Y6 – Spring – Block 3 – Step 1 – Find a rule – one step Answers

Question Answer

1

2

a)

b)

multiply the number of ants by 6

3

a) 55b) 43c) 100d) 5

4

a) 36b) 23c) 35d) 27

5a) × 5b) + 7

6

7a) 50b) −50

8Both6 + 9 = 15 and 6 × 2.5 = 15

3 6 9 12 15 30

4 109 12

32

6 303 4

96

30

18

15.5

4

−2

Y6 – Spring – Block 3 – Step 1 – Find a rule – one step Answers (continued)

Question Answer

9

+ 9

13 14 19 29 109

× 4

16 20 40 80 400

Y6 – Spring – Block 3 – Step 2 – Find a rule – two step Answers

Question Answer

1

2

JackThe order of operations means that the outputs will be different, e.g.:1 × 5 = 5 and 5 + 2 = 7 1 + 2 = 3 and 3 × 5 = 15

Jack

3

a)

b)

c)

7 12 17 27 52 252

15 20 25 35 60 260

9

29

44

7

11

16

96

11

5

0

4.5

19

Y6 – Spring – Block 3 – Step 2 – Find a rule – two step Answers (continued)

Question Answer

4

For two additions or two multiplications, it does not matter which order they are done in. Addition and multiplication are both commutative.For a multiplication and a subtraction the order of operations does matter.

5

a) × 10b) + 10c) × 4No. Only two-step machines where both operations are addition/subtraction or multiplication/division can be written with one step.

6

a)

b) 4

7a) £4.45b) 24

!

!

28 013 73

Y6 – Spring – Block 3 – Step 3 – Forming expressions Answers

Question Answer

1

b) 3𝑥 + 5c) 3𝑥d) 𝑥 + 3e) 2𝑥 + 5f) 5𝑥 + 2g) 2𝑥 + 6h) 4𝑥 + 9

2

a) 1 multilink cube and 2 base 10 cubesb) 2 multilink cubesc) 3 multilink cubes and 1 base 10 cubed) 1 multilink cube and 6 base 10 cubesChildren should all have the same numbers of multilink and base 10 cubes, but the order may be different.

3

b) 5𝑎 + 2c) 4𝑝 + 2d) 4𝑚+ 1

4

a) + 4 𝑦 + 4b) × 2 2𝑦c) − 3 𝑦 − 3d) ÷ 10 !

10

5

5 less than 𝒚

𝒚 mul$plied by 𝒚

Y6 – Spring – Block 3 – Step 3 – Forming expressions Answers (continued)

Question Answer

6

a) 3𝑎b) 4𝑏c) 6𝑥d) 2𝑎 + 2𝑏e) 3𝑥 + 2𝑦

7

a)

b)

c)

d)

𝒅2

𝒅2

2𝒂

2𝒃 + 10

𝒄4

𝒄4

𝒄4

𝒄4

Y6 – Spring – Block 3 – Step 4 – Substitution Answers

Question Answer

1

a) 13b) 3c) 23

2

a) 7b) 60c) multiple possible answers, e.g.:

+ +

3

4

a) 16b) 4c) 20d) 26e) 13f) 8

5 1

6Yes.In addition the order of the values does not matter. Addition is commutative.

7

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

8$5 𝑎 + 5 5𝑎 𝑎2

9multiple possible answers, e.g.:

𝑎 + 25 3𝑎 − 5 55 − 𝑎 8$3

25

2.5

14

5

12

−2

22

35

Y6 – Spring – Block 3 – Step 4 – Substitution Answers (continued)

Question Answer

10

10

50

60

35

100

9

49

59

245

7

20

Y6 – Spring – Block 3 – Step 5 – Formulae Answers

Question Answer

1

a)

b)

c)

d) 303 × 10 = 30

2

a)

b) 𝑑 = 7𝑤c) 224

3

a) area = 𝑎𝑏perimeter = 2𝑎 + 2𝑏

b) area = 136 cm2

perimeter = 50 cm

4

a) area = 𝑑2perimeter = 4𝑑

b) area = 72.25 cm2

perimeter = 34 cm

5

a)

b) 31c)

6a) £29b) 𝑐 = 12ℎ + 5

7a) £15.50b) 𝑐 = 2𝑛 + 1.5

6 9 12 15

14 21 35 70

10 13 16

Y6 – Spring – Block 3 – Step 6 – Forming equations Answers

Question Answer

1

2

a) 𝑠 + 5 = 17b) 2 + ℎ = 11c) 21 + 𝑠 + 2𝑚 = 39child’s problem involving prices and totals

3

a) 2𝑎 = 14b) %

4 = 3c) 2𝑐 + 10 = 16d) 𝑑 + 5 = 12Children may express the bar models differently, e.g. part b) as 𝑏 = 3 × 4

4

a)

b)

c)

d)

5Tommy: 𝑥 − 3 = 10Rosie: 2𝑥 + 5 = 19

𝑎 𝑎 𝑎21

6 9𝑐

𝑏10

𝑏 6

7 7𝑑

Y6 – Spring – Block 3 – Step 6 – Forming equations Answers (continued)

Question Answer

6

a) The answer should always be 5b) child’s representation of Annie’s trick

There are always 5 base 10 ones left.c) 𝑥

2𝑥2𝑥 + 10𝑥 + 5𝑥

d) child’s number problem

Y6 – Spring – Block 3 – Step 7 – Solve simple one-step equations Answers

Question Answer

1

a) 3𝑥 = 6= 2

b) 𝑥 + 4 = 18= 14

2

a) There are 6 counters on the table and 𝑐 counters under the cup. There are 10 counters in total, so 𝑐 + 6 = 10

b) 𝑐 = 4c) 4

3

a) 2𝑎 = 8𝑎 = 4

b) 𝑎 + 10 = 15𝑎 = 5

c) $3 = 3𝑎 = 9

d) 𝑎 = 6 + 7𝑎 = 13

4

In the second line, Nijah has subtracted 8 from both sides, when she should have added 8 to both sides.correct answer: 𝑥 = 28

