Maths Answers

Maths Answers Spring Year 5/6

Week 1:

Temperature (E)

Temperature (H)

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 5 degrees. 5. The temperature rose 6 degrees from Tuesday night to its highest on Wednesday. 6. The temperature rose 7 degrees from Thursday night to its highest on Friday. 7. There is a difference of 13 degrees between the mildest and coldest temperatures.

Week 2:

Mental addition and subtraction

1. 3002 + 450 = 3452 2. 9784 - 704 = 9080 3. 4723 + 402 = 5125 4. 2538 + 2001 = 4539 5. 9826 - 803 = 9023 6. 4782 - 502 = 4280

© Hamilton Trust Year 5/6 Spring Maths Answers 7. 3782 + 200 = 3982 8. 3782 + 198 = 3980 9. 4658 - 100 = 4558 10. 4658 - 97 = 4561 11. 3478 + 1000 = 4478 12. 3478 + 999 = 4477 13. 5298 - 1000 = 4298 14. 5298 - 999 = 4299 15. 4578 + 321 = 4899 16. 8734 - 6031 = 2703 17. 23,472 - 2222 = 21,250 18. 45,310 + 3409 = 48,719 19. 8345 + 397 = 8742 20. 7935 - 298 = 7637 21. 3458 + 1997 = 5455 22. 9768 - 2995 = 6773 23. 45,237 + 3900 = 49,137 24. 57,345 - 2998 = 54,347

Mental addition and subtraction

1. 3478 + 1000 = 4478 2. 3478 + 999 = 4477 3. 5298 - 1000 = 4298 4. 5298 - 999 = 4299 5. 8345 + 397 = 8742 6. 7935 - 298 = 7637 7. 3458 + 1997 = 5455 8. 9768 - 2995 = 6773 9. 45,237 + 3900 = 49,137 10. 57,345 - 2998 = 54,347 11. 7.28 + 1.99 = 9.27 12. 8.46 + 2.97 = 11.43 13. 9.38 - 2.01 = 7.37 14. 9.38 - 1.99 = 7.39 15. 5.36 + 2.98 = 8.34 16. 8.27 - 2.95 = 5.32 17. 8.41 + 1.97 = 10.38 18. 9.39 - 1.95 = 7.44

Order of brackets and operations

1. (20 + 3) x 10 = 230 2. 20 + 3 x 10 = 50 3. 20 x 3 + 10 = 70 4. 20 x (3 + 10) = 260 5. 20 x 3 + 20 x 10 = 260 6. (20 - 3) x (20 + 10) = 510 7. 20 - 3 + 20 ÷ 10 = 19 8. 100 x 5 + 500 = 1000 9. 70 + 60 ÷ 2 = 100 10. 50 + 250 ÷ 5 = 100

Room make over

Item Change from £50 Change from £100 Bean bag £24.21 £74.21 CD player £1.33 £51.33 Duvet set £14.52 £64.52 Lamp shade £35.76 £85.76 Curtains £4.75 £54.75 Rug £20.51 £70.51 Tin of paint £28.01 £78.01

Pair of Items Change from £100 Bean bag and CD player £25.54 Bean bag and Duvet set £38.73 Bean bag and Lamp shade £59.97 Bean bag and Curtains £28.96 Bean bag and Rug £44.72 Bean bag and Tin of paint £52.22 CD player and Duvet set £15.85 CD player and Lamp shade £37.09

© Hamilton Trust Year 5/6 Spring Maths Answers CD player and Curtains £6.08 CD player and Rug £21.84 CD player and Tin of paint £29.34 Duvet set and Lamp shade £50.28 Duvet set and Curtains £19.27 Duvet set and Rug £35.03 Duvet set and Tin of paint £42.53 Lamp shade and Curtains £40.51 Lamp shade and Rug £56.27 Lamp shade and Tin of paint £63.77 Curtains and Rug £25.26 Curtains and Tin of paint £32.76 Rug and Tin of paint £48.52

