
b
False
c
True
d
True
e
False – there is no chance that you will
take a shirt with stripes.
100
8
8
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
2
Tally
Total
Heads
IIII IIII IIII IIII III
23
Tails
IIII IIII IIII IIII IIII II
27
c
Depends on learner’s answer to b.
For example: I drew 1 sphere, 1 cylinder
and 1 square-based pyramid because there
must be at least one of each of these in
the bag because Arun saw them. I drew
2 cubes because Arun took more cubes
out of the bag than any other shape.
d
Shapes could be taken out of the bag
more times.
a
17
c
A coin flip has two equally likely
outcomes. In the simulation odd is
more likely than even.
d
There should be the same number of even
and odd outcomes, for example random
numbers from 1 to 2.
a
4
Exercise 8.1
1
a
Arrow pointing to the unlikely section.
b
Arrow pointing to even chance.
3
c, d Answers depend on context.
2
a
Arrow pointing to certain.
b
Arrow pointing to impossible.
c
Arrow pointing to unlikely.
d
Arrow pointing to even chance.
3
Spheres and cubes are equally likely.
4
a
8
c
even chance
d
S, M (either order)
5
b
4
e
E
4
Results and comments will depend on learner’s
experiment.
Exercise 8.2
0, 1, 2, 3, 4, 5
b
Learner’s own answer.
c, d Learner’s own answers.
2
e
Bar chart of learner’s results.
f
Answer depends on the result of the
learner’s experiment. (The outcomes are
not equally likely.)
g
Throw the dice and record the results
more times. Alternatively, write down all
the possible outcomes.
a
b
3
Think like a mathematician
More than one solution, for example: It is
unlikely that Sofia will take an S from the bag.
Or: It is impossible that Sofia will take a B
from the bag.
a
b
33
c–e Learner’s own answers.
Think like a mathematician
1
b
i
True
ii
False
iii
True
iv
False
Five shapes including at least one each of
a cube, sphere, cylinder and square-based
pyramid.
Results and comments will depend on learner’s
simulations.
The learner will see from their generated numbers
that Zara’s statement is wrong. This can be
explained to the learner by saying that, because
the numbers are all equally likely, it is probable
that there will be a similar number of each, but
each time a number is generated all the numbers
have the same chance of being selected no matter
whether they have been selected before or not.
It would be usual for the numbers not all to have
been generated the same number of times even
though they are all equally likely to be generated.
The experimental probability will gradually get
closer to the value of the theoretical probability as
more trials are performed.
Check your progress
1
a
unlikely
c
impossible
b
even chance
2
Taking a lemon sweet and taking a lime sweet
are equally likely.
3
a
16
d
It is likely that a seed will grow.
b
10
c
6
9
9
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Unit 9 Addition and
subtraction of fractions
Check your progress
1
Getting started
4
1
c
or 1
4
3
6
b
4
answer is
1
a
2
a
10
4
7
b
7
b
10
11
b
10
20
d
12
19
e
f
20
3
a
b
6
4
c
d
12
7
e
f
15
3
3
1
B, C and E
2
a
Obtuse angles are between 90 degrees and
180 degrees.
b
Acute angles are between 0 degrees and
90 degrees.
11
9
15
12
3
360 degrees
9
4
B 130 degrees
8
4
Exercise 10.1
15
1
B, D and E
2
a
right angle
b
acute
c
reflex
d
obtuse
e
reflex
a
b
b
e
c
b, a, d, c, e
a
Between (and including) 70 degrees to
89 degrees.
b
Between (and including) 190 degrees to
210 degrees.
c
Between (and including) 91 degrees to
110 degrees.
d
Between (and including) 330 degrees and
359 degrees.
1
8
7
12
Answer less
than 1
Answer of 1 Answer
more than 1
a
c
d
b
3
7
10
1
4
=
+
1
2
1
6
8
10
+
=
1
2
4
b
c
5
7
Think like a mathematician
=
1
12
10
3
a
8
Getting started
6
7
1
6
3
6
8
Unit 10 Angles
6
c
3
4
.
