Y3 – Autumn – Block 3 – Step 1 – Equal groups Answers

Question Answer

1

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

2

a) child’s arrangements of 30 cubes in 6 groups of 5b) child’s drawing of groups in part a)

The cubes could represent any 30 objects.

3

4child’s arrangements of 6 coins in 3 groups of 22

5 child’s story about 5 groups of 0

6

a)

b)

7

a)

b) 5c) The number of counters increases by the number in a group.

Y3 – Autumn – Block 3 – Step 1 – Equal groups Answers (continued)

Question Answer

8

a) six ways:1 group of 122 groups of 63 groups of 44 groups of 56 groups of 212 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 Answer

1

a) There are 3 equal groups with 6 in each group.6 + 6 + 6 = 183 × 6 = 18

b) There are 4 equal groups with 5 in each group.5 + 5 + 5 + 5 = 204 × 5 = 20

c) There are 2 equal groups with 4 in each group.4 + 4 = 82 × 4 = 8

2

3

5 × 2 = 5 + 5 = 105 × 3 = 5 + 5 + 5 = 155 × 4 = 5 + 5 + 5 + 5 = 205 × 5 = 5 + 5 + 5 + 5 + 5 = 25

5 × 6 = 5 + 5 + 5 + 5 + 5 + 5 = 30

4

possible answers:1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 1616 × 1 = 16

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 168 × 2 = 16

4 + 4 + 4 + 4 = 164 × 4 = 16

8 + 8 = 162 × 8 = 16

5

a) 4b) 2c) 5

3 × 55 × 3

10 + 10

Y2 – Autumn – Block 4 – Step 6 – Use arrays Answers

Question Answer

1

5 + 5 + 5 = 153 × 5 = 15There are 15 pears.

2

6 + 6 = 122 × 6 = 12There are 12 stars.

3

4 + 4 + 4 = 123 × 4 = 123 + 3 + 3 + 3 = 124 × 3 = 12The numbers in the multiplication are the same.

42 × 9 = 189 × 2 = 18

5 7 × 3 = 21The array could be drawn as 3 rows of 7

6

possible arrays:1 row of 122 rows of 63 rows of 44 rows of 36 rows of 212 rows of 1

Y2 – Autumn – Block 4 – Step 6 – Use arrays Answers (continued)

Question Answer

7

8

Y2 – Autumn – Block 4 – Step 7 – The 2 times-table Answers

Question Answer

1

a) 5 × 2 = 10b) 7 × 2 = 14c) 4 × £2 = £8

2

a)

b)

3

a)

b)

c)

4

a) 6b) 18c) 10d) 2e) 6f) 24g) 1h) 0i) 7j) 11

5 Rosie has £16

6

other possible ways:0 × 2 + 10 × 21 × 2 + 9 × 22 × 2 + 8 × 24 × 2 + 6 × 25 × 2 + 5 × 26 × 2 + 4 × 27 × 2 + 3 × 28 × 2 + 2 × 29 × 2 + 1 × 210 × 2 + 0 × 2Children can discuss how many different ways there are to write 10 × 2

6 8 10 14 16

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4

10

4

Y2 – Autumn – Block 4 – Step 8 – The 5 times-table Answers

Question Answer

1

a)

b) child’s drawing showing 4 × 5, e.g. array of 4 rows of 5 counters

2

a)

b)

The numbers go up in 5s.

3

a) 25b) 45c) 30d) 8e) 7f) 55g) 1h) 0i) 2j) 12

410 × 5p = 50pRon has 50p.

5

7 × 5 < 5 × 86 × 5 = 4 × 5 + 2 × 52 × 5 = 3 × 5 − 1 × 512 × 2 = 2 × 12

6 Jack spends £25

15 20 25 30 40

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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

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.

3

a) 20b) 10c) 8d) 4Yes. We needed to exchange each ten for 10 ones for parts c) and d).

4

a) 30 ÷ 5 = 6b) 30 is the total number of flowers, 5 is the number of vases and 6 is the number of

flowers in each vase.

5

A 4B 5C 10D 10

children’s stories to match the divisions

C

B

A

D

Y2 – Spring – Block 1 – Step 2 – Make equal groups – grouping Answers

Question Answer

1 There are 10 apples.There are 2 apples on each plate.There are 5 plates.

2 The counters are in groups of 3There are 5 groups.

3

a) chairs circled in 4 groups of 5b) 4c) 20 ÷ 5 = 4

4

a) 30 ÷ 10 = 330 is made of 3 equal groups of 10

b) 30 ÷ 5 = 630 is made of 6 equal groups of 5

c) other possible equal groups:30 equal groups of 115 equal groups of 210 equal groups of 35 equal groups of 62 equal groups of 151 group of 30

524 ÷ 2 = 12Eva needs 12 pots.