Trio of items Change from £100 Bean bag, CD player & Lamp shade £11.30 Bean bag, CD player & Tin of paint £3.55 Bean bag, Duvet set & Lamp shade £24.49 Bean bag, Duvet set & Rug £9.24 Bean bag, Duvet set & Tin of paint £16.74 Bean bag, Lamp shade & Curtains £14.72 Bean bag, Lamp shade & Rug £30.48 Bean bag, Lamp shade & Tin of paint £37.98 Bean bag, Curtains & Tin of paint £6.97 Bean bag, Rug & Tin of paint £22.73 CD player, Duvet set & Lamp shade £1.61 CD player, Lamp shade & Rug £7.60 CD player, Lamp shade & Tin of paint £15.10 Duvet set, Lamp shade & Curtains £5.03 Duvet set, Lamp shade & Rug £20.79 Duvet set, Lamp shade & Tin of paint £28.29 Duvet set, Rug & Tin of paint £13.04 Lamp shade, Curtains & Rug £11.02 Lamp shade, Curtains & Tin of paint £18.52 Lamp shade, Rug & Tin of paint £34.28 Curtains, Rug & Tin of paint £3.27

Estimating differences

<£5 >£5 £29.25 - £25.99 = £3.26 £23.75 - £18.25 = £5.50 £74.49 - £69.99 = £4.50 £54.29 - £48.95 = £5.34 £23.35 - £18.75 = £4.60 £42.65 - £38.49 = £4.16

Word problems

© Hamilton Trust Year 5/6 Spring Maths Answers 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.

Week 3:

Place value addition and subtraction

1. 4 + 0.53 = 4.53 2. 6.07 + 0.5 = 6.57 3. 5.78 - 0.08 = 5.7 4. 8.64 - 0.6 = 8.04 5. 8.23 + 0.1 = 8.33 6. 4.56 + 0.01 = 4.57 7. 8.47 - 0.01 = 8.46 8. 9.35 - 0.1 = 9.25 9. 6.21 + 0.2 = 6.41 10. 9.34 - 0.2 = 9.14 11. 8.25 + 0.03 = 8.28 12. 7.38 - 0.03 = 7.35 13. 9.34 + 0.11 = 9.45 14. 8.53 - 0.11 = 8.42 15. 4.73 + 1.01 = 5.74 16. 8.14 - 1.01 = 7.13 17. 4.27 + 1.2 = 5.47 18. 8.75 - 1.02 = 7.73 19. 3.24 + 1.23 = 4.47 20. 9.87 - 1.81 = 8.06

Place value addition and subtraction

1. 4.538 + 0.2 = 4.738 2. 4.538 + 0.03 = 4.568 3. 4.538 - 0.004 = 4.534 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

Multiplying by 10, 100 and 1000

A motorbike weighs the same as 100 bags of potatoes. A Land Rover weighs the same as 10 motorbikes.

Rounding decimals to the nearest whole number

2.25 → 2 2.6 → 3 3.5 → 4 3.3 → 3 2.49 → 2 2.75 → 3 3.15 → 3 3.78 → 4

5.2 → 5 5.1 → 5 6.4 → 6 6.52 → 7 5.35 → 5 5.83 → 6 6.95 → 7 6.19 → 6

Adding decimals (E)

1. 34.5 + 27.3 = 61.8 6. 5.42 + 6.37 = 11.79

© Hamilton Trust Year 5/6 Spring Maths Answers 2. 62.7 + 23.5 = 86.2 7. 4.48 + 3.27 = 7.75 3. 24.8 + 43.9 = 68.7 8. 5.63 + 2.84 = 8.47 4. 46.7 + 25.5 = 72.2 9. 6.57 + 2.48 = 9.05 5. 47.8 + 34.4 = 82.2 10. 7.85 + 4.56 = 12.41

Adding decimals (H)

