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Maths Answers

Spring Year 6

Week 1:

Temperature

1. Thursday was the coldest night.

2. Tuesday was the mildest night.

3. On Monday, the temperature fell by 8 degrees.

4. On Friday, the temperature fell by 2 degrees.

5. The day with the biggest drop in temperature was Monday.

6. There is a difference of 11 degrees between the mildest and coldest temperatures.

7. Children will provide questions and answers here.

Week 2:

Mental addition and subtraction

1. 3478 + 1000 = 4478 2. 3478 + 999 = 4477

4. 5298 - 999 = 4299

7. 3458 + 1997 = 5455

10. 57,345 - 2998 = 54,347 11. 7.28 + 1.99 = 9.27

13. 9.38 - 2.01 = 7.37 14. 9.38 - 1.99 = 7.39

16. 8.27 - 2.95 = 5.32

5. 8345 + 397 = 8742

8. 9768 - 2995 = 6773

17. 8.41 + 1.97 = 10.38

3. 5298 - 1000 = 4298

6. 7935 - 298 = 7637

9. 45,237 + 3900 = 49,137

12. 8.46 + 2.97 = 11.43

15. 5.36 + 2.98 = 8.34

18. 9.39 - 1.95 = 7.44

Order of brackets and operations

1. (20 + 3) x 10 = 230

4. 20 x (3 + 10) = 260

2. 20 + 3 x 10 = 50

5. 20 x 3 + 20 x 10 = 260

7. 20 - 3 + 20 ÷ 10 = 19

10. 50 + 250 ÷ 5 = 100

8. 100 x 5 + 500 = 1000

Order of brackets and operations (E)

1. (4 + 6) ÷ 2 = 5

4. (10 – 8) x 4 = 8

2. 10 x (5 - 3) = 20

5. 4 x 3 – 2 = 10

8. 10 - 6 ÷ 3 = 8 7. 10 – 3 x 2 = 4

10. 17 + 12 - 4 = 25

Word problems

1. Matt has 18 packs of buns now.

2. Sasha has 12 packs of buns.

3. The total cost of the order is £63.90.

4. The total cost of the order is £44.95.

5. Zak has earned £6 in total.

6. The total order will cost £34.20.

3. 20 x 3 + 10 = 70

6. (20 - 3) x (20 + 10) = 510

9. 70 + 60 ÷ 2 = 100

3. 20 ÷ (3 + 2) = 4

6. 15 ÷ 3 + 4 = 9

9. 4 + 2 x 5 = 14

© Hamilton Trust Year 6 Spring Maths Answers

Week 3:

Place value addition and subtraction

1. 4.538 + 0.2 = 4.738

3. 4.538 - 0.004 = 4.534

2. 4.538 + 0.03 = 4.568

4. 4.538 - 0.02 = 4.518

5. 6.231 + 0.11 = 6.341

7. 6.231 + 0.011 = 6.242

9. 5.846 - 0.13 = 5.716

11. 5.846 - 0.204 = 5.642

6. 6.231 + 0.101 = 6.332

8. 5.846 - 0.211 = 5.635

10. 5.846 - 0.013 = 5.833

12. 4.789 + 0.001 = 4.79

Multiply and Divide by 10, 100 and 1000

1. 4326 ÷ 100 = 43.26

3. 7840 ÷ 100 = 78.4

2. 4326 ÷ 1000 = 4.326

4. 7840 ÷ 1000 = 7.84

5. 783 ÷ 1000 = 0.783

7. 4.535 × 100 = 453.5

9. 0.786 × 1000 = 786

11. 789,234 ÷ 1000 = 789.234

13. 45,830 ÷ 1000 = 45.83

15. 0.65 × 1000 = 650

6. 783 ÷ 100 = 7.83

8. 4.535 × 1000 = 4535

10. 0.786 × 100 = 78.6

12. 234 × 100 = 23,400

14. 0.079 × 1000 = 79

16. 4.507 x 100 = 450.7

Multiplying and Dividing by 10, 100 and 1000

A motorbike weighs the same as 100 bags of potatoes.

