Y3 – Autumn – Block 3 – Step 1 – Equal groups Answers
Question
1
2
Answer
a) There are 4 plates.
Each plate has 3 cakes.
There are 4 equal groups of 3
b) There are 4 bags.
Each plate has 5 apples.
There are 4 equal groups of 5
a) child’s arrangements of 30 cubes in 6 groups of 5
b) child’s drawing of groups in part a)
The cubes could represent any 30 objects.
3
4
5
child’s arrangements of 6 coins in 3 groups of 2
2
child’s story about 5 groups of 0
a)
6
b)
a)
7
b) 5
c) The number of counters increases by the number in a group.
Y3 – Autumn – Block 3 – Step 1 – Equal groups Answers (continued)
Question
8
Answer
a) six ways:
1 group of 12
2 groups of 6
3 groups of 4
4 groups of 5
6 groups of 2
12 groups of 1
b) Go through each number from 1 to 12, trying to make groups of that number.
Y2 – Autumn – Block 4 – Step 4 – Multiplication sentences using the × symbol Answers
Question
1
Answer
a) There are 3 equal groups with 6 in each group.
6 + 6 + 6 = 18
3 × 6 = 18
b) There are 4 equal groups with 5 in each group.
5 + 5 + 5 + 5 = 20
4 × 5 = 20
c) There are 2 equal groups with 4 in each group.
4+4=8
2×4=8
3×5
2
5×3
10 + 10
3
5 × 2 = 5 + 5 = 10
5 × 3 = 5 + 5 + 5 = 15
5 × 4 = 5 + 5 + 5 + 5 = 20
5 × 5 = 5 + 5 + 5 + 5 + 5 = 25
5 × 6 = 5 + 5 + 5 + 5 + 5 + 5 = 30
possible answers:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 16
16 × 1 = 16
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16
8 × 2 = 16
4
4 + 4 + 4 + 4 = 16
4 × 4 = 16
8 + 8 = 16
2 × 8 = 16
5
a) 4
b) 2
c) 5
Y2 – Autumn – Block 4 – Step 6 – Use arrays Answers
Question
1
2
3
4
5
6
Answer
5 + 5 + 5 = 15
3 × 5 = 15
There are 15 pears.
6 + 6 = 12
2 × 6 = 12
There are 12 stars.
4 + 4 + 4 = 12
3 × 4 = 12
3 + 3 + 3 + 3 = 12
4 × 3 = 12
The numbers in the multiplication are the same.
2 × 9 = 18
9 × 2 = 18
7 × 3 = 21
The array could be drawn as 3 rows of 7
possible arrays:
1 row of 12
2 rows of 6
3 rows of 4
4 rows of 3
6 rows of 2
12 rows of 1
Y2 – Autumn – Block 4 – Step 6 – Use arrays Answers (continued)
Question
7
8
Answer
Y2 – Autumn – Block 4 – Step 7 – The 2 times-table Answers
Question
1
Answer
a) 5 × 2 = 10
b) 7 × 2 = 14
c) 4 × £2 = £8
a)
2
6
8 10
14 16
b)
✔
a)
4
b)
10
3
c)
4
5
6
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
4
6
18
10
2
6
24
1
0
7
11
Rosie has £16
other possible ways:
0 × 2 + 10 × 2
1×2+9×2
2×2+8×2
4×2+6×2
5×2+5×2
6×2+4×2
7×2+3×2
8×2+2×2
9×2+1×2
10 × 2 + 0 × 2
Children can discuss how many different ways there are to write 10 × 2
Y2 – Autumn – Block 4 – Step 8 – The 5 times-table Answers
Question
Answer
a)
1
b) child’s drawing showing 4 × 5, e.g. array of 4 rows of 5 counters
a)
15 20 25 30
b)
2
3
4
5
6
✔
The numbers go up in 5s.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
25
45
30
8
7
55
1
0
2
12
10 × 5p = 50p
Ron has 50p.
7×5<5×8
6×5=4×5+2×5
2×5=3×5−1×5
12 × 2 = 2 × 12
Jack spends £25
40
Y2 – Spring – Block 1 – Step 1 – Make equal groups – sharing Answers
Question
Answer
1
There are 2 boxes.
There are 6 apples in each box.
2
3
4
a) There are 2 groups.
There are 10 cubes in each group.
b) There are 5 groups.
There are 4 cubes in each group.
c) Yes.
