CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Learner’s Book answers
1 Numbers to 1000
Getting started
1
36
45
46
47
56
77
80
87
90
97
98
99
246
255
22
42
23
51
52
781
53
42
2
87
10 20 30 40 50 60 70 80 90 100
70, 30, 50, 60
155
135
458
460
142
145
468
470
155
478
153
782
783
428 = 400 + 20 + 8, 913 = 900 + 10 + 3,
576 = 500 + 70 + 6; 395 = 300 + 90 + 5.
3
a
215
b
632
4
564
5
3 tens, 30; 9 ones, 9; 9 hundreds, 900; 9 tens, 90;
8 ones, 8; 2 hundreds, 200.
132
152
147
2
Exercise 1.1
1
146
792
62
42
3
145
772
32
0
257
266
100
11
21
256
154
1, 4, 7 and 8 tens, 10, 40, 70, 80.
Think like a mathematician
480
The unused place value cards are: 500, 800, 10, 60,
2 and 6. All the possible numbers are: 512, 516,
562, 566, 812, 816, 862 and 866.
488
490
6
498
500
479
eight hundred and seventy-three,
eight hundred and fifty-three,
three hundred and seventy-eight,
three hundred and fifty-eight.
1
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Exercise 1.2
1
790
220
310
320
330
880
890
900
990
420
650
100, 700, 400, 900, 700, 600
5
598
Think like a mathematician
The number should be greater than or equal to
x 95 and less than (x + 1)05, where x is any nonnegative whole number. For instance,
x = 2: 295, 296, 297, 298, 299, 300, 301, 302, 303,
304 ➝ all round to 300 …
a643 is greater than 458 and 458 is
less than 643.
b 475 is greater than 472 and 472 is
less than 475.
c 883 is greater than 838 and 838 is
less than 883.
3
smallest 38, 475, 563, 621, greatest 679
4
greatest 834, 483, 438, 384, smallest 48
5
48 marked about halfway between 0 and 100,
384 marked approximately three-quarters of
the way between 300 and 400, 438 marked
less than halfway between 400 and 500, 483
marked about three-quarters of the way
between 400 and 500, 834 marked less than
halfway between 800 and 900.
x = 9: 995, 996, 997, 998, 999, 1000, 1001, 1002,
1003, 1004 ➝ all round to 1000
Sofia is correct, as 100, 200, 300, …, and 1000 are
in the above list.
Check your progress
1
374
383
384
385
394
6
Estimates from 160 to 190, 310 to 340, 830
to 870.
2
7
Any number less than 263, any number greater
than 671, any number greater than 457, any
number less than 346.
3
744
746
754
756
764
765
766
774
776
784
786
7 ones, 7; 7 hundreds, 700; 7 tens, 70; 3 ones, 3;
8 hundreds, 800; 4 tens, 40.
Number
Round to the
nearest 10
234
230
200
Think like a mathematician
471
470
500
Learners’ own statements and answers.
896
900
900
750
750
800
303
300
300
987
990
1000
Exercise 1.3
1
200 to 300 spots, or 200 to 400 spots. There
are 287 spots.
2
a
b
c
2
4
x = 1: 195, 196, 197, 198, 199, 200, 201, 202, 203,
204 ➝ all round to 200
660
750
2
120, 680, 390, 910, 740, 600
x = 0: 95, 96, 97, 98, 99, 100, 101, 102, 103, 104 ➝
all round to 100
550
640
3
Round to the
nearest 100
No, 500 to 600 would be a better estimate.
Yes, the mass of 24 grams is between
20 grams and 30 grams for 200 to 300 beans.
700 to 800 beans or 700 to 900 beans.
Cambridge Primary Mathematics 3 – Moseley & Rees © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
2 Statistics: Tally charts
and frequency tables
Think like a mathematician
Getting started
1
1
Animal
Tally
Learners’ own answers.
Check your progress
a
c
2
giraffes
third week
4
b
Fruits
Votes
32
mango
lions
camels
apple
meerkats
grapes
fish
banana
penguins
total
seals
1
Learners’ own answers.
2
a
b
c
d
3
4
Football is liked the most.
Cricket and basketball are liked by the
same number of people.
50 people took part in the survey.
For example, the tables do not say how
often the games are played; the tables do
not tell you if they surveyed boys or girls.
Tally
Frequency
30
2
40
5
50
2
60
3
70
2
80
6
90
4
Learners’ own answers.
Favourite hobby
Tally
Frequency
3 Addition, subtraction
and money
painting
2
dancing
1
Getting started
football
4
1
reading
5
a
d
3
Score
3
Exercise 2.1
49
2
b reading
c dancing
Learners’ discussion should mention that
the information tells you what activities
are most popular, so you could plan these
for the club sessions. You might also want
to know what people’s favourite snacks
and drinks are, and so on.
54
68
56
75
99
77
89
64
83
2
Answer depends on the numbers chosen.
3
For example: $10, $5, $1, half dollar (50c),
quarter dollar (25c), two dimes (2 × 10c), one
nickel (5c); three $5 (3 × $5), $1, three quarter
dollars (3 × 25c), two dimes (2 × 10c).
Cambridge Primary Mathematics 3 – Moseley & Rees © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Exercise 3.1
Exercise 3.3
1
Learners’ own calculations.
1
$4.50, $8.70, $24.05, $10, $0.99
2
Learners’ own calculations.
2
3
estimate: 130 + 50 = 180; learners’ own choice
of method, 134 + 53 = 187.
$20 and 45c, $9 and 75c, $15 and no cents,
$2 and 9c, $0 and 30c
3
a
$30 and 76c
b
$80
c
95c
d
8c
4
estimate: 220 + 70 = 290; learners’ own choice
of method, 215 + 67 = 282.
5
estimate: 150 + 140 = 290; learners’ own choice
of method, 148 + 136 = 284.
6
estimate: 440 + 330 = 770; learners’ own choice
of method, 439 + 326 = 765.