A Land Rover weighs the same as 10 motorbikes.

Adding distances: Pairs of distances with a total less than 7m

5.2m + 1.78m

4.35m + 2.4m

3.56m + 3.42m

3.42m + 3.56m

2.78m + 3.56m

2.4m + 4.35m

2.4m + 1.78m

4.35m + 1.78m

3.56m + 2.78m

3.42m + 2.78m

2.78m + 3.42m

2.4m + 3.56m

3.56m + 2.4m

3.42m + 2.4m

2.78m + 2.4m

2.4m + 3.42m

1.78m + 5.2m

1.78m + 2.78m

1.78m + 4.35m

1.78m + 2.4m

1.78m + 3.56m

3.56m + 1.78m

3.42m + 1.78m

2.78m + 1.78m

2.4m + 2.78m

1.78m + 4.42m

Week 4:

Interpreting pie charts

1. Walking is the most common way to come to school for each age group.

2. Cycling to school is very different, as is going by car. This is probably due to the difference in age between Year 2 and Year 6 children.

3. More Year 2 children walk to school; slightly lower percentage-wise but a larger sample of children.

© Hamilton Trust Year 6 Spring Maths Answers

4.

Walk

Bus

Car

Bike

Scooter

Drawing pie charts

Times table

Year 2 children

15

3

12

0

6

Year 6 children

12

2

3

6

1

2

3

4

5

6

Number of children who found this difficult

0

0

0

0

2

Degrees

0

0

0

0

60

7

8

9

10

4

3

1

0

120

90

30

0

11

12

0

2

0

60

Week 5:

Solve problems involving rate

1. A blue whale calf will grow 70cm in four weeks.

2. It will take 280 days to double its birth length.

3. Taking six months as 182 days, it will put on 16,380kg.

4. It will have drunk 72,800l of milk in that time.

5. An adult whale will eat about 1095 tonnes of krill in a year.

6. It will take the child about 3 years and 4 months to double its height.

7. A blue whale calf has the faster growing rate.

Scaling up

Dinosaur Actual height Actual length

Tyrannosaurus Rex

Brachiosaurus

Velociraptor

Diplodocus

Plateosaurus

7m

15.2m

0.6m

7.4m

2.2m

15.2m

30.4m

1.8m

27m

7.8m

© Hamilton Trust Year 6 Spring Maths Answers

Dimensions for dinosaur toys

Dinosaur

Allosaurus

Triceratops

Stegosaurus

Spinosaurus

Brontosaurus

Toy’s height

2.6cm

1.45cm

1.9cm

Toy’s length

6.1cm

4.2cm

4.45cm

2.7cm

2.3cm

6.6cm

11.5cm

Place value multiplications

6x4=24

3x8=24

4x5=20

12x3=36

6x40=240

3x80=240

4x50=200

12x30=360

6x400=2400

3x800=2400

60x40=2400

30x80=2400

60x400=24000

30x800=24000

60x4000=240000

30x8000=240000

4x500=2000 40x50=2000 40x500=20000 40x5000=200000

12x300=3600 120x30=3600 120x300=36000 120x3000=360000

Multiplications

1. 345 x 24 = 8280

2. 264 x 32 = 8448

3. 335 x 23 = 7705

4. 253 x 35 = 8855

5. 426 x 24 = 10,224

Word problems

1. How many hours in a year are there? 8760 (365 x 24 = 8760)

2. Sita eats 5148 fish. (156 x 33 = 5148)

Week 6:

Fact web

£320

75% is £240, 50% is £160, 25% is £80, 20% is £64, 10% is £32, 1% is £3.20.

Fact web

£150

75% is £112.50, 50% is £75, 25% is £37.50, 20% is £30, 10% is £15, 1% is £1.50.

Fact web

£328

75% is £246, 50% is £164, 25% is £82, 20% is £65.60, 10% is £32.80, 1% is £3.28.