20 can also be divided into:
20 equal groups of 1
10 equal groups of 2
4 equal groups of 5.
a) 20
b) 10
c) 8
d) 4
Yes. We needed to exchange each ten for 10 ones for parts c) and d).
a) 30 ÷ 5 = 6
b) 30 is the total number of flowers, 5 is the number of vases and 6 is the number of
flowers in each vase.
A
B
C
D
4
5
10
10
B
5
C
A
D
children’s stories to match the divisions
Y2 – Spring – Block 1 – Step 2 – Make equal groups – grouping Answers
Question
1
2
3
4
5
6
Answer
There are 10 apples.
There are 2 apples on each plate.
There are 5 plates.
The counters are in groups of 3
There are 5 groups.
a) chairs circled in 4 groups of 5
b) 4
c) 20 ÷ 5 = 4
a) 30 ÷ 10 = 3
30 is made of 3 equal groups of 10
b) 30 ÷ 5 = 6
30 is made of 6 equal groups of 5
c) other possible equal groups:
30 equal groups of 1
15 equal groups of 2
10 equal groups of 3
5 equal groups of 6
2 equal groups of 15
1 group of 30
24 ÷ 2 = 12
Eva needs 12 pots.
No.
other possible groups:
40 equal groups of 1
20 equal groups of 2
8 equal groups of 5
5 equal groups of 8
2 equal groups of 20
1 group of 40
Y2 – Spring – Block 1 – Step 3 – Divide by 2 Answers
Question
1
2
3
4
Answer
a) There are 2 groups.
There are 6 cherries in each group.
12 ÷ 2 = 6 2 × 6 = 12
b) There are 2 muffins in each group.
There are 5 groups.
10 ÷ 2 = 5 5 × 2 = 10
a) 4 × 2 = 8
8÷2=4
b) 8 × 2 = 16
16 ÷ 2 = 8
a) 7
b) 14 ÷ 2 = 7
a) 6
b) 10
Count up in 2s from 0 to 20 or work out what number times 2 gives 10
5
22 ÷ 2 = 11
Alex needs 11 pots.
6
Yes.
Dora can use the number that when it is multiplied by 2 gives the number she is dividing by.
7
a)
b)
c)
d)
e)
f)
g)
h)
3
5
7
0
10
12
18
22
Y2 – Spring – Block 1 – Step 5 – Divide by 5 Answers
Question
1
2
3
Answer
a) counters circled in 6 groups of 5
b) There are 5 counters in each group.
There are 6 groups.
30 ÷ 5 = 6
6 × 5 = 30
There are 15 sweets.
There are 5 party bags.
There are 3 sweets in each bag.
15 ÷ 5 = 3
a) 4 × 5 = 20
20 ÷ 5 = 4
b) 8 × 5 = 40
40 ÷ 5 = 8
4
5
6
7
45 ÷ 5 = 9
9 boats are needed.
a)
b)
c)
d)
e)
f)
g)
h)
3
5
10
12
35
55
40
0
20p
Y2 – Spring – Block 1 – Step 6 – Divide by 10 Answers
Question
1
2
3
4
Answer
There are 60 crayons.
There are 10 crayons in each pack.
60 ÷ 10 = 6
6 packs can be made.
40 ÷ 10 = 4
5 × 10 = 50
10 × 5 = 50
50 ÷ 10 = 5
50 ÷ 5 = 10
a)
b)
c)
d)
e)
7
8
1
2
60
5
40 ÷ 10 = 4 or 40 ÷ 4 = 10
4 × 10 = 40 or 10 × 4 = 40
6
100 ÷ 10 = 10
Tommy can fill 10 pages.
7
6 kg
Y3 – Autumn – Block 3 – Step 2 – Multiply by 3 Answers
Question
1
2
Answer
a) There are 6 equal groups of 3
3 + 3 + 3 + 3 + 3 + 3 = 18
6 × 3 = 18
b) There are 4 equal groups of 3
12 = 3 + 3 + 3 + 3
12 = 4 × 3
c) There are 7 equal groups of 3
3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
7 × 3 = 21
The numbers in the multiplication can be written either way round:
3 × 6 = 18
3 × 4 = 12
3 × 7 = 21
a) 5 × 3 = 15
3 × 5 = 15
b) 10 × 3 = 30
3 × 10 = 30
child’s number story, e.g.
There are 6 plates with 3
cakes on each plate.