Think like a mathematician
All the possibilities:
Think like a mathematician
Learners recognise that they need to use the two
lowest value coins and banknotes ($1 + $2 + 1c +
5c = $3.06) to find the smallest possible value, and
use the two highest value banknotes and coins
($100 + $50 + 50c + 25c = $150.75) to find the
greatest value of Zara’s money.
4
242 + 139 = 381
243 + 138 = 381
a18 + 26 = 44, Sumi spends 44c, 50 − 44 = 6,
Sumi will have 6c change.
b
37 + 37 = 74, Virun spends 74c,
90 − 74 = 16, Virun will have 16c change.
c
75 − 12 = 63
244 + 137 = 381
245 + 136 = 381
246 + 135 = 381
Highlighter + eraser = 37c + 26c = 63c
247 + 134 = 381
Thick felt pen + pencil = 45c + 18c = 63c.
5
248 + 133 = 381
249 + 132 = 381
b
Exercise 3.2
1
46 − 8 = 38, 48 − 6 = 42, 68 − 4 = 64, 64 − 8 = 56,
86 − 4 = 82, 84 − 6 = 78
2
For example: 573 − 9 = 564, 975 − 3 = 972.
3
estimate: 180 − 30 = 150, 178 − 25 = 153
4
estimate: 260 − 40 = 220, 262 − 37 = 225
5
estimate: 470 − 270 = 200, 472 − 267 = 205
6
estimate: 680 − 550 = 130, 683 − 548 = 135
7
494 – 149 = 345
4
= $8. 8 ÷ 2 = 4, or 4 + 4 = 8,
$50 −
= $17. Inverse: $17 + $33 = $50.
= $33. The trainers cost $33.
8
$6 and 50c −
= $1 and 20c. Inverse:
$6 and 50c − $1 and 20c = $5 and 30c.
= $5 and 30c. The comic costs $5 and 30c.
9
491 – 146 = 345
493 – 148 = 345
+
= $4. One ice cream costs $4.
All the possibilities:
492 – 147 = 345
Any two drinks that total less than
$5; for example, tea and orange
juice $2 + $2 and 20c = $4 and 20c.
Change $5 − $4 and 20c = 80c.
6
Think like a mathematician
490 – 145 = 345
a$3 + $1 and 10c + $3 and 25c = $7 and 35c,
$10 − $7 and 35c = $2 and 65c
Learners’ own problem, such as paying for
something with $50 and getting $21 change.
Check your progress
1
estimate: 150 + 230 = 380; learners’ own choice
of method, 147 + 225 = 372.
2
estimate: 380 − 160 = 220; learners’ own choice
of method, 384 − 158 = 226.
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
$50 −
= $24. Inverse: $24 + $26 = $50.
5
= $26. The jacket costs $26.
4 3D shapes
Getting started
1
one or more curved surfaces: sphere, cylinder;
all faces rectangular: cube, yellow cuboid, blue
cuboid; more than five vertices: cube, yellow
cuboid, blue cuboid
2
Fewer than six vertices: sphere, cylinder,
triangle-based pyramid, square-based
pyramid.
Exercise 4.1
1
Curved edges
Straight edges
tinned
tomatoes
biscuits
A prism has two ends that are the same shape
and size. The faces are flat. The remaining
shapes don’t have those properties.
6
cereal
Learners’ own labels, lines and shapes.
2
Learners’ own answers.
3
Learners’ own answers.
4
What can it be?
It is a …
A shape that has faces that
are triangles and a square
squarebased
pyramid
A shape that has no vertices sphere
5
A shape that has 8 faces
hexagonal
prism
A shape that has 6 faces
cuboid
A shape that has a curved
surface and a circular face
cone
Name of
shape
Prism,
Properties
pyramid
or neither
cube
prism
12 edges
6 faces
8 vertices
cylinder
neither
0 edges
2 faces
and 1
curved
surface
0 vertices
triangular
prism
prism
9 edges
5 faces
6 vertices
hexagonal prism
prism
18 edges
8 faces
12 vertices
squarebased
pyramid
8 edges
5 faces
5 vertices
pyramid
7
Results will depend on the throw of the dice.
8
Learners’ sketch of a cuboid, two cubes joined
together and another 3D shape with the
correct name.
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Think like a mathematician
a
18
b
8
c
18
d
16
numbers as they have 5 ones. The numbers in
the overlap are all even numbers because they
have 0 ones.
Multiples of 10 circle: all numbers are
multiples of 10. The numbers in the overlap are
even numbers as they have 0 ones. There are
no numbers in the right-hand side of the circle
because all multiples of 10 are also multiples
of 5 and so they belong in the overlap.
Number of different rectangular prisms
that can be made depends on the number of
bricks chosen.
For rules and patterns, learners must look at
factors, as well as odd and even numbers.
9
Outside the circles: numbers are not multiples
of 5 or 10. All numbers have a ones digit that
is not 5 or 0.
Learners’ own answers.
Check your progress
132
1
Learners’ own answers.
2
cylinder, sphere; learners’ own explanations.
3
A prism is a three-dimensional (3D) shape
with flat faces. It has two ends that are the
same shape and size. A prism has the same
cross-section all along the shape from end to
end. If you cut through it, you would see the
same 2D shape at either end.
A pyramid is also a 3D shape. It has a polygon
base and flat triangular faces that join at a
point called the apex.
5 Multiplication and
division
Getting started
1
1 × 10 = 10, 2 × 5 = 10, 5 × 2 = 10, 10 × 1 = 10
There are two pairs of facts: 1 × 10 = 10 and
10 × 1 = 10, 2 × 5 = 10 and 5 × 2 = 10. Learners
may suggest that, just like addition, they can
multiply in any order.
2
50 ÷ 10 = 5, 25 ÷ 5 = 5, 10 ÷ 2 = 5, 5 ÷ 1 = 5
3
204, 214, 224, 234
multiple
multiple
120 of 10
of 5
45
350
675
490
805
740
215
387
401
96
Think like a mathematician
Sofia is right. Any multiples of 10 are also
multiples of 2 and 5, as 10 = 2 × 5.