3
a
5
3
10
Exercise 9.1
4
8
2
Yuri has added the numerators together and
added the denominators together. The correct
3
d
8
3
2
12
a
4
b
8
3
3
8
7
5
2
3
a
+
1
7
10
18
=
1
3
+
1
18
1
5
10
10
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
e
Between (and including) 150 degrees to
170 degrees.
f
Between (and including) 271 degrees and
290 degrees.
5
a = 75°, b = 125°, c = 100°, d = 150°
6
a
90°
b
40°
c
110°
d
40°
3
About 4500 times.
4
2356
5
The estimate is not a good one. It should be
300 × 60 = 18 000.
6
1152 boxes
7
Arun multiplied by 1 hundred not 1 ten.
He may have spotted the error if he had
estimated the answer before calculating it.
The correct answer is:
Think like a mathematician
a = 105°, b = 75°, c = 40°, d = 140°
The angles opposite each other are equal.
×
Check your progress
1
2
2
a
obtuse
b
reflex
c
acute
d
reflex
e
right angle
f
reflex
a
Between 50° and 70°.
8
925
b
Between 160° and 179°.
9
a
11 328
c
Between 250° and 269°.
b
10 203
c
35 532
2
2
4
1
2
4
0
4
8
8
8
3
The angles on a straight line add up to 180°.
4
a
80°
b
160°
Think like a mathematician
c
100°
d
50°
34 × 56 = 1904
35 × 46 = 1610
34 × 65 = 2210
35 × 64 = 2240
Unit 11 Multiplication
and division
43 × 56 = 2408
53 × 46 = 2438
43 × 65 = 2795
53 × 64 = 3392
36 × 45 = 1620
63 × 45 = 2835
Getting started
36 × 54 = 1944
63 × 54 = 3402
Largest: 63 × 54 = 3402
1
13 r6
2
7461
3
25 × 3 =75
4
54 ÷ 6 because it has the answer 9 and all the
other answers are 8.
1
a
2
34 days
a
3
a
4
List or table showing:
5
5310
Smallest: 35 × 46 = 1610
Exercise 11.2
b
1350
Exercise 11.1
1
2
57
127 r3
b
124
c
37
b
105 r3
c
40 r6
a
3600
b
480
Less than 10:
88 ÷ 9
c
2100
d
540
Between 10 and 20: 91 ÷ 9, 94 ÷ 8, 96 ÷ 6
e
3600
f
320
More than 20:
86 ÷ 3, 98 ÷ 4
30 × 80, 60 × 40, 120 × 20
11
11
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
5
a
19
6
a
92
7
3
2
5
b
21
b
24
2
4
c
14
c
4
1
7
7
a
any multiple of 8
b
any multiple of 20
c
any multiple of 100
Think like a mathematician
Think like a mathematician
Sometimes true.
Largest: 954 ÷ 9 = 106
Exercise 11.3
Learners will show they are convincing (TWM.04)
when they test examples and notice that in some
cases the sum is divisible by 8 (for example
2 + 4 + 6 + 8 = 20 which is not divisible by 8 but
2 + 8 + 10 + 12 = 32 which is divisible by 8).
1
Check your progress
Other answers: 459 ÷ 9 = 51
549 ÷ 9 = 61
594 ÷ 9 = 66
2
495 ÷ 9 = 55
945 ÷ 9 = 105
a
366, 234 444, 14 432, 160, 422, 790 124, 146
b
234 444, 14 432, 160, 790 124
1
a
2856
2
a
19
632, 488, 784
The last two digits are divisible by 4.
3
3
divisible by 4
52
1104
b
28
2
3
divisible by 8
divisible by 5
400
304
3
5
b
even
23 456
c
56
c
12
5
7
not divisible by 8
62 848
51 466
25
76 343 97 631
odd
205
203
502
4
Numbers in the intersection are divisible by 4
and 5.
15 × 30 or 30 × 15
4
No because 14 is not a multiple of 4.
Unit 12 Data
5
a
152, 156, 160, 164, 168, 172, 176, 180
Getting started
b
152, 160, 168, 176
1
6
a
11
b
c
There are 28 children in Hexagon Class.
7
There are 30 children in Pentagon Class.
divisible by 4
d
12 404
divisible by 8
969 696
43 200
2
56 824
Possible answer: I think that more
children are taller in Pentagon Class than
in Hexagon Class because the children in
Pentagon Class might be older. Accept
any other valid choice provided it is
clearly explained.