6

No.other possible groups:40 equal groups of 120 equal groups of 28 equal groups of 55 equal groups of 82 equal groups of 201 group of 40

Y2 – Spring – Block 1 – Step 3 – Divide by 2 Answers

Question Answer

1

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

2

a) 4 × 2 = 88 ÷ 2 = 4

b) 8 × 2 = 1616 ÷ 2 = 8

3a) 7b) 14 ÷ 2 = 7

4

a) 6b) 10Count up in 2s from 0 to 20 or work out what number times 2 gives 10

522 ÷ 2 = 11Alex needs 11 pots.

6Yes.Dora can use the number that when it is multiplied by 2 gives the number she is dividing by.

7

a) 3b) 5c) 7d) 0e) 10f) 12g) 18h) 22

Y2 – Spring – Block 1 – Step 5 – Divide by 5 Answers

Question Answer

1

a) counters circled in 6 groups of 5b) There are 5 counters in each group.

There are 6 groups.30 ÷ 5 = 66 × 5 = 30

2

There are 15 sweets.There are 5 party bags.There are 3 sweets in each bag.15 ÷ 5 = 3

3

a) 4 × 5 = 2020 ÷ 5 = 4

b) 8 × 5 = 4040 ÷ 5 = 8

4

545 ÷ 5 = 99 boats are needed.

6

a) 3b) 5c) 10d) 12e) 35f) 55g) 40h) 0

7 20p

Y2 – Spring – Block 1 – Step 6 – Divide by 10 Answers

Question Answer

1

There are 60 crayons.There are 10 crayons in each pack.60 ÷ 10 = 66 packs can be made.

2 40 ÷ 10 = 4

3

5 × 10 = 5010 × 5 = 5050 ÷ 10 = 550 ÷ 5 = 10

4

a) 7b) 8c) 1d) 2e) 60

540 ÷ 10 = 4 or 40 ÷ 4 = 104 × 10 = 40 or 10 × 4 = 40

6100 ÷ 10 = 10Tommy can fill 10 pages.

7 6 kg

Y3 – Autumn – Block 3 – Step 2 – Multiply by 3 Answers

Question Answer

1

a) There are 6 equal groups of 33 + 3 + 3 + 3 + 3 + 3 = 186 × 3 = 18

b) There are 4 equal groups of 312 = 3 + 3 + 3 + 3 12 = 4 × 3

c) There are 7 equal groups of 33 + 3 + 3 + 3 + 3 + 3 + 3 = 217 × 3 = 21

The numbers in the multiplication can be written either way round: 3 × 6 = 183 × 4 = 123 × 7 = 21

2

a) 5 × 3 = 153 × 5 = 15

b) 10 × 3 = 303 × 10 = 30

3

4

5No.6 lots of 3 is 3 more than 5 lots of 3

6 or

All the others represent 5 × 3 All the others are lots of 3. The coins are lots of 5

3 + 3 + 3 + 3 + 3 + 3 = 18

3 3 3 3 3 318

child’s number story, e.g. There are 6 plates with 3

cakes on each plate.

9 12 15

4 3 5 3

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Y3 – Autumn – Block 3 – Step 3 – Divide by 3 Answers

Question Answer

1

There are 3 plates.Each plate has 4 cubes.12 divided into 3 equal groups is 4

2 There will be 5 pencils in each pot.

3

6

49 boxes of 3 cakes can be filled.

5An alternative bar model would be 3 bars of 11

6

a) 21 ÷ 3 = 7b) 36 ÷ 3 = 12c) 24 ÷ 3 = 8

7

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

3 3 3 3 3 3 3 3 3 3 3

Y3 – Autumn – Block 3 – Step 4 – The 3 times-table Answers

Question Answer

1a) 8 × 3 = 24b) 3 × 4 = 12

2

3 × 5 = 155 × 3 = 1515 ÷ 3 = 515 ÷ 5 = 3

3

a) 18b) 9c) 33d) 15e) 36f) 0

4

a) 2 × 3 = 64 × 3 = 128 × 3 = 24

b) 6 = 3 × 212 = 3 × 418 = 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.

5

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.