© Hamilton Trust Year 6 Spring Maths Answers

Finding unit and non unit fractions of 240

¼ of 240 is 60 ¾ of 240 is 180

1/3 of 240 is 80

1/6 of 240 is 40

1/8 of 240 is 30

2/3 of 240 is 160

5/6 of 240 is 200

3/8 of 240 is 90 5/8 of 240 is 150

1/10 of 240 is 24

1/12 of 240 is 20

Week 7:

Write a formula

1. The cost of n stamps is 52n (in pence) or 0.52n (in pounds).

7/8 of 240 is 210

2. The number of wheels on n cars is 4n.

3. The number of months in n years is 12n.

4. For n fence panels, n + 1 fence posts are needed.

5. The change from £10 after buying n apples at 25p each is £(10 - 0.25n).

6. The time to cook a chicken weighing n kg, at 45 minutes per kilogram and 20 extra minutes is 45n + 20 minutes.

7. The distance travelled when a bike wheel turns 20 times and the circumference of the wheel is n, is 20n.

8. The price of an item cost n pounds after VAT of 20% added is £1.2n.

Solving equations

1. a = 8

2. b = 5

3. c = 12

4. d = 30

5. e = 6

6. f = 3

7. e = 72°

8. a = 62°

9. c = 110°

10. d = 40°

Solving equations (E)

1. a = 5

2. b = 7

3. c = 12

4. d = 20

5. e =13

6. f = 6

7. g = 12

8. h = 4

9. a = 55°

10. b = 35°

© Hamilton Trust Year 6 Spring Maths Answers

Equations with 2 unknowns

a + b - 2 = 8:

a = 0 b = 10, a = 1 b = 9, a = 2 b = 8, a = 3 b = 7, a = 4 b = 6, a = 5 b = 5, a = 6 b = 4, a = 7 b = 3, a = 8 b = 2, a = 9 b = 1, a = 10 b = 0.

c x d = 20:

c = 1 d = 20, c = 2 d = 10, c = 4 d = 5, c = 5 d = 4, c = 10 d = 2, c = 20 d = 1.

14 – e = f:

e = 0 f = 14, e = 1 f = 13, e = 2 f = 12, e = 3, f = 11, e = 4 f = 10, e = 5 f = 9, e = 6 f = 8, e =

7 f = 7, e = 8 f= 6, e = 9 f = 5, e = 10 f = 4, e = 11 f = 3, e = 12 f= 2, e = 13 f = 1, e= 14 f= 0

2g + h = 10:

g = 0 h = 10, g = 1 h = 8, g = 2 h = 6, g = 3 h = 4, g = 4 h = 2, g = 5 h = 0.

a + b = 10 and a x b = 21:

a = 7 b = 3

c x d-16 and c – d = 6:

c = 8 d = 2

e + f = 12 and e – f = 4:

e = 8 f = 4

Equations with 2 unknowns (E)

a + b = 9:

a = 0 b = 9, a = 1 b = 8, a = 2 b = 7, a = 3 b = 6, a = 4 b = 5, a = 5 b = 4, a = 6 b = 3, a = 7 b = 2, a = 8 b = 1, a = 9 b = 0.

c x d = 15:

c = 1 d = 15, c = 3 d = 5, c = 5 d = 3, c = 15 d = 1.

10 – e = f:

e = 0 f = 10, e = 1 f = 9, e = 2 f = 8, e = 3 f = 7, e = 4 f = 6, e = 5 f = 5, e = 6 f = 4, e = 7 f= 3, e = 8 f = 2, e = 9 f = 1, e = 10 f = 0.

g + h + 1 = 11:

g = 0 h = 10, g = 1 h = 9, g = 2 h = 8, g = 3 h = 7, g = 4 h = 6, g = 5 h = 5, g = 6 h = 4, g = 7 h = 3, g = 8 h = 2, g = 9 h = 1, g = 10 h = 0.

j x k - 1 = 15:

j = 1 k = 16, j= 2 k = 8, j = 4 k = 4, j = 8 k =2, j = 16 k = 1.