25%
Exercise 12.1
1
987 204
24 302
a
13
b
c
There is more than one possible answer.
For example: The zoo should aim their new
play area at 2- to 4-year-olds because 37 of
the children at the zoo were 2 to 4 years old.
2
12
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
0.6 kg or 600 g
b
0.4 kg or 400 g
c
1.2 kg or 1200 g or 1 kg and 200 g
d
1.7 kg or 1700 g
e
Week 5
a
1
4
a
b
5
1
3
Ice cream
flavour
b
0
d
50%
Frequency Proportion
Strawberry
500
25%
Vanilla
100
5%
Mint
400
20%
Chocolate
980
49%
Blackcurrant
20
1%
A bar chart showing the number of
visitors each month for Hotel Beachfront
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
c
b
Number of visitors
3
a
51%
a
Months
Hotel Snowy Mountain
Month Tally
Number
of visitors
c
The number of visitors goes up then
back down.
Jan
IIII IIII IIII IIII IIII IIII
30
d
Feb
IIII IIII IIII IIII IIII III
28
Mar
IIII IIII IIII IIII II
22
A dot plot showing the number of visitors
each month for Hotel Snowy Mountain
Apr
IIII IIII III
13
May
IIII IIII
10
June
IIII III
8
July
IIII III
8
Aug
IIII III
8
Sept
IIII IIII
9
Oct
IIII IIII
10
Nov
IIII IIII IIII III
18
Dec
IIII IIII IIII IIII IIII III
28
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Number of visitors
2
Months
e
The number of visitors goes down then
back up.
13
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
More than one possible answer. For
example, ‘If the hotels are in the Northern
hemisphere, Hotel Beachfront attracts
more visitors in the summer because it is
by a sunny beach. Hotel Snowy Mountain
attracts more visitors in the winter because
it has winter sports such a skiing.’
6
Skiing
Not skiing
Surfing
Jen
Leo
Ari
Mai
Not surfing
Zoe
Kai
Ron
Gia
5
18
16
10
8
6
0
0
b
Although 3 runners took between 15
and 20 minutes to complete the race,
it is possible that none of them took
20 minutes to complete the race.
Temperature (°C)
b
c
14
40
80 x-axis
50
60
70
Height (cm)
More than one possible answer, for example:
In frequency diagrams there are no gaps
between the bars. In bar charts there are
gaps between the bars.
b
Frequency diagrams and bar charts both
use bars to show frequency.
c
Learner’s own answers.
a
11 °C
d
12 noon and 4 p.m.
b
9 a.m.
c
6
20
30
40
Time (minutes)
50
60
50
60
Cup 2
0
Frequency
30
10
12
10
8
6
4
2
0
A frequency diagram showing
the heights of dogs
a
4
12
2
3
y-axis
7
6
5
4
3
2
1
0
3
14
4
a
2
Cup 1
20
Exercise 12.2
1
a
Temperature (°C)
f
10
20 30 40
Time (minutes)
c
The line is flat at the start and then goes up.
d
The line goes down then is flat at the end.
e
For example: Cup 1 was put in a warm
place, cup 2 was put in a cold place.
Accept any other valid choice provided it
is clearly explained.
f
Learner’s own answers.
Answers should match the data in the
learners’ investigation.
Check your progress
1
10 °C
2
a
Rectangle of 40 squares (for example
8 squares by 5 squares). Key showing
five different colours for the five insects.
Squares in the rectangle coloured
according to the key: beetle 20, butterfly
5, ladybird 3, moth 2, wasp 10.
b
50%
a
The frequency goes up and then
down again.
b
The frequency goes up and then
down again.
c
More children in Class B have longer
thumbs. More children in Class A have
shorter thumbs.
14
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
d
The children in Class A might be younger
than the children in Class B.
A frequency diagram showing the
mass of parcels to be loaded into a van
Frequency
3
8
7
6
5
4
3
2
1
0
2
3
4
0
2
4
6
8
Mass of parcels (kg)
10
5
4
a
18 cm
b
8 cm
c
5.5 cm
d
6
2.5 hours or 2 hours 30 minutes
Getting started
2
3
6
a
2
3
b
8
=
4
6
6
8
9
12
= =
b
True
c
False. The ratio of white squares to black
squares is 3 : 1.
d
True
e
True
a
True
b
False
c
False
d
True
a
2:3:5
b
3:5:2
c
5:3:2
d
a
2:4:1
b
=
4
10
7
Fraction
1
2
10
Exercise 13.1
a
E.g.
b
E.g.
