maths answers - hamilton trust web viewmaths answers. spring year . 6. week 1: temperature. 1. ......

Maths AnswersSpring Year 6

Week 1:

Temperature1. 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 subtraction1. 3478 + 1000 = 4478 2. 3478 + 999 = 4477 3. 5298 - 1000 = 42984. 5298 - 999 = 4299 5. 8345 + 397 = 8742 6. 7935 - 298 = 76377. 3458 + 1997 = 5455 8. 9768 - 2995 = 6773 9. 45,237 + 3900 = 49,13710. 57,345 - 2998 = 54,347 11. 7.28 + 1.99 = 9.27 12. 8.46 + 2.97 = 11.4313. 9.38 - 2.01 = 7.37 14. 9.38 - 1.99 = 7.39 15. 5.36 + 2.98 = 8.3416. 8.27 - 2.95 = 5.32 17. 8.41 + 1.97 = 10.38 18. 9.39 - 1.95 = 7.44

Order of brackets and operations1. (20 + 3) x 10 = 230 2. 20 + 3 x 10 = 50 3. 20 x 3 + 10 = 704. 20 x (3 + 10) = 260 5. 20 x 3 + 20 x 10 = 260 6. (20 - 3) x (20 + 10) = 5107. 20 - 3 + 20 ÷ 10 = 19 8. 100 x 5 + 500 = 1000 9. 70 + 60 ÷ 2 = 10010. 50 + 250 ÷ 5 = 100

Order of brackets and operations (E)1. (4 + 6) ÷ 2 = 5 2. 10 x (5 - 3) = 20 3. 20 ÷ (3 + 2) = 44. (10 – 8) x 4 = 8 5. 4 x 3 – 2 = 10 6. 15 ÷ 3 + 4 = 97. 10 – 3 x 2 = 4 8. 10 - 6 ÷ 3 = 8 9. 4 + 2 x 5 = 1410. 17 + 12 - 4 = 25

Word problems1. 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.

© Hamilton Trust Year 6 Spring Maths Answers

Week 3:

Place value addition and subtraction1. 4.538 + 0.2 = 4.738 2. 4.538 + 0.03 = 4.5683. 4.538 - 0.004 = 4.534 4. 4.538 - 0.02 = 4.5185. 6.231 + 0.11 = 6.341 6. 6.231 + 0.101 = 6.3327. 6.231 + 0.011 = 6.242 8. 5.846 - 0.211 = 5.6359. 5.846 - 0.13 = 5.716 10. 5.846 - 0.013 = 5.83311. 5.846 - 0.204 = 5.642 12. 4.789 + 0.001 = 4.79

Multiply and Divide by 10, 100 and 10001. 4326 ÷ 100 = 43.26 2. 4326 ÷ 1000 = 4.3263. 7840 ÷ 100 = 78.4 4. 7840 ÷ 1000 = 7.845. 783 ÷ 1000 = 0.783 6. 783 ÷ 100 = 7.837. 4.535 × 100 = 453.5 8. 4.535 × 1000 = 45359. 0.786 × 1000 = 786 10. 0.786 × 100 = 78.6

11. 789,234 ÷ 1000 = 789.234 12. 234 × 100 = 23,40013. 45,830 ÷ 1000 = 45.83 14. 0.079 × 1000 = 7915. 0.65 × 1000 = 650 16. 4.507 x 100 = 450.7

Multiplying and Dividing by 10, 100 and 1000A 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 7m5.2m + 1.78m4.35m + 2.4m 4.35m + 1.78m3.56m + 3.42m 3.56m + 2.78m 3.56m + 2.4m 3.56m + 1.78m3.42m + 3.56m 3.42m + 2.78m 3.42m + 2.4m 3.42m + 1.78m2.78m + 3.56m 2.78m + 3.42m 2.78m + 2.4m 2.78m + 1.78m2.4m + 4.35m 2.4m + 3.56m 2.4m + 3.42m 2.4m + 2.78m 2.4m + 1.78m1.78m + 5.2m 1.78m + 4.35m 1.78m + 3.56m 1.78m + 4.42m 1.78m + 2.78m 1.78m + 2.4m

Week 4:

Interpreting pie charts1. 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.