© Hamilton Trust Year 6 Spring Maths Answers

Sequences

1. 40, 400, 4n

2. 41, 401, 4n + 1

3. 50, 500, 5n

4. 49, 499, 5n - 1

5. 51, 501, 5n + 1

6. 100, 1000, 10n

7. 102, 1002, 20n + 2

8. 98, 998, 10n – 2

Week 8

Multiplying fractions

1/2 x 1/3 = 1/6

2/3 x 2/3 = 4/9

1/2 x 2/3 = 2/6 = 1/3 1/4 x 2/3 = 2/12 = 1/6

1/2 x 1/5 = 1/10

1/2 x 3/5 = 3/10

1/3 x 3/4 = 3/12 = 1/4

1/3 x 1/5 = 1/15

2/3 x 3/4 = 6/12 = 1/2

2/3 x 1/5 = 2/15

1/5 x 1/4 = 1/20

2/5 x 1/4 = 2/20 = 1/10 5/6 x 2/3 = 10/18 = 5/9

E.g. 2/3 x 3/5 or 1/5 x 6/3 = 6/15

Dividing fractions (H)

1/3 ÷ 2 = 1/6

1/3 ÷ 3 = 1/9

2/3 ÷ 2 = 2/6 = 1/3

2/3 ÷ 4 = 2/12 = 1/6

1/5 ÷ 3 = 1/15

2/5 ÷ 2 = 2/10 = 1/5

2/5 ÷ 4 = 2/20 = 1/10

3/5 ÷ 2 = 3/10

4/5 ÷ 2 = 4/10 = 2/5

Dividing fractions (E)

1/3 ÷ 2 = 1/6

1/3 ÷ 3 = 1/9

2/3 ÷ 2 = 2/6 = 1/3

2/3 ÷ 4 = 2/12 = 1/6

1/4 ÷ 2 = 1/8

1/4 ÷ 3 = 1/12

3/4 ÷ 3 = 3/12 = 1/4

3/4 ÷ 2 = 3/8

3/5 x 3/4 = 9/20

1/6 ÷ 2 = 1/12

1/6 ÷ 3 = 1/18

5/6 ÷ 2 = 5/12

1/5 ÷ 2 = 1/10

2/5 ÷ 2 = 2/10 = 1/5

2/5 ÷ 4 = 2/20 = 1/10

4/5 ÷ 2 = 4/10 = 2/5

© Hamilton Trust Year 6 Spring Maths Answers

Long division (M)

1 x 17 = 17

2 x 17 = 34

3 x 17 = 51

4 x 17 = 68

5 x 17 = 85

6 x 17 = 102

1. 425 ÷ 17 = 25

2. 547 ÷ 17 = 32 r 3

3. 697 ÷ 17 = 41

10 x 17 = 170

20 x 17 = 340

30 x 17 = 510

40 x 17 = 680

50 x 17 = 850

60 x 17 = 1020

1 x 165 = 165

2 x 165 = 330

3 x 165 = 495

4 x 165 = 660

5 x 165 = 825

6 x 165 = 990

1. 394 ÷ 165 = 2 r 64

2. 774 ÷ 165 = 4 r 114

3. 936 ÷ 165 = 5 r 111

1 x 21 = 21

2 x 21 = 42

3 x 21 = 63

4 x 21 = 84

10 x 21 = 210

20 x 21 = 420

30 x 21 = 630

40 x 21 = 840

50 x 21 = 1050

60 x 21 = 1260

5 x 21 = 105

6 x 21 = 126

1. 295 ÷ 21 = 14 r 1

2. 483 ÷ 21 = 23

3. 720 ÷ 21 = 34 r 6

© Hamilton Trust Year 6 Spring Maths Answers

Long division (E)

1 x 13 = 13

2 x 13 = 26

3 x 13 = 39

4 x 13 = 52

5 x 13 = 65

6 x 13 = 78

1. 417 ÷ 13 = 32 r 1

2. 210 ÷ 13 = 16 r 2

3. 331 ÷ 13 = 25 r 6

4. 565 ÷ 13 = 43 r 6

5. 711 ÷ 13 = 54 r 9

Long division (MH)