4
5 × 6 = 30, 6 × 5 = 30, 30 = 5 × 6, 30 = 6 × 5,
30 ÷ 5 = 6, 30 ÷ 6 = 5, 6 = 30 ÷ 5, 5 = 30 ÷ 6
5
No, there are two mistakes. 30 = 10 ÷ 3 should
be 3 = 30 ÷ 10 and 30 = 3 ÷ 10 should be
10 = 30 ÷ 3.
Think like a mathematician
Learners’ own answers.
6
Learners’ own completed multiplications.
7
Each one becomes a ten and each ten becomes
a hundred so the whole number is ten times
bigger. For example, 28 × 10 = 280; the 20
becomes 200 and the 8 becomes 80. When you
multiply a 1-digit and 2-digit number by 10,
the answer is always an even number because
there is always a 0 in the ones place.
Exercise 5.1
1
rings around 76, 532, 210, 1000, 784, 38, 670
2
A multiple of 2 is made up of groups of two.
Even numbers of objects can always be put
into groups of two (pairs).
3
6
Multiples of 5 circle: all numbers are multiples
of 5. The numbers on the left are all odd
numbers to 1000
100s
2
10s
1s
2
8
8
0
8
23 × 10 = 230, so 230 pencils.
9
16, 21, 26, 31
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Exercise 5.2
1
4 × 6 = 24
2
24, 28, 32, 36, 40. All these numbers are
multiples of 4 and are even because they have
an even number in the ones place.
3
2 × 7 = 14
2×3=6
2 × 5 = 10
2×4=8
double →
double →
← halve
← halve
8 × 5 = 40
5
coloured: 72, 80, 88, 96, 104, 112, 120. All
these numbers are multiples of 8 and are
even because they have an even number in the
ones place.
6
2 × 9 = 18 double → 4 × 9 = 36 double → 8 × 9 = 72
2 × 5 = 10 double → 4 × 5 = 20 double → 8 × 5 = 40
2 × 6 = 12 ← halve 4 × 6 = 24 ← halve 8 × 6 = 48
← halve 4 × 3 = 12 ← halve 8 × 3 = 24
7
9, 13, 17, 21, 25. All these numbers are odd
because adding an even number to an odd
number gives an odd number. They all have an
odd number in the ones place.
8
8, 27 and 43. Both numbers are odd because
adding an even number to an odd number
gives an odd number. They both have an odd
number of ones in the ones place.
9
There are many possible solutions including 5,
13, 21, 29, 37; term-to-term rule add 8
Think like a mathematician
Zara’s conjecture is right. The sum of any two
even numbers is an even number and the difference
between any two even numbers is an even number.
Learners’ own discussion.
Exercise 5.3
1
2
7
1
3× 3
6× 6
2 3 4 5 6 7 8 9 10
6 9 12 15 18 21 24 27 30
12 18 24 30 36 42 48 54 60
6 × 5 = 30
6 × 7 = 42
6 × 8 = 48
6 × 9 = 54
Coloured 9, 18, 27, 36, 45, 54, 63, 72, 81,
90, 99. The number that is coloured moves
one place back to the left on the next row.
To find the next multiple of 9, the ones
digit decreases by 1 and the tens digit increases
by 1. The numbers coloured are odd, even,
odd, even and so on. Learners may have other
ideas.
5
For example, add the multiplication tables for
3 and 6 (3 × 2 = 6, 6 × 2 =12, 9 × 2 = 18) or add
the multiplication tables for 4 and 5 (4 × 2 = 8,
5 × 2 = 10, 9 × 2 = 18).
6
wall 3, 3, 3, middle row 9, 9, top 81;
wall 1, 9, 1, middle row 9, 9, top 81.
7
aLearners’ own sequence with a term-toterm rule of add 9.
b
The numbers will be multiples of the
start number, so they will follow the
same pattern as the multiplication table
products for that number.
8
Dominos (or ten frames or something else to
show that 5 + 3 = 8) with five spots and three
spots, drawn four times.
8 × 4 = 5 × 4 + 3 × 4 = 20 + 12 = 32.
9
9 × 6 = 54, 54 ÷ 6 = 9, 54 ÷ 9 = 6, 9 × 3 = 27,
12 × 9 = 108. Learners may have other ideas.
37, 29, 21, 13, 5; term-to term rule subtract 8
13, 17, 21, 25, 29; term-to-term rule add 4
double →
double →
← halve
← halve
4
4 × 7 = 28
4 × 3 = 12
4 × 5 = 20
4 × 4 = 16
4
2×3=6
3 × 5 = 15
3 × 7 = 21
3 × 8 = 24
3 × 9 = 27
3
Think like a mathematician
The digit sums of multiples of 3 and 6 are always
either 3, 6 or 9. The digit sums of multiples of 9
are always 9.
Check your progress
1
6 × 9 = 54, 54 = 6 × 9, 9 × 6 = 54, 54 = 9 × 6,
54 ÷ 6 = 9, 9 = 54 ÷ 6, 54 ÷ 9 = 6, 6 = 54 ÷ 9
2
rings around 50, 340, 580, 700 and 10
3
80, 30, 270, 45, 32, 42, 20, 48, 27
4
7, 13, 19, 25, 31, 37
3 × 4 = 6 × 2, 3 × 6 = 6 × 3, 3 × 8 = 6 × 4,
3 × 10 = 6 × 5
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
6 Measurement, area
and perimeter
10 table:
a
a
100 cm
280 cm
b
3m
b
15 km
road sign:
1
a–d Learners’ own answers.
2
a–d Learners’ own answers.
a
20 km
Think like a mathematician
Exercise 6.1
The shortest route Silas can take while keeping to
the edges of the bricks is to travel one and a half
1
lengths and two widths. 30 × 1 + 15 × 2 = 75 cm
1
Learners’ own answers.
2
Learners’ own answers.
3
Distance with 2 continents: km
2
Learners’ own answers on other routes.
Length of a seal: m
Size of a saucepan: cm
An Olympic marathon: km
Length of your foot: cm
Length of a rowing boat: m
Exercise 6.2
1
These shapes all have 4 sides, straight sides
and lines of symmetry.