4.Year 2 children Year 6 children

Walk 15 12Bus 3 2Car 12 3Bike 0 6

Scooter 6 1

Drawing pie charts

Times table Number of children who found this difficult

Degrees

2 0 03 0 04 0 05 0 06 2 607 4 1208 3 909 1 30

10 0 011 0 012 2 60

Week 5:

Solve problems involving rate1. 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 lengthTyrannosaurus Rex 7m 15.2m

Brachiosaurus 15.2m 30.4mVelociraptor 0.6m 1.8mDiplodocus 7.4m 27m

Plateosaurus 2.2m 7.8m


Dimensions for dinosaur toys

Dinosaur Toy’s height Toy’s lengthAllosaurus 2.6cm 6.1cmTriceratops 1.45cm 4.2cmStegosaurus 1.9cm 4.45cmSpinosaurus 2.7cm 6.6cm

Brontosaurus 2.3cm 11.5cm

Place value multiplications

6x4=24 6x40=240 6x400=2400 60x40=2400 60x400=24000 60x4000=2400003x8=24 3x80=240 3x800=2400 30x80=2400 30x800=24000 30x8000=2400004x5=20 4x50=200 4x500=2000 40x50=2000 40x500=20000 40x5000=20000012x3=36 12x30=360 12x300=3600 120x30=3600 120x300=36000 120x3000=360000

Multiplications1. 345 x 24 = 82802. 264 x 32 = 84483. 335 x 23 = 77054. 253 x 35 = 88555. 426 x 24 = 10,224

Word problems1. 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£32075% is £240, 50% is £160, 25% is £80, 20% is £64, 10% is £32, 1% is £3.20.

Fact web£15075% is £112.50, 50% is £75, 25% is £37.50, 20% is £30, 10% is £15, 1% is £1.50.

Fact web£32875% is £246, 50% is £164, 25% is £82, 20% is £65.60, 10% is £32.80, 1% is £3.28.


Finding unit and non unit fractions of 240¼ of 240 is 60 ¾ of 240 is 1801/3 of 240 is 80 2/3 of 240 is 1601/6 of 240 is 40 5/6 of 240 is 2001/8 of 240 is 30 3/8 of 240 is 90 5/8 of 240 is 150 7/8 of 240 is 2101/10 of 240 is 241/12 of 240 is 20

Week 7:

Write a formula1. 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 equations1. a = 82. b = 53. c = 124. d = 305. e = 66. f = 37. e = 72°8. a = 62°9. c = 110°10. d = 40°

Solving equations (E)1. a = 52. b = 73. c = 124. d = 205. e =136. f = 67. g = 128. h = 49. a = 55°10. b = 35°


Equations with 2 unknownsa + 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.


Sequences1. 40, 400, 4n2. 41, 401, 4n + 13. 50, 500, 5n4. 49, 499, 5n - 15. 51, 501, 5n + 16. 100, 1000, 10n7. 102, 1002, 20n + 28. 98, 998, 10n – 2

Week 8

Multiplying fractions1/2 x 1/3 = 1/6 1/2 x 2/3 = 2/6 = 1/3 1/4 x 2/3 = 2/12 = 1/62/3 x 2/3 = 4/9

1/2 x 1/5 = 1/10 1/3 x 1/5 = 1/15 2/3 x 1/5 = 2/151/2 x 3/5 = 3/10

1/3 x 3/4 = 3/12 = 1/4 2/3 x 3/4 = 6/12 = 1/2 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 3/5 x 3/4 = 9/20

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

Dividing fractions (H)1/3 ÷ 2 = 1/6 1/5 ÷ 3 = 1/15 1/6 ÷ 2 = 1/121/3 ÷ 3 = 1/9 2/5 ÷ 2 = 2/10 = 1/5 1/6 ÷ 3 = 1/182/3 ÷ 2 = 2/6 = 1/3 2/5 ÷ 4 = 2/20 = 1/10 5/6 ÷ 2 = 5/122/3 ÷ 4 = 2/12 = 1/6 3/5 ÷ 2 = 3/10