5

a) 𝑥 = 13b) 𝑦 = 8c) 𝑚 = 5.5d) 𝑔 = 18e) 𝑡 = 37f) 𝑢 = 18

6𝑥 − 5 = 1015

714𝑎 = 42𝑎 = 3 cm

8

4ℎ = 40 2ℎ + 2𝑠 = 32 ℎ + 𝑠 + 2𝑡 = 20

10 6 2

32

20

24 2828

Y6 – Spring – Block 3 – Step 8 – Solve two-step equations Answers

Question Answer

1a) 2𝑥 + 4 = 20b) = 8

2 𝑥 = 12

3

a) 2𝑦 + 4 = 16b) 𝑦 = 6c) 6

4

a) 2𝑎 + 9 = 21𝑎 = 6

b) 3𝑏 + 10 = 46𝑏 = 12

5

a) 𝑥 = 6b) 𝑥 = 4c) 𝑝 = 3.5d) 𝑦 = 0.5e) 𝑔 = 4.8f) 𝑦 = 8

6a) 2𝑥 + 3 = 15b) 6

7Alex is 11Brett is 14

8

a) One banana costs 32pOne orange costs 28p

b) 2 oranges and 3 bananas cost £1.52 and 2 oranges and 2 bananas cost £1.20so 1 banana costs £1.52 − £1.20 = £0.32 or 32p.Then substitute the value for the cost of a banana to find the cost of an orange.

Y6 – Spring – Block 3 – Step 9 – Find pairs of values (1) Answers

Question Answer

1

a) multiple possible answers, e.g.:

b) multiple possible answers, e.g.:

c) The answers are the same but the representations are different.

2

a) multiple possible answers, e.g.:

b) Children may have given different answers.c) No.

The cookie would not cost anything.

3

multiple possible answers, e.g.:

As 𝑎 increases, 𝑏 decreases.

4

multiple possible answers, e.g.:

5

𝑎 = 1, 𝑏 = 24𝑎 = 2, 𝑏 = 12𝑎 = 3, 𝑏 = 8𝑎 = 4, 𝑏 = 6𝑎 = 6, 𝑏 = 4𝑎 = 8, 𝑏 = 3𝑎 = 12, 𝑏 = 2𝑎 = 24, 𝑏 = 1

6multiple possible answers, e.g.:A = 100 g B = 300 g

1 2 3 4 5 6

11 10 9 8 7 6

1 2 3 4 5 6

11 10 9 8 7 6

10p 20p 30p 40p 25p 49p

80p 70p 60p 50p 65p 41p

8 7 6 5 4 3 2 1

8 8 8 8 8 8

3 4 5 6 7

15 14 13 12 11 10 6 2

4 4 4 4 4 4

16 15 14 10 619 18 17

4 4

Y6 – Spring – Block 3 – Step 9 – Find pairs of values (1) Answers (continued)

Question Answer

7

8

9 8 7 6 7 6 5

2 3 4 5 3 4 4

1 1 1 1 2 2 3

Y6 – Spring – Block 3 – Step 10 – Find pairs of values (2) Answers

Question Answer

1

a) Yes.3 + 3 + 4 = 10

b) = 2c) multiple possible answers, e.g.:

= 1 = 8 = 2 = 6 = 2.5 = 5

2

3

a)

b) If 𝑐 was 6, then 𝑑 would be greater than 15

4

12 10 8 6 4 2 0

4 6 8 10 12 14

14 14 14 14

4 7 10 12

6 9 12 15

2 2

Y6 – Spring – Block 3 – Step 10 – Find pairs of values (2) Answers (continued)

Question Answer

5

a) 2𝑥 + 2𝑦 = 28b) 𝑥 = 1, 𝑦 = 13

𝑥 = 2, 𝑦 = 12𝑥 = 3, 𝑦 = 11𝑥 = 4, 𝑦 = 10𝑥 = 5, 𝑦 = 9𝑥 = 6, 𝑦 = 8𝑥 = 7, 𝑦 = 7𝑥 = 8, 𝑦 = 6𝑥 = 9, 𝑦 = 5𝑥 = 10, 𝑦 = 4𝑥 = 11, 𝑦 = 3𝑥 = 12, 𝑦 = 2𝑥 = 13, 𝑦 = 1Work systematically from 𝑥 = 1, increasing it by 1 each time.

6

10 pencils, 0 pens7 pencils, 2 pens4 pencils, 4 pens1 pencil, 6 pens

7

There are 13 possible sets of cards:4 4 7 95 5 6 83 6 6 94 6 6 85 6 6 71 7 7 92 7 7 84 7 7 61 7 8 82 6 8 83 5 8 81 5 9 92 4 9 9

8

a) multiple possible answers, e.g.:𝑎 = 3, 𝑏 = 8

b) There are eight possible answers with integer values for 𝑎 and 𝑏:𝑎 = 1, 𝑏 = 24𝑎 = 2, 𝑏 = 12𝑎 = 3, 𝑏 = 8𝑎 = 4, 𝑏 = 6𝑎 = 6, 𝑏 = 4𝑎 = 8, 𝑏 = 3𝑎 = 12, 𝑏 = 2𝑎 = 24, 𝑏 = 1