1 x 24 = 24

2 x 24 = 48

3 x 24 = 72

4 x 24 = 96

5 x 24 = 120

6 x 24 = 144

1. 828 ÷ 24 = 34 r 12

2. 630 ÷ 24 = 26 r 6

3. 988 ÷ 24 = 41 r 4

4. 435 ÷ 24 = 18 r 3

1 x 27 = 27

2 x 27 = 54

3 x 27 = 81

4 x 27 = 108

5 x 27 = 135

6 x 27 = 162

5. 597 ÷ 27 = 22 r 3

6. 938 ÷ 27 = 34 r 20

7. 693 ÷ 27 = 25 r 18

8. 711 ÷ 27 = 26 r 9

10 x 13 = 130

20 x 13 = 260

30 x 13 = 390

40 x 13 = 520

50 x 13 = 650

60 x 13 = 780

10 x 24 = 240

20 x 24 = 480

30 x 24 = 720

40 x 24 = 960

50 x 24 = 1200

60 x 24 = 1440

10 x 27 = 270

20 x 27 = 540

30 x 27 = 810

40 x 27 = 1080

50 x 27 = 1350

60 x 27 = 1620

© Hamilton Trust Year 6 Spring Maths Answers

Long division

1 x 15 = 15

2 x 15 = 30

3 x 15 = 45

4 x 15 = 60

5 x 15 = 75

1. 200 ÷ 15 = 13 r 5

2. 250 ÷ 15 = 16 r 10

3. 365 ÷ 15 = 24 r 5

4. 620 ÷ 15 = 41 r 5

5. 545 ÷ 15 = 36 r 5

6. 440 ÷ 15 = 29 r 5

Week 9:

Area of triangles

1/2 of 3 x 4 = 6cm²

1/2 of 4 x 6 = 12cm²

Area of triangles (E)

1/2 of 3 x 4 = 6cm²

1/2 of 4 x 6 = 12cm²

Find volumes of cuboids (H)

10 x 3 x 4 = 120cm³

8 x 3 x 5 = 120cm³

60 ÷ 20 = 3cm

Find volumes of cuboids (E)

10 x 3 x 4 = 120cm³

8 x 3 x 5 = 120cm³

Week 10:

Missing number problems

1. a = 7

2. b = 9

3. c = 5

4. d = 5

5. e =7

6. f = 5

7. g = 3

8. h = 9

1/2 of 2 x 6 = 6cm²

8 x 4 = 32cm²

1/2 of 2 x 6 = 6cm²

8 x 4 = 32cm²

6 x 5 x 3 = 90cm³

6 x 6 x 6 = 216cm³

120 ÷ 20 = 6cm

6 x 5 x 3 = 90cm³

6 x 6 x 6 = 216cm³

© Hamilton Trust

1/2 of 3 x 5 = 7.5cm²

1/2 of 3 x 5 = 7.5cm²

4 x 4 x 3 = 48cm³

7 x 8 x 4 = 224cm³

4 x 4 x 3 = 48cm³

7 x 8 x 4 = 224cm³

Year 6 Spring Maths Answers

Scaling up

The area of the rectangle is 6 x 3.5 = 21cm².

The area of a rectangle with each side twice the length is 12 x 7 = 84cm².

The area of a rectangle with each side three times the original length is 18 x 10.5 =

189cm².

If the lengths increase by x 2, the area increases by x 2², if the lengths increase by x 3, the area increases by x 3².

The same thing happens for the triangle and parallelogram, the angles remain the same.

Pizza recipe

Base

Flour

Yeast

4 pizzas

500g

10g

1 pizza

125g

2.5g 5g

2 pizzas

250g

6 pizzas

750g

15g

8 pizzas

1000g/1kg

20g

Salt

Sugar

Oil

Water

Topping

Tomatoes

Cheese

Garlic

Onion

½ tsp

½ tsp

4 tbsp

250ml

400g

200g

1 clove

1 onion

1/8 tsp

1/8 tsp

1 tbsp

62.5ml

100g

50g

¼ clove

¼ onion

¼ tsp

¼ tsp

2 tbsp

125ml

200g

100g

½ clove

½ onion

¾ tsp

3/5 tsp

6 tbsp

375ml

600g

300g

1 and ½ cloves

1 and ½ onions

1 tsp

1 tsp

8 tbsp

500ml

800g

400g

2 cloves

2 onions

Ratio problems

1. 7 children are aged 10 and 21 are aged 11. The ratio of 11 year old children to 10 year old children is 3:1.