4:1:2
4
7
1
The diagram shows white circles and
black circles in the ratio 1 : 2.
Think like a mathematician
a
Approximately 320 cm
b
Fatima
12
Check your progress
18
1
Percentage
a
False. The ratio of yellow to blue in the
green paint is 2 : 1.
b
False. The proportion of red in the purple
3
paint is .
7
50%
c
True
d
False. 3 in every 7 parts of purple paint
are red.
e
True
10%
(or equivalent)
9
and 30%
Sofia has confused ratio and proportion.
One in every three circles is white.
1
10
3
10
5
12
4
1
False. 3 out of 4 squares are white.
c
Unit 13 Ratio and
proportion
1
a
90%
2
Marcus has confused ratio and proportion.
He saw one triangle and two circles which is
the ratio of triangles to circles 1 : 2.
It should be 1 out of every 3 shapes is
a triangle.
15
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Pink carpet $288
Unit 14 Area and
perimeter
Lilac floral carpet $360
Grey and white striped carpet $504
Getting started
Check your progress
1
The area of the lake is approximately 9 km .
2
a
3
17 cm2
2
b
2
28 cm
2
a
Estimate between 10 cm and 18 cm.
b
14 cm
2
a
6m
3
a
Area 3 km2, perimeter 8 km
b
Area 30 m2, perimeter 30 m
c
Area 72 cm2, perimeter 38 cm
22 cm
Exercise 14.1
1
1
a
12 cm
b
6 cm2
c
12 cm
d
7 cm2
e
The blue and red triangles have the same
perimeters, but different areas.
f
Rectangle with a perimeter of 12 cm, for
example 5 cm long and 1 cm wide.
g
Rectangle with an area of 6 cm2, for
example 3 cm long and 2 cm wide.
a
Estimate between 14 cm and 22 cm.
b
18 cm
Think like a mathematician
4
3
4
5
6
7
8
a
40 m
b
10 mm
c
4 km
d
30 m
e
3 cm
a
120 m
b
c
38 km
e
62 cm
a
8m
Many possible answers; examples include
a rectangle 4 cm long by 3 cm wide and a
rectangle 12 cm long by 1 cm wide.
Unit 15 Multiplying and
dividing fractions and
decimals
Getting started
2
The smallest area is 7 cm , the largest area is
16 cm2.
b
1
2
3
6
and
4
8
2
9
3
2
46 mm
4
a
34
b
476
d
100 m
5
a
10
b
127
10 cm
b
14 cm
c
16 cm
d
40 cm
a
B and C
b
D and F
c
A and E
a
37 m2
b
46 m2
c
42 km2
Costs are:
Exercise 15.1
1
3
4
. Accept any correct diagram, for example:
+ 14
+ 14
1
4
0
1
4
1
4
+ 14
2
4
3
4
4
4
1
4
Red carpet $432
Blue dotty carpet $384
Green carpet $312
16
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
2
6
5
4
1
or 1 . Accept any correct diagram,
a
5
for example:
+ 15
1
5
+ 15
2
5
1
5
+ 15
3
5
+ 15
+ 15
4
5
1
5
1
5
5
5
7
5
6
5
5
1
5
4
2
1
2
1
2
=
7.2
3
b
with suitable diagram.
÷ 10
1.3 × 7
×5 =
6
5
(= 1)
1
a
1
5
13 ÷ 10
= 13 × 7 ÷
b
10
1
18
c
= 91 ÷
×3=
×2=
4
4÷2=
2
3
3÷2=
2
2
2÷2=
2
=
3
2
2
a
3
A = 4, B = 3, C = 1
2.8
b
a
6
3.5 × 7 is the only one with a decimal answer.
(1.4 × 5 = 7, 2.5 × 8 = 20, 1.8 × 5 = 9 and
3.5 × 6 = 21 but 3.5 × 7 = 24.5)
7
107.8
8
a
2
Exercise 15.2
1.2
5
2
is the same as dividing by 3.