7

a)

b)

18

12 12 12

Y3 – Autumn – Block 3 – Step 4 – The 3 times-table Answers (continued)

Question Answer

8 Eva

9

a)

b) 5 × 3 = 15c) 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

10

13 × 3 = 393 × 15 = 4514 × 3 = 4224 × 3 = 72

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

6

9

4

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Y3 – Autumn – Block 3 – Step 5 – Multiply by 4 Answers

Question Answer

1

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 2 × 4 = 8

3

4

5 4 × 5 = 205 × 4 = 20

6

7 × 4 = 28

7 Teddy has 40 sweets.

8Yes.Mrs Wilson has 48 litres of juice.

9Yes.2 × 2 = 4

8

12

16

28

Y3 – Autumn – Block 3 – Step 6 – Divide by 4 Answers

Question Answer

1

There are 4 plates.Each plate has 3 cakes.12 shared into 4 equal groups is 3

2

4 circles of 4 flowersa) 4b) There are 4 groups of 4 in 16

3a) 8b) 32 ÷ 4 = 8

424 ÷ 4 = 6There will be 6 apples in each bag.

5 5 boxes of muffins can be filled.

67 × 4 = 28Yes, Alex’s method always works.

732 ÷ 4 = 11

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 2A number divided by 2 is twice the same number divided by 4

11 1111 11

does not divide equally

does not divide equally

2

3

4

6

5

8

7

16

14 does not divide equally

1

2

3

4

Y3 – Autumn – Block 3 – Step 7 – The 4 times-table Answers

Question Answer

1a) 8 × 4 = 32b) 4 × 3 = 12

2

a) 24b) 12c) 28d) 12e) 0f) 36g) 6h) 2i) 0j) 44k) 20l) 4

3

4 × 7 = 287 × 4 = 2828 ÷ 4 = 728 ÷ 7 = 4

4

a) 2 × 4 = 84 × 4 = 168 × 4 = 32

b) 8 = 4 × 216 = 4 × 432 = 4 × 8

c) 3 × 4 = 123 × 8 = 243 × 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

5

a) =b) >c) <d) <e) =f) =

6 24 cm

7 £52

Y3 – Autumn – Block 3 – Step 7 – The 4 times-table Answers (continued)

Question Answer

8

9Eva is correct.4 is even, so any number times 4 is also even.

16

20

4

Y3 – Autumn – Block 3 – Step 8 – Multiply by 8 Answers

Question Answer

1

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

a) 3 × 8 = 24b) 8 × 3 = 24In both parts, 3 and 8 are multiplied together to make 24In part a), there are 3 lots of 8. In part b), there are 8 lots of 3

4

5 × 8 = 40Other ways of working this out include:8 + 8 + 8 + 8 + 8 = 4010 × 4 = 40

5

a) 7 × 8b)

c)

6a) 80b) 48

7

a) Both Annie and Jack are correct.Jack: 4 × 2 = 8Annie: 2 × 2 × 2 = 8

b) 8 × 4 = 328 × 9 = 7211 × 8 = 88

56

8 8 8

24

Y3 – Autumn – Block 3 – Step 9 – Divide by 8 Answers

Question Answer

1

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

2

a)

40 ÷ 8 = 5b)

40 ÷ 5 = 8

332p ÷ 8 = 4p

4

a)

24 ÷ 2 = 12b)

24 ÷ 4 = 6c)

24 ÷ 8 = 3When the number being divided by is halved, the result is doubled.

5 5

6

a), b)

c) child’s number story for 40 ÷ 8 = 5

12 12

6 666

3 33 3 3 3 3 3

8 8 8 8 8 8 8

7 7 7 7 7 7 77

Y3 – Autumn – Block 3 – Step 9 – Divide by 8 Answers (continued)

Question Answer

7 Numbers that divide by 8 exactly must be even, so cannot be 23 or 65So 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 Answer

1a) 5 × 8 = 40b) 4 × 8 = 32

2

a)

b)

3a) 8 × 8 = 64b) 64 ÷ 8 = 8

4

a) 48b) 7c) 80d) 32e) 9f) 88g) 40h) 8

5 8 × 1 = 8

6

a) 2 × 8 = 164 × 8 = 328 × 8 = 64

b) 8 = 8 × 116 = 8 × 232 = 8 × 4

When one of the numbers being multiplied is doubled, the product also doubles.

7

a) 56Possible methods include:add 8 five timeswork out 5 × 8 and add to 16work out 7 × 8

b) 571 more than 7 × 8

8 72

32 40 48 56

72 64 56 48 40

Y3 – Autumn – Block 3 – Step 10 – The 8 times-table Answers (continued)

Question Answer

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-table2 × 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.

2 4

16 3248

366 12