4/5 ÷ 2 = 4/10 = 2/5

Dividing fractions (E)1/3 ÷ 2 = 1/6 1/4 ÷ 2 = 1/8 1/5 ÷ 2 = 1/101/3 ÷ 3 = 1/9 1/4 ÷ 3 = 1/12 2/5 ÷ 2 = 2/10 = 1/52/3 ÷ 2 = 2/6 = 1/3 3/4 ÷ 3 = 3/12 = 1/4 2/5 ÷ 4 = 2/20 = 1/102/3 ÷ 4 = 2/12 = 1/6 3/4 ÷ 2 = 3/8 4/5 ÷ 2 = 4/10 = 2/5


Long division (M)1 x 17 = 17 10 x 17 = 1702 x 17 = 34 20 x 17 = 3403 x 17 = 51 30 x 17 = 5104 x 17 = 68 40 x 17 = 6805 x 17 = 85 50 x 17 = 8506 x 17 = 102 60 x 17 = 1020

1. 425 ÷ 17 = 252. 547 ÷ 17 = 32 r 33. 697 ÷ 17 = 41

1 x 165 = 1652 x 165 = 3303 x 165 = 4954 x 165 = 6605 x 165 = 8256 x 165 = 990

1. 394 ÷ 165 = 2 r 642. 774 ÷ 165 = 4 r 1143. 936 ÷ 165 = 5 r 111

1 x 21 = 21 10 x 21 = 2102 x 21 = 42 20 x 21 = 4203 x 21 = 63 30 x 21 = 6304 x 21 = 84 40 x 21 = 8405 x 21 = 105 50 x 21 = 10506 x 21 = 126 60 x 21 = 1260

1. 295 ÷ 21 = 14 r 12. 483 ÷ 21 = 233. 720 ÷ 21 = 34 r 6


Long division (E)1 x 13 = 13 10 x 13 = 1302 x 13 = 26 20 x 13 = 2603 x 13 = 39 30 x 13 = 3904 x 13 = 52 40 x 13 = 5205 x 13 = 65 50 x 13 = 6506 x 13 = 78 60 x 13 = 780

1. 417 ÷ 13 = 32 r 12. 210 ÷ 13 = 16 r 23. 331 ÷ 13 = 25 r 64. 565 ÷ 13 = 43 r 65. 711 ÷ 13 = 54 r 9

Long division (MH)1 x 24 = 24 10 x 24 = 2402 x 24 = 48 20 x 24 = 4803 x 24 = 72 30 x 24 = 7204 x 24 = 96 40 x 24 = 9605 x 24 = 120 50 x 24 = 12006 x 24 = 144 60 x 24 = 1440

1. 828 ÷ 24 = 34 r 122. 630 ÷ 24 = 26 r 63. 988 ÷ 24 = 41 r 44. 435 ÷ 24 = 18 r 3

1 x 27 = 27 10 x 27 = 2702 x 27 = 54 20 x 27 = 5403 x 27 = 81 30 x 27 = 8104 x 27 = 108 40 x 27 = 10805 x 27 = 135 50 x 27 = 13506 x 27 = 162 60 x 27 = 1620

5. 597 ÷ 27 = 22 r 36. 938 ÷ 27 = 34 r 207. 693 ÷ 27 = 25 r 188. 711 ÷ 27 = 26 r 9


Long division

1 x 15 = 152 x 15 = 303 x 15 = 454 x 15 = 605 x 15 = 75

1. 200 ÷ 15 = 13 r 52. 250 ÷ 15 = 16 r 103. 365 ÷ 15 = 24 r 54. 620 ÷ 15 = 41 r 55. 545 ÷ 15 = 36 r 56. 440 ÷ 15 = 29 r 5

Week 9:

Area of triangles1/2 of 3 x 4 = 6cm² 1/2 of 2 x 6 = 6cm² 1/2 of 3 x 5 = 7.5cm²1/2 of 4 x 6 = 12cm² 8 x 4 = 32cm²

Area of triangles (E)1/2 of 3 x 4 = 6cm² 1/2 of 2 x 6 = 6cm² 1/2 of 3 x 5 = 7.5cm²1/2 of 4 x 6 = 12cm² 8 x 4 = 32cm²