1
9.1
b
4.2
7
3
Multiplying by and dividing by 2 give the
2
same answer.
Multiplying by
10
4
2
1
1
10
20
bottle
×4=
×7
1
Think like a mathematician
1
72
Arun has multiplied both the numerator
and the denominator by 5. He should only
have multiplied the numerator.
5
7
=
÷ 10
Learner’s preference explained.
1
6
9
=8×
1
5
4
9
×
8 ÷ 10
+ 15
1
5
0
3
0.8 × 9
2.5
c
2.7
11.2
b
29.2
c
131
Think like a mathematician
There are many different answers. Look for
learners who work in a systematic way and then
comment on their solutions. For example, the
largest answer is 325.8 (54.3 × 6) and the smallest
answer is 136.8 (45.6 × 3).
34.5 × 6 35.4 × 6 43.5 × 6 45.3 × 6 53.4 × 6 54.3 × 6
= 207 = 212.4 = 261 = 271.8 = 320.4 = 325.8
34.6 × 5 36.4 × 5 43.6 × 5 46.3 × 5 63.4 × 5 64.3 × 5
= 173 = 182 = 218 = 231.5 = 317 = 321.5
35.6 × 4 36.5 × 4 53.6 × 4 56.3 × 4 63.5 × 4 65.3 × 4
= 142.4 = 146 = 214.4 = 225.2 = 254 = 261.2
45.6 × 3 46.5 × 3 54.6 × 3 56.4 × 3 64.5 × 3 65.4 × 3
= 136.8 = 139.5 = 163.8 = 169.2 = 193.5 = 196.2
17
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Check your progress
1
a
2
a
3
a
4
5
b
6
1
b
18
b
11.1
9
4
1
56
14
2
c
c
c
7
7
or 1
30
3
468.9
4
10
×
7
9
4
0.5
3.5
4.5
2
0.6
4.2
5.4
2.4
0.2
1.4
1.8
0.8
Eduardo
b
Francis
c
51.5 seconds, 52.3 seconds, 52.6 seconds,
52.9 seconds, 53.1 seconds, 53.4 seconds
a
Arun
b
Learner’s own answers.
1
1
5
a
a
Number of days
0.5 1
Number of hours
12 24 36 48 60 72
1.5 2
b
Number of hours
0.5 1
1.5 2
c
2
3
2.5 3
5
a
36 minutes
b
1 hour and 15 minutes (or 75 minutes)
c
1 hour and 6 minutes (or 66 minutes)
d
2 hours and 21 minutes (or 141 minutes)
a
29 minutes
a
There are 60 seconds in a minute.
b
There are 60 minutes in an hour.
c
There are 24 hours in a day.
d
There are 12 months in a year.
b
2 hours and 10 minutes (or 130 minutes)
e
The month of April has 30 days.
c
21 minutes
f
The month of July has 31 days.
d
23 minutes
a
135 minutes
a
Train A (10:11)
b
Train B (12:32)
b
1 hour 35 minutes
c
Train B (12:32)
d
Train C (14:23)
a
1.50 p.m. or ten minutes to 2 in
the afternoon
b
25 minutes
c
16:00 or 4 o’clock in the afternoon
or 4 p.m.
Exercise 16.1
1
1.5 2
Number of seconds 30 60 90 120 150 180
Getting started
1
2.5 3
Number of minutes 30 60 90 120 150 180
Number of minutes 0.5 1
Unit 16 Time
2.5 3
Answers will be dependent on the learner’s
environment and life experiences. Possible
answers include:
a
blink
b
write my name
c
watch an advert on TV
d
boil an egg.
6
7
8
17:04
9
a
5 hours difference
b
15 hours difference
c
6 hours difference
d
11 hours difference
10 a
14:21
b
18:44
c
23:03
d
17:18
11 Anchorage
18
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
Think like a mathematician
00:23 (Marcus) is correct. 14:23 (Sofia) is
incorrect; she has calculated the time 5 hours
behind rather than 5 hours ahead. 19:23 (Zara)
is incorrect; she has worked out the end-time of
the call for Amy but not taken into account the
5-hour time difference. 23:83 (Arun) is incorrect;
he has added on 48 minutes without counting on
correctly past the hour.
