Year 6 Mark Scheme Reasoning and Problem Solving

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Q1


One triangle is shaded

For example:

1

Accept any one triangle shaded.

0.1

1

29

100

,

30

100

,

31

100

,

1

Accept equivalent fractions, for example:

16

50

Q2

4,023

1

4,063

1

Q3

15

1

Q4

-3 in the first box
7 in the second box

2

1 mark is given for one correct answer in the correct
box.
2 marks are given for both answers correct in the
correct boxes.

Q5

12 cm

2

1

Q6

8 m

1

Look for children using the column subtraction
method instead of using mental subtraction of
21 m – 13 m

Rehan

1

32

100

33

100

34

100

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Q7

25

1

Q8

2

Award 1 mark for any three numbers correctly placed
in the diagram.
Award 2 marks for all numbers correctly placed.
If 48 has not been placed as it does not fit in the
diagram, accept all the numbers as correct.

Q9

1
4

1

Children give value reason why 0.75 is smaller
than

7

8

1

Valid reasons include:

- Children say that 0.75 is equivalent to

3

4

and

7

8

is greater than

3

4

- Children say that

7

8

is equivalent to 0.875

which is a larger number than 0.75

Q10

0.3 kg

3

Award 3 marks for the correct answer.

Award 2 marks for two steps of correct mathematical
calculation.

Award 1 mark for one step of correct mathematical
calculation.

13

2

12

24

48

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Examples of correct calculations could be:
- Children find the mass of the two tins of beans by
finding the difference between 5.1 kg and 7.5 kg –
giving 2.4 kg
- Children find the mass of one tin of beans by
dividing 2.4 by 2 – giving 1.2 kg for one tin of beans.
- Children find the mass 6 tins of beans by
multiplying 1.2 by 6 – giving 7.2 kg
- Children find the mass of the box by subtracting the
mass of the beans from the mass of the box and
beans – 7.5 – 7.2 = 0.3 kg

Q11

54 km

2

Award 2 marks for the correct answer of 54 km

Award 1 mark for identifying 3 × 18 km to find the
whole race without the correct answer.

Q12

250 g

1

825 g

2

Award 2 marks for the correct answer.
Award 1 mark for one step of correct mathematical
working.
Possible method:
8 pancakes × 3 = 24 pancakes
275 × 3 = 825 g

Q13

51 cm

2

2

Award 2 marks for the correct answer.
Award 1 mark for one step of correct mathematical
working.
Possible method:

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- 15 × 5 = 75 cm

2

to find the area of the whole

rectangle.

- 8 × 3 = 24 cm

2

to find the area of the missing

rectangle.

- 75 – 24 = 51 cm

2

Q14

62

1

3

1

Q15

84 p or £0.84

2

Award 2 marks for the correct answer.
Award 1 mark for one step of correct mathematical
working.

Possible methods:

- £1.32 x 3 = £3.96 for 3 bags of apples.
- 40 p × 12 = £4.80 for 12 single apples.
- £4.80 − £3.96 to find the difference in price

of 84 p or £0.84

Q16

48 cm

3

1

Q17

3,750 m

2

Award 2 marks for the correct answer.
Award 1 mark for one step of correct mathematical
working.

Possible methods:

- 5 km = 5,000 km
- 5,000 km divided by 4 to find one quarter of

5,000 km which is 1,250 km

- 1,250 km multiplied by 3 to give three quarters

which is 3,750 km.

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Q18

50

2

Award 2 marks for the correct answer.
Award 1 mark for one step of correct mathematical
working.

Possible working may be:

Bilal

Charlie

Bilal

Charlie

5

10

10

10

10

10

5

5

15


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