2
It has 3 sides and 3 vertices. All sides are
straight.
3
5 × 5 square with a perimeter of 20 cm
Width of a mobile phone: cm
6 × 6 square with a perimeter of 24 cm
Length of a golf course: km
The perimeter of each square in the sequence
is 4 cm longer than the perimeter of the
previous square.
Height of your bedroom door: m
Width of a glove: cm
4
4
Learners’ own answers.
5
Learners’ own answers.
6
Learners’ own answers.
7
a
learners’ own estimates; 4 cm
b
learners’ own estimates; 2 cm
a
7 m = 700 cm
b
250 cm = 2 and m
c
3 and m = 350 cm
d
1
km = 500 m
2
e
3
750 m = km
4
f
1
km = 250 m
4
9
b
bed:
Getting started
8
110 cm
a
regular:
b
irregular:
c
Learners’ own answers.
1
2
1
2
5
the distance between two continents
the length of a long journey
For example: ten sticks can be a rectangle with
3, 3, 2, 2 sticks on four sides; or a rectangle
with 4, 4, 1, 1 sticks on four sides.
For example: 12 sticks can be a rectangle with
4, 4, 2, 2 sticks on four sides; or a rectangle
with 5, 5, 1, 1 sticks on four sides; or a square
with 3 sticks on each side.
the distance of a marathon race
8
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
6
a
12 cm
b
14 cm
c
18 m
d
20 cm
e
28 km
f
20 cm
4
Think like a mathematician
a
24 cm
b
The next square will be 5 cm by 5 cm,
perimeter = 20 cm.
aFor example: a rectangle with sides 10 cm,
10 cm, 20 cm, 20 cm has area 200 square
cm; a rectangle with sides 15 cm, 15 cm,
15 cm, 15 cm has area 225 square cm.
b
For example: a square with sides 6, 6, 6, 6
has area 36 square units; a rectangle with
sides 10, 2, 10, 2 has area 20 square units.
c
For example: a rectangle with sides 4, 4, 1,
1 has area 4 square units; a rectangle with
sides 3, 3, 2, 2, has area 6 square units.
The next square will be 4 cm by 4 cm,
perimeter = 16 cm.
c
The next square will be 3 cm by 3 cm,
perimeter = 12 cm.
The next square will be 2 cm by 2 cm,
perimeter = 8 cm.
Final square will be 1 cm by 1 cm,
perimeter = 4 cm.
7 Fractions of shapes
Getting started
1
For example:
d, e Perimeter measurements are 24 cm, 20 cm,
16 cm, 12 cm, 8 cm and 4 cm. All are multiples
of four, all are even numbers, descending by 4
each time.
Exercise 6.3
1
a
20 square units
b
16 square units
c
3 square units
d
6 square units
2
Yes (6 square units). Learners’ own answers.
3
a
each side 9 units
b
perimeter 36 units (9 + 9 + 9 + 9)
Think like a mathematician
Thandiwe is incorrect. For example, a rectangle
with side lengths 3 m, 3 m, 10 m, 10 m and another
rectangle with side lengths 4 m, 4 m, 9 m, 9 m
both have a perimeter of 26 metres. But the first
rectangle has an area of 30 square metres and the
second rectangle has an area of 36 square metres.
Exercise 7.1
Check your progress
1
1
2
3
9
a
2.5 m, 7 m, 9 m
b
1
5
4
a
total length 19 cm
b
For example: 10 cm, 3 cm, 3 cm; 6 cm, 4 cm
6 cm; 1 cm, 12 cm, 3 cm. There are many
possible answers.
km,
1
3
4
km,
3
4
4
km, 8 km
a
8 cm, 30 m
b
Learners’ own answers.
2
a
3
10
is green.
b
5
10
or a half is yellow.
c
2
10
is not coloured.
a
one slice
c
1 2
,
10 10
b
two slices
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
a
1 2 1 2
= , =
2 4 5 10
b
Learners’ own answers.
4
Learners’ own answers.
5
2 1
= ,
4 2
so the learner would need to draw
1
2
b
Learners’ own designs and answers.
Check your progress
1
a
34 minutes past 8 or 26 minutes to 9
4
Learners’ own answers.
5
a
18 minutes past 6
b
14 minutes to 3
c
24 minutes past 6
d
42 minutes past 9 or 18 minutes to 10
Think like a mathematician
is shaded, is not shaded.
3
10
f
a and e, b and d, c and f.
Think like a mathematician
1
2
17 minutes past 4
3
another two triangles. Where the learner
positions the triangles is their choice.
a
e
a
Five light bars can make 2, 3 or 5.
b
4, 5 and 6 light bars can match the number
shown on the display (that is, 4 light bars can
make the number 4; 5 light bars can make
the number 5; and 6 light bars can make the
number 6).
1
2
b
2
Check your progress
1
3 sides
2
3
10 sides
2
10
coloured
coloured
2
8 Time
a
quarter past 7
b
half past 2
c
quarter to 3
d
quarter past 10
e
9 o’clock
Exercise 8.1
1
2
10
aminute hand pointing to 3; time around
quarter past 3
b minute hand pointing close to 7; time
around 25 minutes to 7
c
minute hand pointing to 12; time is
12 o’clock
b
13 minutes past 3
c
27 minutes past 9
d
52 minutes past 1 or 8 minutes to 2
16 minutes past 8
b
10 minutes to 4
c
24 minutes past 11
d
40 minutes past 9 or 20 minutes to 10
atwenty-two minutes to three or
thirty-eight minutes past two
b
nine minutes past five
c
thirty-seven minutes past seven or
twenty-three minutes to eight
d
quarter past six or fifteen minutes past six
3
a
5:07
4
clock c; learners’ own answers.
Getting started
1
a
b
2:36
c
10:48
9 More addition and
subtraction
Getting started
1
estimate 520 + 350 = 870; learners’ own choice
of method, 519 + 348 = 867
2
estimate 380 − 170 = 210; learners’ own choice
of method, 375 − 168 = 207
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
Xiang has forgotten to regroup 73 into 60 and
13 so that he can subtract 5 ones. Instead, he
has subtracted 3 ones from 5 ones, which is
incorrect.