3
4
2
3
a
2 hours and 3 minutes
b
112 minutes
a
48 minutes
b
1 hour and 23 minutes
c
From D to E
a
6 hours
b
13:12, 1.12 p.m. or twelve minutes past 1
c
1 hour and 18 minutes
Unit 17 Number and
the laws of arithmetic
2
a
True
b
False
c
True
d
False
Arun: 19 × 2 × 5 = 38 × 5 = 190
Marcus: 19 × 2 × 5 = 19 × 10 = 190
Marcus’s method is better because he
multiplied two numbers to give 10 and it is
easy to multiply by 10.
Exercise 17.1
1
Any four calculations multiplying together
2, 5, 6 and 7 in any order. The answer is
always 420.
2
a
False – the numbers are different.
b
False – division is not commutative.
18 ÷ 6 = 3 but 6 ÷ 18 =
6
18
c
True
d
False – subtraction is not commutative.
56 − 6 = 50 but 6 − 56 = −50
b
25 × 4 × 9, 100 × 9, = 900
(Learners may work differently)
36 × 8 = 30 × 8 + 6 × 8 = 240 + 48 = 288
b
48 × 7 = 50 × 7 − 2 × 7 = 350 − 14 = 336
c
19 × 6 = 20 × 6 − 1 × 6 = 120 − 6 = 114
a
50 × 2 × 16 = 100 × 16 = 1600
b
25 × 4 × 17 = 100 × 17 = 1700
c
15 × 6 × 17 = 90 × 17 = 1530
6
a
69
7
a
4+6÷3=6
b
5 × 6 – 2 = 28
c
5+9÷3=8
d
8 ÷ 2 – 4 = 0 or 8 – 2 × 4 = 0
5
b
c
0
57
8
54 × 6 = 324, 22 × 3 = 66, 41 × 5 = 205,
19 × 4 = 76, 37 × 6 = 222
Any method acceptable.
It is likely that 41 × 5 and 19 × 4 will be
done mentally:
41 × 5 = half of 41 × 10 = 205
19 × 4 = 20 fours – 1 four = 76
9
a
Sofia 21
b
Learner’s own answer.
Getting started
1
10 × 2 = 20, 7 × 2 = 14, = 34
a
Check your progress
1
a
Arun 42
Zara 38
Think like a mathematician
The answer is a 4-digit number. The thousands
and hundreds digits form the first 2-digit number
and the tens and ones digits form the second
2-digit number.
Check your progress
1
An explanation showing that the order of
multiplication can be changed to give the
products of 6 × 9 and 5 × 2, for example:
6 × 9 is 54 and the other numbers are 5 × 2
which is 10.
2
Marcus should cross out one column not one
dot. His answer should be 76.
3
a
4
20 × 7 = 140, 4 × 7 = 28, = 168
18
b
10
c
54
19
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CAMBRIDGE PRIMARY MATHEMATICS 5: TEACHER’S RESOURCE
6
Unit 18 Position and
direction
(2, 2) and (4, 4)
(6, 4) and (4, 6)
(0, 2) and (2, 0)
Getting started
1
Three possible solutions:
7
A (0, 1)
B (2, 6)
C (3, 0)
D (4, 4)
a
Purple triangle A to red triangle B.
b
Red square A to orange square B.
c
Yellow pentagon B to orange pentagon A.
d
Purple rectangle A to blue rectangle B.
8
E (6, 5)
2
y
B
5
A
4
3
C
2
1
0
Check your progress
D
E
1
3
2
3
4
5
x
G
Exercise 18.1
1
a
(3, 0)
b
(0, 2)
d
(4, 1)
e
(3, 1)
2
Sarah
3
C
4
a
b
c
5
c
(0, 2)
1
(4, 1)
2
(0, 5)
3
(6, 4)
4
2 squares left and 1 square down.
(2, 1)
(3, 3)
(4, 0)
5
The position of Z is approximately (5, 8).
Good estimates are (5, 8) (5, 9) (5, 7) (4, 8)
(4, 9) (4, 7) (6, 8), (6, 9), (6, 7).
Learner’s own answer.
Learner’s own answer.
(4, 3)
20
20