Find volumes of cuboids (H)10 x 3 x 4 = 120cm³ 6 x 5 x 3 = 90cm³ 4 x 4 x 3 = 48cm³8 x 3 x 5 = 120cm³ 6 x 6 x 6 = 216cm³ 7 x 8 x 4 = 224cm³60 ÷ 20 = 3cm 120 ÷ 20 = 6cm

Find volumes of cuboids (E)10 x 3 x 4 = 120cm³ 6 x 5 x 3 = 90cm³ 4 x 4 x 3 = 48cm³8 x 3 x 5 = 120cm³ 6 x 6 x 6 = 216cm³ 7 x 8 x 4 = 224cm³

Week 10:

Missing number problems1. a = 72. b = 93. c = 54. d = 55. e =76. f = 57. g = 38. h = 9


Scaling upThe 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 4 pizzas 1 pizza 2 pizzas 6 pizzas 8 pizzasFlour 500g 125g 250g 750g 1000g/1kgYeast 10g 2.5g 5g 15g 20gSalt ½ tsp 1/8 tsp ¼ tsp ¾ tsp 1 tspSugar ½ tsp 1/8 tsp ¼ tsp 3/5 tsp 1 tspOil 4 tbsp 1 tbsp 2 tbsp 6 tbsp 8 tbspWater 250ml 62.5ml 125ml 375ml 500mlToppingTomatoes 400g 100g 200g 600g 800gCheese 200g 50g 100g 300g 400gGarlic 1 clove ¼ clove ½ clove 1 and ½

cloves2 cloves

Onion 1 onion ¼ onion ½ onion 1 and ½ onions

2 onions

Ratio problems1. 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.


Equivalent percentagesSwimming 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 2/32. 1946 ÷ 6 = 324 1/33. 3183 ÷ 4 = 795 3/44. 9326 ÷ 7 = 1332 2/75. 2442 ÷ 11 = 2226. 4752 ÷ 11 = 4327. 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 packs11. 253 ÷ 12 = 21 1/12 packs 22 packs need to be bought12. 962 ÷ 8 = 120 2/8 cm (120 1/4 cm)

Short division (E)1. 733 ÷ 3 = 244 1/32. 946 ÷ 6 = 157 2/33. 4783 ÷ 4 = 1195 3/44. 6326 ÷ 4 = 1581 1/25. 3142 ÷ 4 = 785 1/26. 3784 ÷ 5 = 756 4/57. 365 ÷ 7 = 52 1/78. 535 ÷ 4 = 133 3/49. 253 ÷ 6 = 42 1/6 43 packs of eggs must be bought10. 562 ÷ 4 = 140 1/2 cm


Long division544 ÷ 17 = 32 544 ÷ 18 = 30 4/18 (30 2/9)673 ÷ 17 = 39 10/17 673 ÷ 18 = 37 7/18673 ÷ 21 = 32 1/21 754 ÷ 21 = 35 19/21832 ÷ 21 = 39 13/21 832 ÷ 26 = 32936 ÷ 26 = 36 986 ÷ 26 = 37 24/26 (37 12/13)986 ÷ 32 = 30 26/32 (30 13/16) 992 ÷ 26 = 38 4/26 (38 2/13)992 ÷ 32 = 31

936 ÷ 17 = 55 1/17 936 ÷ 18 = 52986 ÷ 17 = 58 986 ÷ 18 = 54 14/18 (54 7/9)992 ÷ 17 = 58 6/17 992 ÷ 18 = 55 2/18 (55 1/9)

Long division1 x 15 = 152 x 15 = 303 x 15 = 454 x 15 = 605 x 15 = 75

1. 525 ÷ 15 = 35 2. 634 ÷ 15 = 42 4/15 3. 789 ÷ 15 = 52 9/15 (52 3/5)

1 x 23 = 232 x 23 = 463 x 23 = 694 x 23 = 925 x 23 = 115

4. 368 ÷ 23 = 16 5. 785 ÷ 23 = 34 3/23 6. 581 ÷ 23 = 25 6/23

1 x 32 = 322 x 32 = 643 x 32 = 964 x 32 = 1285 x 32 = 160

7. 487 ÷ 32 = 15 7/32 8. 711 ÷ 32 = 22 7/32 9. 995 ÷ 32 = 31 3/32


maths answers - hamilton trust web viewmaths answers. spring year . 6. week 1: temperature. 1. ......

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