2
estimate 250 − 80 = 170, 246 − 84 = 162
100s
10s
1s
473 − 245
= 400 + 70 + 3 − 200 − 40 − 5
= 400 + 60 + 13 − 200 − 40 − 5
= 400 − 200 + 60 − 40 + 13 − 5
= 200 + 20 + 8 = 228
a
estimate 150 − 60 = 90, 148 − 60 = 88
Exercise 9.1
b
estimate 250 − 80 = 170, 245 − 82 = 163
c
estimate 330 − 70 = 260, 326 − 71 = 255
1
d
estimate 530 − 90 = 440, 534 − 93 = 441
a
estimate 340 − 160 = 180, 339 − 163 = 176
b
estimate 360 − 170 = 190, 355 − 172 = 183
c
estimate 650 − 390 = 260, 647 − 386 = 261
d
estimate 520 − 250 = 270, 518 − 248 = 270
2
3
a
estimate 40 + 60 = 100, 43 + 56 = 99
b
estimate 70 + 30 = 100, 67 + 29 = 96
4
estimate 60 + 50 = 110, 64 + 53 = 117
100s
10s
1s
5
3
a
estimate 80 + 60 = 140, 84 + 62 = 146
b
estimate 70 + 90 = 160, 71 + 87 = 158
c
estimate 60 + 70 = 130, 64 + 72 = 136
d
estimate 80 + 30 = 110, 75 + 34 = 109
Think like a mathematician
The numbers could be 96 + 41, 46 + 91, 86 + 51,
56 + 81, 76 + 61, 66 + 71.
4
a
estimate 230 + 50 = 280, 233 + 50 = 283
b
estimate 180 + 60 = 240, 178 + 60 = 238
c
estimate 150 + 70 = 220, 154 + 65 = 219
d
estimate 190 + 60 = 250, 191 + 56 = 247
e
estimate 290 + 350 = 640, 286 + 352 = 638
f
estimate 470 + 170 = 640, 473 + 166 = 639
5
Learners’ own answers.
6
Learners’ own answers.
7
Learners’ own answers.
1
11
b
300 + 150 + 2
d
200 + 100 + 9
= 17
Think like a mathematician
307 – 147 = 160
317 – 157 = 160
327 – 167 = 160
337 – 177 = 160
347 – 187 = 160
357 – 197 = 160
Triangle and square must both be odd or both
even to give the even result of 6 tens required.
Exercise 9.3
2
c
= 92
b
1
Exercise 9.2
a
a
35 + 65 = 100
b
53 + 47 = 100
c
77 + 23 = 100
d
81 + 19 = 100
e
8 + 92 = 100
520 + 480, 530 + 470, 540 + 460, 550 + 450,
560 + 440, 570 + 430, 580 + 420, 590 + 410
600 + 160 + 3
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
4
5
a
35 + 65 = 100, 350 + 650 = 1000
b
a
370 + 290 = 660
b
550 + 180 = 730
53 + 47 = 100, 530 + 470 = 1000
c
670 − 290 = 380
d
740 − 460 = 280
c
77 + 23 = 100, 770 + 230 = 1000
e
370 + 360 = 730
f
820 − 350 = 470
d
81 + 19 = 100, 810 + 190 = 1000
e
8 + 92 = 100, 80 + 920 = 1000
a
880 + 120 = 1000
b
470 + 530 = 1000
c
240 + 760 = 1000
d
510 + 490 = 1000
Getting started
e
340 + 230 = 570
f
750 + 150 = 900
1
a
six ducks
g
560 + 290 = 850
h
370 + 350 = 720
b
three elephants
i
670 + 140 = 810
j
390 + 180 = 570
c
two more turtles
a
980 − 260 = 720
b
740 − 340 = 400
d
18 animals all together
c
670 − 380 = 290
d
810 − 520 = 290
e
two fewer lions
e
760 − 490 = 270
f
520 − 370 = 150
g
850 − 480 = 370
i
630 − 470 = 160
Think like a mathematician
There are 18 different pairs of 3-digit multiples of
10, with a total of 540: (100, 440), (110, 430),
(120, 420), (130, 410), (140, 400), (150, 390),
(160, 380), (170, 370), (180, 360), (190, 350),
(200, 340), (210, 330), (220, 320), (230, 310),
(240, 300), (250, 290), (260, 280) and (270, 270).
3
10 Graphs
Exercise 10.1
1
a
5 and a half hours
b
1 and a half hours more
c
Sunday has 5 and a half hours of
sunshine,
Friday has 13 hours of sunshine.
Title: Number of hours of sunshine
Check your progress
Saturday
1
Sunday
Learners’ own method.
a
estimate 260 + 170 = 430, 263 + 174 = 437
b
estimate 480 + 350 = 830, 475 + 353 = 828
c
estimate 360 − 190 = 170, 358 − 187 = 171
2
2
estimate 740 − 470 = 270, 736 − 472 = 264
Number
Complement
to 100
54
46
19
91
81
77
33
23
= 1 hour
of sunshine
a
y
9
Animals in the pet shop
8
7
6
Number
Complement
to 1000
440
660
753
247
288
722
560
Number of animals
d
5
4
3
2
1
0
turtle rabbit
fish
cat
guinea x
pig
Animals
712
b
12
Key
Friday
Learners’ own answers.
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
a–e Learners’ own answers.
4
a–d Learners’ own answers.
5
Learners’ own answers.
2
Has vertices
2D
Think like a mathematician
Not 2D
Learners’ own answers.
3
Exercise 10.2
1
odd
Numbers 1 to 20
2
4
8
10
14
multiples
of 2 and 3
16
20
5
7
b
31
multiples of 3
multiples of 2
2
6
a
19
17
18
15
17
4
13
11
multiples of 5
5
29
35
40
10
16
8
Even
Not even
18 12 24
15 21
11 17 23
Learners’ own answers.
a–e Learners’ own answers.