1. 67.8 + 35.9 = 103.7 2. 45.8 + 26.7 = 72.5 3. 5.42 + 6.37 = 11.79 4. 4.48 + 3.27 = 7.75 5. 5.63 + 2.84 = 8.47 6. 6.57 + 2.48 = 9.05 7. 7.85 + 4.56 = 12.41 8. 37.2 + 4.28 = 41.48 9. 24.6 + 3.84 = 28.44 10. 47.4 + 8.7 = 56.1 11. 3.78 + 21.8 = 25.58 12. 45.5 + 2.52 = 48.02

Week 4:

Translations

New co-ordinates:-

1. (-1,1), (-1,4), (3,4) and (3,1) 2. (1,6), (2,5), (4,5), (5,6), (4,7) and (2,7) 3. (-1,5), (-1,6) and (2,5) 4. (-3,1), (-1,3), (3,3) and (1,1) 5. (1,6), (2,7), (4,7) and (5,6)

© Hamilton Trust Year 5/6 Spring Maths Answers The Y co-ordinate increases when you move a shape up and decreases when you move it down. The X co-ordinate decreases when you move a shape to the left and increases when you move it to the right.

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. 4. Year 2 children Year 6 children Walk 15 12 Bus 3 2 Car 12 3 Bike 0 6 Scooter 6 1

Week 5:

Whole class practice

1. 12 2. 7 3. 4 4. 3 5. 3

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 7m 15.2m

Mental strategies for division

1. 780 ÷ 10 = 78 780 ÷ 20 = 39 780 ÷ 5 = 156 2. 430 ÷ 10 = 43 430 ÷ 20 = 21.5 430 ÷ 5 = 86 3. 370 ÷ 10 = 37 370 ÷ 20 = 18.5 370 ÷ 5 = 74 4. 270 ÷ 3 = 90 270 ÷ 6 = 45 5. 312 ÷ 3 = 104 312 ÷ 6 = 52 6. 123 ÷ 3 = 41 123 ÷ 6 = 20.5 7. 336 ÷ 2 = 168 336 ÷ 4 = 84 336 ÷ 8 = 42 8. 656 ÷ 2 = 328 656 ÷ 4 = 164 656 ÷ 8 = 82 9. 172 ÷ 2 = 86 172 ÷ 4 = 43 172 ÷ 8 = 21.5 10. 260 ÷ 2 = 130 260 ÷ 4 = 65 200 ÷ 8 = 32.5

Dimensions for dinosaur toys

Dinosaur Toy’s height Toy’s length Allosaurus 2.6cm 6.1cm Triceratops 1.45cm 4.2cm Stegosaurus 1.9cm 4.45cm Spinosaurus 2.7cm 6.6cm Brontosaurus 2.3cm 11.5cm

Multiplication

1. 3 x 3421 = 10,263 2. 4 x 4923 = 19,692 3. 7 x 4235 = 29,645 4. 5 x 6748 = 33,740 5. 5156 x 6 = 30,936 6. 2021 x 4 = 8084 7. 8267 x 5 = 41,335 8. 4278 x 8 = 34,224

Week 6:

1. 2/3 > 3/6 2. 2/3 > 2/9 3. 3/10 >1/5 4. ¾ < 7/8 5. 5/6 < 11/12 6. 7/10 > 3/5 7. 1/3 < 5/12 8. 2/5 < 7/15 9. 7/10 > 13/20 10. 1/3 > 4/15 11. ½ > 2/5 12. 2/3 < 4/5

13. ½, 5/8, ¾ 14. ½, 3/5, 7/10 15. 4/15, 1/3, 2/5 16. 7/10, 4/5, 17/20

150 ÷ 2 = 75 140 ÷ 2 = 70 160 ÷ 2 = 80 150 ÷ 5 = 30 140 ÷ 5 = 28 160 ÷ 5 = 32 150 ÷ 6 = 25 140 ÷ 6 = 23 1/3 160 ÷ 6 = 26 2/3 150 ÷ 4 = 37 1/2 140 ÷ 4 = 35 160 ÷ 4 = 40 150 ÷ 8 = 18 3/4 140 ÷ 8 = 17 1/2 160 ÷ 8 = 20 150 ÷ 7 = 21 3/7 140 ÷ 7 = 20 160 ÷ 7 = 22 6/7 150 ÷ 9 = 16 2/3 140 ÷ 9 = 15 5/9 160 ÷ 9 = 17 7/9 150 ÷ 3 = 50 140 ÷ 3 = 46 2/3 160 ÷ 3 = 53 1/3

