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 2. 20 + 3 x 10 = 50
4. 20 x (3 + 10) = 260
7. 20 - 3 + 20 ÷ 10 = 19
5. 20 x 3 + 20 x 10 = 260
8. 100 x 5 + 500 = 1000
10. 50 + 250 ÷ 5 = 100
Order of brackets and operations (E)
1. (4 + 6) ÷ 2 = 5 2. 10 x (5 - 3) = 20
4. (10 – 8) x 4 = 8
7. 10 – 3 x 2 = 4
10. 17 + 12 - 4 = 25
5. 4 x 3 – 2 = 10
8. 10 - 6 ÷ 3 = 8
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 6. 6.231 + 0.101 = 6.332
7. 6.231 + 0.011 = 6.242 8. 5.846 - 0.211 = 5.635
9. 5.846 - 0.13 = 5.716 10. 5.846 - 0.013 = 5.833
11. 5.846 - 0.204 = 5.642 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 6x40=240 6x400=2400 60x40=2400 60x400=24000 60x4000=240000
3x8=24 3x80=240 3x800=2400 30x80=2400 30x800=24000 30x8000=240000
4x5=20 4x50=200 4x500=2000 40x50=2000 40x500=20000 40x5000=200000
12x3=36 12x30=360 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 7/8 of 240 is 210
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).
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