4Learners’ own answers but labels can be two
arms/not two arms, four arms/not four arms,
odd number of legs/not odd number of legs
and even number of legs/not even number
of legs.
Learners’ own answers.
a
three times
b
Learners’ own answers.
11 More multiplication
and division
Getting started
1
8 × 4 = 32, 32 = 8 × 4, 4 × 8 = 32, 32 = 4 × 8,
32 ÷ 8 = 4, 4 = 32 ÷ 8, 32 ÷ 4 = 8, 8 = 32 ÷ 4
2
Add the multiplication tables for 5 and 3
or for 6 and 2; double and double again
the multiplication table for 2; double the
multiplication table for 4.
3
a
24
b
4
c
42
d
50
e
10
f
130
g
72
h
2
i
0
Think like a mathematician
13
25
3
9
12
Not a multiple of 3 10 16 20 22
b
19
Learners’ own answers.
Multiple of 3
3
Numbers
a
1
Does not have
vertices
Exercise 11.1
Check your progress
1
24, 8, 18, 63, 48, 36
1
2
Each product is the result of a number
multiplied by itself.
3
24 ÷ 8 = 3 or 24 ÷ 3 = 8; 8 ÷ 4 = 2 or 8 ÷ 2 = 4;
18 ÷ 6 = 3 or 18 ÷ 3 = 6; 63 ÷ 9 = 7 or 63 ÷ 7 = 9;
48 ÷ 6 = 8 or 48 ÷ 8 = 6; 36 ÷ 4 = 9 or 36 ÷ 9 = 4
aThree monsters have two legs, two
monsters have three legs, two monsters
have four legs.
b
Learners’ own answers.
c
For example, sort them by the number
of arms.
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Think like a mathematician
2
The numbers on the diagonal line are shown only
once because the diagonal line is a mirror line. For
numbers that are not on the diagonal lines, we can
find their reflection in the other half.
4
28, 4 and 7: 4 × 7 = 28, 28 = 4 × 7, 7 × 4 = 28,
28 = 7 × 4, 28 ÷ 4 = 7, 7 = 28 ÷ 4, 28 ÷ 7 = 4,
4 = 28 ÷ 7.
72, 8 and 9: 8 × 9 = 72, 72 = 8 × 9, 9 × 8 = 72,
72 = 9 × 8, 72 ÷ 8 = 9, 9 = 72 ÷ 8, 72 ÷ 9 = 8,
8 = 72 ÷ 9.
3
Learners may have other estimates or use
other methods.
a
estimate: 40 × 4 = 160, 35 × 4 = 140;
b
estimate: 60 × 3 = 180, 58 × 3 = 174;
c
estimate: 90 × 2 = 180, 94 × 2 = 188;
d
estimate: 80 × 5 = 400, 76 × 5 = 380.
Learners’ own answers.
Think like a mathematician
The number is 60.
4
46 ÷ 4 = 11 r2, so 12 tubes are needed for 46
balls.
5
36 ÷ 5 = 7 r1, so each child gets seven marbles
with one marble left over.
6
37 ÷ 10 = 3 r7, so four benches are needed for
37 children.
Exercise 11.2
7
Learners’ own answers.
1
Learners’ own order of multiplication.
a 5 × 4 × 3 = 60
b 6 × 5 × 3 = 90
c 6 × 4 × 2 = 48
d 8 × 3 × 2 = 48
Check your progress
1
Learners’ own answers.
2
Learners’ own order of multiplication.
2
Learners’ own answers.
3
a
b
c
d
3
Learners’ own answers.
4
72 ÷ 3 because there will be more groups of 3
in 72 than there will be groups of 4.
5
6
a
b
c
d
54, 63, 72; rule is + 9
38, 43, 48; rule is + 5
115, 123, 131; rule is + 8
99, 90, 81; rule is – 9.
100, 92, 84, 76, 68
13 × 4 = 10 × 4 + 3 × 4 = 40 + 12 = 52
18 × 5 = 10 × 5 + 8 × 5 = 50 + 40 = 90
12 × 2 = 10 × 2 + 2 × 2 = 20 + 4 = 24
15 × 3 = 10 × 3 + 5 × 3 = 30 + 15 = 45
Learners may use other methods; for
example, for 18 × 5 use 18 × 10 = 180, halve
it, 18 × 5 = 90.
4
5
a
c
e
b
d
f
28 ÷ 4 = 7
53 ÷ 5 = 10 r3
10 ÷ 4 = 2 r2
25 ÷ 2 = 12 r1
32 ÷ 4 = 8
46 ÷ 3 = 15 r1
Each child gets seven sweets, with two left
over: 30 ÷ 4 = 7 r2.
Think like a mathematician
The number can be 11, 13, 17 or 19.
Getting started
1
5
b
1
3
1
a
c
2
No, of the same whole is greater than
1
5
×
20
3
4
80
12
estimate: 20 × 4 = 80
1
4
1
10
of
the same whole. If the whole is split into five
equal pieces, each piece will be larger than if it
was split into ten equal pieces.
3
Dad eats four slices, Mum eats four slices,
1
5
Hinata eats two slices; that is, or
Exercise 11.3
1
12 More fractions
2
.
10
Exercise 12.1
1
a
2
50 cm
5 cm
b
10 cm
80 + 12 = 92, 23 × 4 = 92
14
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
4
a
Ring drawn around any two marbles.
b
9
10
12 cars
5
1
2
1
3
1
4
1
10
3
4
10
X
5
2
15
20
4
1
5
5
a
2 1
=
4 2
b
2 1
>
5 5
c
1 2
<
3 3
d
7
9
<
10 10
e
1 1
>
5 10
f
1 1
> .
2 3
6
1 1
4 5
1 1
4 4
1 1
5 4
1
3
1
4
of something is more than of the same
1
3
something, so of $100 is more than
6
27
The number is 60, or any multiple of 60.
8
Think like a mathematician
1
2
b
1
2
of 24 = 12, 24 ÷ 2 = 12
We can also say that D is five times bigger than A.