18
3
3
3
3
3
3
3
3 + 3 + 3 + 3 + 3 + 3 = 18
9
4
5
12
4
15
3
5
3
No.
6 lots of 3 is 3 more than 5 lots of 3
✔
or
6
✔
All the others represent 5 × 3
All the others are lots of 3. The coins are lots of 5
Y3 – Autumn – Block 3 – Step 3 – Divide by 3 Answers
Question
1
2
Answer
There are 3 plates.
Each plate has 4 cubes.
12 divided into 3 equal groups is 4
There will be 5 pencils in each pot.
3
6
4
5
9 boxes of 3 cakes can be filled.
3
3
3
3
3
3
3
3
3
3
3
An alternative bar model would be 3 bars of 11
6
7
a) 21 ÷ 3 = 7
b) 36 ÷ 3 = 12
c) 24 ÷ 3 = 8
Yes.
We can move one square from the right-hand column and move it to the left-hand column.
The columns are then all the same height, so the number can be divided by 3
Y3 – Autumn – Block 3 – Step 4 – The 3 times-table Answers
Question
1
2
3
4
5
Answer
a) 8 × 3 = 24
b) 3 × 4 = 12
3 × 5 = 15
5 × 3 = 15
15 ÷ 3 = 5
15 ÷ 5 = 3
a)
b)
c)
d)
e)
f)
18
9
33
15
36
0
a) 2 × 3 = 6
4 × 3 = 12
8 × 3 = 24
b) 6 = 3 × 2
12 = 3 × 4
18 = 3 × 6
In part a), the number multiplying by 3 doubles each time and the answer doubles each
time.
In part b), the answer goes up by 6 each time and the number multiplying by 3 goes up by 2
each time.
a)
b)
c)
d)
e)
f)
=
>
<
>
>
<
6
The shaded squares form diagonal lines. The squares in each row are one square further
back than the row above.
a)
7
18
b)
12
12
12
Y3 – Autumn – Block 3 – Step 4 – The 3 times-table Answers (continued)
Question
8
Answer
Eva
a)
✔
✔
6
9
9
✔
4
✔
b) 5 × 3 = 15
c) They alternate odd and even.
If the number multiplying 3 is odd, the product is odd.
If the number multiplying 3 is even, the product is even.
d) odd
13 × 3 = 39
3 × 15 = 45
14 × 3 = 42
24 × 3 = 72
10
13 × 3 is 3 more than 12 × 3
3 × 15 is 9 more than 12 × 3
14 × 3 is 6 more than 12 × 3
24 × 3 is twice 12 × 3
Y3 – Autumn – Block 3 – Step 5 – Multiply by 4 Answers
Question
1
2
Answer
a) There are 5 bags of pears.
There are 4 pears in each bag.
There are 20 pears in total.
b) There are 3 plates.
There are 4 doughnuts on each plate.
There are 12 doughnuts in total.
2×4=8
8
12
3
16
4
5
4 × 5 = 20
5 × 4 = 20
28
6
7 × 4 = 28
7
Teddy has 40 sweets.
8
Yes.
Mrs Wilson has 48 litres of juice.
9
Yes.
2×2=4
Y3 – Autumn – Block 3 – Step 6 – Divide by 4 Answers
Question
1
2
Answer
There are 4 plates.
Each plate has 3 cakes.
12 shared into 4 equal groups is 3
4 circles of 4 flowers
a) 4
b) There are 4 groups of 4 in 16
3
a) 8
b) 32 ÷ 4 = 8
4
24 ÷ 4 = 6
There will be 6 apples in each bag.
5
6
7
5 boxes of muffins can be filled.
7 × 4 = 28
Yes, Alex’s method always works.
11
11
11
11
32 ÷ 4 = 11
2
1
3
does not divide equally
4
2
5
does not divide equally
6
3
14
7
does not divide equally
16
8
4
8
All the numbers that are can be divided equally by 2 can also be divided equally by 4, but
not all the numbers that can be divided equally by 4 can be divided equally by 2
A number divided by 2 is twice the same number divided by 4
Y3 – Autumn – Block 3 – Step 7 – The 4 times-table Answers
Question
1
2
3
4
5
6
7
Answer
a) 8 × 4 = 32
b) 4 × 3 = 12
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
24
12
28
12
0
36
6
2
0
44
20
4
4 × 7 = 28
7 × 4 = 28
28 ÷ 4 = 7
28 ÷ 7 = 4
a) 2 × 4 = 8
4 × 4 = 16
8 × 4 = 32
b) 8 = 4 × 2
16 = 4 × 4
32 = 4 × 8
c) 3 × 4 = 12
3 × 8 = 24
3 × 12 = 36
In parts a) and b), when one of the numbers being multiplied doubles, the product doubles.