2. 18 children have school dinners and 9 have packed lunches. The ratio of children who have school dinners to children who have packed lunches is 2:1.

3. There are 20 boys and 10 girls in the class.

4. There would be 40 boys and 20 girls in the year group.

© Hamilton Trust Year 6 Spring Maths Answers

Equivalent percentages

Swimming 50%

Cycling 30%

Football 20%

Bananas 40%

Apples 30%

Oranges 30%

Dogs 50%

Cats 20%

Rabbits 30%

Week 11:

Short division (H)

1. 7133 ÷ 3 = 2377 2/3

2. 1946 ÷ 6 = 324 1/3

3. 3183 ÷ 4 = 795 3/4

4. 9326 ÷ 7 = 1332 2/7

5. 2442 ÷ 11 = 222

6. 4752 ÷ 11 = 432

7. 3784 ÷ 12 = 315 4/12 (315 1/3)

8. 9524 ÷ 12 = 793 8/12 (793 2/3)

9. 365 ÷ 12 = 30 5/12 366 ÷ 12 = 30 6/12 (30 1/2)

10. 1453 ÷ 5 = 290 3/5 packs

11. 253 ÷ 12 = 21 1/12 packs 22 packs need to be bought

12. 962 ÷ 8 = 120 2/8 cm (120 1/4 cm)

Short division (E)

1. 733 ÷ 3 = 244 1/3

2. 946 ÷ 6 = 157 2/3

3. 4783 ÷ 4 = 1195 3/4

4. 6326 ÷ 4 = 1581 1/2

5. 3142 ÷ 4 = 785 1/2

6. 3784 ÷ 5 = 756 4/5

7. 365 ÷ 7 = 52 1/7

8. 535 ÷ 4 = 133 3/4

9. 253 ÷ 6 = 42 1/6 43 packs of eggs must be bought

10. 562 ÷ 4 = 140 1/2 cm

© Hamilton Trust Year 6 Spring Maths Answers

Long division

544 ÷ 17 = 32

673 ÷ 17 = 39 10/17

673 ÷ 21 = 32 1/21

832 ÷ 21 = 39 13/21

936 ÷ 26 = 36

986 ÷ 32 = 30 26/32 (30 13/16)

992 ÷ 32 = 31

936 ÷ 17 = 55 1/17

986 ÷ 17 = 58

992 ÷ 17 = 58 6/17

Long division

1 x 15 = 15

2 x 15 = 30

3 x 15 = 45

544 ÷ 18 = 30 4/18 (30 2/9)

673 ÷ 18 = 37 7/18

754 ÷ 21 = 35 19/21

832 ÷ 26 = 32

986 ÷ 26 = 37 24/26 (37 12/13)

992 ÷ 26 = 38 4/26 (38 2/13)

936 ÷ 18 = 52

986 ÷ 18 = 54 14/18 (54 7/9)

992 ÷ 18 = 55 2/18 (55 1/9)

4 x 15 = 60

5 x 15 = 75

1. 525 ÷ 15 = 35

1 x 23 = 23

2 x 23 = 46

3 x 23 = 69

4 x 23 = 92

5 x 23 = 115

4. 368 ÷ 23 = 16

1 x 32 = 32

2 x 32 = 64

3 x 32 = 96

4 x 32 = 128

5 x 32 = 160

7. 487 ÷ 32 = 15 7/32

2. 634 ÷ 15 = 42 4/15

5. 785 ÷ 23 = 34 3/23

8. 711 ÷ 32 = 22 7/32

3. 789 ÷ 15 = 52 9/15 (52 3/5)

6. 581 ÷ 23 = 25 6/23

9. 995 ÷ 32 = 31 3/32

© Hamilton Trust Year 6 Spring Maths Answers

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