C is twice as big as A.
c
1
4
of 40 = 10, 40 ÷ 4 = 10.
Example: A = 4, B = 6, C = 8 and D = 20.
1
4
a
of 12 = 3, 12 ÷ 4 = 3;
1
4
of 16 = 4,
of 24 = 6, 24 ÷ 4 = 6;
1
4
7
of 28 = 7,
1
4
1
4
of 36 = 9, 36 ÷ 4 = 9;
1
4
8
a
3 4 5
6
= = =
6 8 10 12
b
3 4 5 6
, , ,
30 40 50 60
c
2 3 4 5
, , ,
8 12 16 20
1
2
For example, is shown.
b
1
4
Each person gets two quarters of a sandwich,
2
4
1
2
or each.
9
1
4
10 1 out of 4, .
1
4
2
4
For a 12 cm line, marked at 3 cm, at 6 cm,
at 9 cm.
1
3
2
3
For a 15 cm line, at 5 cm, at 10 cm,
2
10
at 3 cm.
4 8
,
5 10
and
9
.
10
1
3
Exercise 12.3
Exercise 12.2
3
4
1
4
1
1
1
6
6
6
1
1
1
1
8
8
8
8
1
1
1
1
1
10
10
10
10
10
The fraction list uses multiples of 4, the
divisions are the division table for 4.
which is
1
2
1
2
of 40 = 10,
40 ÷ 4 = 10.
15
of D. We can say
that D > C > B > A.
28 ÷ 4 = 7; of 32 = 8, 32 ÷ 4 = 8;
3
1
10
of 8 = 2, 8 ÷ 4 = 2
1
4
2
1
4
a
16 ÷ 4 = 4; of 20 = 5, 20 ÷ 4 = 5;
1
1
3
Let of A = of B = of C =
1
4
1
4
9
1
4
of $100.
Think like a mathematician
7
1
5
is less than , < ; is greater than , > .
1
4
3
7
+ =
10 10 10
2
Learners’ own diagrams.
1 2
2 3
a
estimate: > ,
b
estimate: > ,
c
estimate: = ,
d
estimate: > ,
1 4
2 5
1 5 1
=
2 10 2
1 3
2 4
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
0 4
1 3
2 2
+ = 1, + = 1, + = 1
4 4
4 4
4 4
4
4 3 1
− =
5 5 5
5
Learners’ own diagrams.
6
a
1
estimate: < ,
2
c
estimate: > ,
3
0
1 7
2 10
0
5
5
5
1
5
4
5
4
5
1
5
5
5
0
5
2
5
2
b
1 1
estimate: < ,
2 5
d
estimate: < ,
3
5
1 1
2 4
3
5
2
5
1− = , 1− = , 1− = , 1− = ,
b
Each side of the scales has a mass of 150 g.
a
500 g < 5 kg
c
1000 g = 1 kg
a
c
b
10 g < 1 kg
80 g
b
70 g
500 g
d
4g
5
Learners’ own answers.
6
Learners’ own answers.
Think like a mathematician
1− = , 1− = =0
For example rows could be:
Think like a mathematician
200 g
500 g
300 g
Learners’ own answers.
700 g
250 g
50 g
400 g
450 g
150 g
7
a
$6
b
$3
c
$24
d
$15
Columns can use the same amounts as above but
set vertically.
Check your progress
1
1 1 1 1 1
, , , ,
10 5 4 3 2
2
a
1 1
<
4 3
d
5 1
=
10 2
3
b
4 2
>
5 5
e
4 10
=
4 10
Challenge answer, for example:
c
1 1
<
10 5
f
2 3
<
3 3
Learners’ own diagrams.
1 2
2 10
a
estimate: < ,
b
1 5
estimate: > , = 1
2 5
c
estimate: > ,
d
estimate: > ,
500 g
50 g
450 g
250 g
350 g
400 g
250 g
600 g
150 g
Within the Challenge square, there are eight ways
to make a total of 1 kg: three rows, three columns
and two diagonals.
Exercise 13.2
1
a
A: 250 ml; B: 750 ml; C: 500 ml
b
container B, container C, container A
c
The same because 1000 ml is the same as
1 litre.
d
Learners should have drawn a line at the
500 ml mark.
a
250 ml = litre
b
750 ml = litre
Getting started
c
1000 ml = 1 litre
d
8 cans = 2 litres
1
e
12 cans = 3 litres
f
16 cans = 4 litres
1 2
2 3
1 3
2 4
13 Measure
2
Learners’ own answers.
3
Exercise 13.1
1
16
4
aThe chocolate bar must have the same
mass as two muffins, so one muffin must
have a mass of 50 g.
One pear has a mass of 40 grams, so 4 pears
have a mass of 160 grams.
1
4
3
4
Marcus is incorrect. His method will only
work if he has two jugs that are the same size
and with the same capacity. Otherwise, a tall
narrow jug could have a higher level of water
than a wider jug but still contain less water.
Cambridge Primary Mathematics 3 – Moseley & Rees © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
4
a
625 ml, rounded to 600 ml
b
Think like a mathematician
490 ml, rounded to 500 ml
Learners’ own posters.
c
250 ml, rounded to 300 ml
5
Learners’ own answers.
Check your progress
6
Learners’ own answers.
1
Think like a mathematician
2
a
1000 millilitres = 500 millilitres + 500 millilitres
(cup A + cup A)
b
700 millilitres = fill cup A, pour into cup B,
200 ml left in cup A, pour this into a container,
fill cup A and pour into the container with
the 200 ml.
c
d
100 millilitre = fill cup B and pour into cup A,
fill cup B again and fill cup A, 100 ml is left
in cup B.
Yes. They can be made as follows. Different
answers are possible.