In part c), when one of the numbers being multiplied goes up by 4, the product goes up by 3
× 4 = 12
a)
b)
c)
d)
e)
f)
=
>
<
<
=
=
24 cm
£52
Y3 – Autumn – Block 3 – Step 7 – The 4 times-table Answers (continued)
Question
Answer
16
8
20
4
9
Eva is correct.
4 is even, so any number times 4 is also even.
Y3 – Autumn – Block 3 – Step 8 – Multiply by 8 Answers
Question
1
Answer
a) There are 5 bags of apples.
There are 8 apples in each bag.
There are 40 apples in total.
b) There are 4 octopuses.
There are 8 arms on each octopus.
There are 32 arms in total.
2
3
4
a) 3 × 8 = 24
b) 8 × 3 = 24
In both parts, 3 and 8 are multiplied together to make 24
In part a), there are 3 lots of 8. In part b), there are 8 lots of 3
5 × 8 = 40
Other ways of working this out include:
8 + 8 + 8 + 8 + 8 = 40
10 × 4 = 40
a) 7 × 8
b)
5
24
c)
8
6
7
56
8
8
a) 80
b) 48
a) Both Annie and Jack are correct.
Jack: 4 × 2 = 8
Annie: 2 × 2 × 2 = 8
b) 8 × 4 = 32
8 × 9 = 72
11 × 8 = 88
Y3 – Autumn – Block 3 – Step 9 – Divide by 8 Answers
Question
1
Answer
a) There are 16 flowers.
There are 8 vases.
There are 2 flowers in each vase.
16 shared into 8 equal groups is 2
b) There are 8 glasses of milk on each tray.
There are 2 trays.
16 shared into 2 equal groups is 8
a)
40 ÷ 8 = 5
2
b)
40 ÷ 5 = 8
3
32p ÷ 8 = 4p
a)
12
24 ÷ 2 = 12
12
b)
6
6
24 ÷ 4 = 6
4
6
6
c)
3 3 3 3 3 3 3 3
24 ÷ 8 = 3
When the number being divided by is halved, the result is doubled.
5
5
a), b)
8 8 8 8 8 8 8
6
7 7 7 7 7 7 7 7
c) child’s number story for 40 ÷ 8 = 5
Y3 – Autumn – Block 3 – Step 9 – Divide by 8 Answers (continued)
Question
7
Answer
Numbers that divide by 8 exactly must be even, so cannot be 23 or 65
So only test whether 28, 32 and 64 can be divided by 8 exactly.
If 32 can be divided by 8 exactly, then so can 64 as it is 2 × 32
Y3 – Autumn – Block 3 – Step 10 – The 8 times-table Answers
Question
1
Answer
a) 5 × 8 = 40
b) 4 × 8 = 32
a)
2
3
4
5
6
7
8
b)
72
32
40
48
56
64
56
48
40
a) 8 × 8 = 64
b) 64 ÷ 8 = 8
a)
b)
c)
d)
e)
f)
g)
h)
48
7
80
32
9
88
40
8
8×1=8
a) 2 × 8 = 16
4 × 8 = 32
8 × 8 = 64
b) 8 = 8 × 1
16 = 8 × 2
32 = 8 × 4
When one of the numbers being multiplied is doubled, the product also doubles.
a) 56
Possible methods include:
add 8 five times
work out 5 × 8 and add to 16
work out 7 × 8
b) 57
1 more than 7 × 8
72
Y3 – Autumn – Block 3 – Step 10 – The 8 times-table Answers (continued)
Question
Answer
2
6
4
36 12
16 32
48
9
There are four empty parts:
• only in the 4 times-table
• only in the 8 times-table
• in the 2 times-table and the 8 times-table, but not the 4 times-table
• in the 4 times-table and the 8 times-table, but not the 2 times-table
2 × 2 = 4: any number that is in the 4 times-table must also be in the 2 times-table.
2 × 4 = 8: any number that is in the 8 times-table must also be in the 2 times-table and the
4 times-table.