•
•
•
•
•
•
•
•
•
•
100 ml: see c
200 ml: fill cup A, pour into cup B, 200 ml
left in cup A
300 ml: cup B
400 ml: twice 200 ml (see above)
500 ml: cup A
600 ml: twice cup B
700 ml: see b
800 ml: cup A + cup B
900 ml: cup A + 400 ml (see above)
1000 ml: see a
3
4
17
b
7 kilograms
c
900 grams
d
3 kilograms
a
400 ml
b
200 ml
c
Learners’ own drawings. The container
holding 350 ml has more water.
a
400 grams
c
24 cm
b
11 days
16 °C
Getting started
1
2
a
8:05
b
11:17
c
2:35
d
1:34
a
b
c
d
1
a
2
aNo, Marianna is not right. The reading is
nearer to 15 °C than to 20 °C.
3
200 grams
14 Time (2)
Exercise 13.3
30 °C
a
b
c
30 °C
10 °C
b
The reading is nearest to 35 °C.
c
marked a little over half way between 25
and 30
a
thermometers B, C, D and E
b
18 °C
c
15 °C
d
thermometer C
e
20 °C
f
Learners’ own answers.
4
Learners’ own answers.
5
Learners’ own answers.
3
a
11 12 1
10
2
9
8
3
7
6
5
4
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b
9
8
c
1
3
7
6
5
4
11 12 1
10
2
9
8
d
Exercise 14.2
11 12 1
10
2
2
3
7
6
5
4
8
6
5
1
2
1
a–g Learners’ own answers.
2
a
26 days
b
22nd March
c
3rd February
d
9th February
a
6th June
b
11th July
c
seven days
d
Stefania was born in 2010, so she will be
20 years old in 2030.
a
174 days
b
15 years old
c
Song’s holiday is longer by 1 day.
a
Saturday 19th April
b
Monday 28th April
4
5
6
two years
7
Learners’ own answers.
8:45
c
Bus 1 and Bus 2
d
Razaan is correct. This timetable shows
the bus travelling in one direction only. It
does not give information about the buses
travelling in the opposite direction, from
school to Razaan’s home.
a
11:23
b
2:58
c
Train 2 and train 6
d
11:25
e
8:01
Check your progress
4
Exercise 14.1
3
b
Learners’ own answers.
3
7
8:50
Think like a mathematician
11 12 1
10
2
9
a
3
a
two months
b
31 days
c
two weeks
a
Wednesday
b
Thursday
c
1:00
d
Tuesday
a
7:30
b
8:42
c
the second train
15 Angles and
movement
Getting started
1
a
Think like a mathematician
Learners’ own answers.
18
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Think like a mathematician
b
a
3 steps
b
3 steps
c
3 steps
d
20 routes
e
no
f
no
g,h Learners’ own answers.
c
5
Learners’ own answers.
6
Learners’ own answers. The last drawing
should be the same as the first drawing.
Check your progress
1
d
Other shapes have no right angles.
2
For example: The two half turns end in the
same place.
west
Exercise 15.1
1
a, b Learners’ own answers.
19
south
Learners’ own answers.
3
a
school
b
pond
c
north
d
east
e
east
f
south
g
south
h
Learners’ own answers.
Learners’ own answers.
N
finish
aMove south one square. Turn one right
angle clockwise. Move west four squares.
Turn one right angle anticlockwise. Move
south three squares. Turn one right angle
anticlockwise. Move east one square. Turn
one right angle clockwise. Move four
squares south.
b
east
start
2
4
north
2
16 Chance
Getting started
1
Learners’ own answers.
2
Learners’ own answers.
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CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
3
Possible
Impossible
A horse will grow
wings and fly.
✓
A carrot will walk.
✓
A baby will cry.
✓
It will rain
somewhere in the
world today.
✓
Exercise 17.1
1
2
a
Exercise 16.1
1It might happen. One domino has more than
eight spots.
2
Learners’ own answers.
3
a
Spinner A could land on 1, 2 or 3.
b
Spinner B could land on 1, 2, 3, 4, 5, 6, 7
or 8.
c
Spinner A is more likely to land on 3,
because there are fewer options. Spinner B
has more options.
d
Learners’ own results.
e
Learners’ own answers.
b
c
Think like a mathematician
Learners’ own answers.
Check your progress
d
1
Learners’ own answers.
2
Might happen. A total of 10 can be made
by 7 + 3 or 6 + 4.
3
Will not happen. You cannot make a total of
20 from any pair of these cards.
4
Learners’ own answers.
17 Pattern and
symmetry
3
a
Getting started
1
20
Learners’ own answers.
Cambridge Primary Mathematics 3 – Moseley & Rees © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
7
b
These shapes have symmetry:
A circle has an infinite number of lines
of symmetry; only four are marked in the
diagram above.
c
4
Learners’ own answers.
Diagram c shows symmetry.
Symmetry means that when an object is split
along a line of symmetry, it will produce two
mirror images.
5
Learners’ own answers.
8
Learners’ own answers. Marcus is correct: a
circle has infinite lines of symmetry.
9
Learners’ own answers. Only the second and
third logos are symmetrical.
Think like a mathematician
Learners’ own answers.
Exercise 17.2
6
1
a
b
9 + 3 = 12, 12 + 3 = 15, 15 + 3 = 18
21
c
The constant is that three circles are
added each time.
2
a
c
4, 6, 8
b 10
The constant is that two squares are
added each time.
3
a,b,c
For example:
For example:
The pentagon can be regular or irregular, as
long as it is symmetrical.
d
The constant is that four squares are
subtracted each time.
4
a
b
c
2, 3, 4
5
The constant is that one cloud is added
each time.
5
a
b,c,d
21
16 to 12 to 8 to 4.
Learners’ own answers.
6
For example: Add a square to the centre of
the top block, but there are other ways.
7
Learners’ own answers.
Cambridge Primary Mathematics 3 – Moseley & Rees © Cambridge University Press 2021
CAMBRIDGE PRIMARY MATHEMATICS 3: TEACHER’S RESOURCE
Think like a mathematician
Check your progress
For example:
1
a
b
2
a, b Learners’ own answers.
3
a
2 to 4 to 6 to 8.
b
There will be eight circles in the
final pattern.
4
Learners’ own answers.
5
Learners’ own answers.
There can also be other solutions where the
squares are not joined.
22
Cambridge Primary Mathematics 3 – Moseley & Rees © Cambridge University Press 2021