210 ÷ 2 = 105 180 ÷ 2 = 90 200 ÷ 2 = 100 210 ÷ 5 = 42 180 ÷ 5 = 36 200 ÷ 5 = 50 210 ÷ 6 = 35 180 ÷ 6 = 30 200 ÷ 6 = 33 1/3 210 ÷ 4 = 52 1/2 180 ÷ 4 = 45 200 ÷ 4 = 50 210 ÷ 8 = 26 1/4 180 ÷ 8 = 22 1/2 200 ÷ 8 = 25 210 ÷ 7 = 30 180 ÷ 7 = 25 5/7 200 ÷ 7 = 28 4/7 210 ÷ 9 = 23 1/3 180 ÷ 9 = 20 200 ÷ 9 = 22 2/9 210 ÷ 3 = 70 180 ÷ 3 = 60 200 ÷ 3 = 66 2/3

120 ÷ 2 = 60 240 ÷ 2 = 120 120 ÷ 5 = 24 240 ÷ 5 = 48 120 ÷ 6 = 20 240 ÷ 6 = 40 120 ÷ 4 = 30 240 ÷ 4 = 60 120 ÷ 8 = 15 240 ÷ 8 = 30 120 ÷ 7 = 17 1/7 240 ÷ 7 = 34 2/7 120 ÷ 9 = 13 1/3 240 ÷ 9 = 26 2/3 120 ÷ 3 = 40 240 ÷ 3 = 80

Hundredths (E)

0.25 = 25/100 = 1/4 0.1 = 10/100 = 1/10 0.2 = 20/100 = 2/10 = 1/5 0.8 = 80/100 = 8/10 = 4/5 0.5 = 50/100 = 5/10 = 1/2 0.75 = 75/100 = 3/4 0.7 = 70/100 = 7/10 0.99 = 99/100

Ordering fractions (H)

1/10, 0.19, 0.2, 1/4, 0.3, 2/5, 0.46, 1/2, 3/5, 0.65, 0.7, 3/4, 0.85, 9/10, 0.91

Fact web

£150 50% is £75, 75% is £112.50, 25% is £37.50, 1% is £1.50, 10% is £15, 20% is £30.

Fact web

£328 50% is £164, 75% is £246, 25% is £82, 1% is £3.28, 10% is £32.80, 20% is £65.60.

Find fractions of amounts (E)

1. 1/10 of 240 is 24 3/10 of 240 is 72 2. 1/3 of 180 is 60 2/3 of 180 is 120 3. 1/4 of 128 is 32 3/4 of 128 is 96 4. 1/5 of 150 is 30 4/5 of 150 is 120 5. 1/7 of 210 is 30 3/7 of 210 is 90 6. 1/9 of 180 is 20 4/9 of 180 is 80 7. 1/6 of 96 is 16 5/6 of 96 is 80 8. 1/5 of 85 is 17 3/5 of 85 is 51 9. 1/8 of 160 is 20 7/8 of 160 is 140 10. 1/3 of 72 is 24 2/3 of 72 is 48

Find fractions of amounts (H)

1. 3/4 of 128 is 96 2. 2/5 of 180 is 72 3. 5/6 of 180 is 150 4. 2/7 of 210 is 60 5. 2/3 of 141 is 94 6. 2/9 of 189 is 42 7. 5/6 of 192 is 160 8. 3/8 of 192 is 72 9. 5/7 of 224 is 160 10. 5/8 of 207 is 129.375

Finding unit and non unit fractions of 240

¼ of 240 is 60 ¾ of 240 is 180 1/3 of 240 is 80 2/3 of 240 is 160 1/6 of 240 is 40 5/6 of 240 is 200 1/8 of 240 is 30 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

1. There are 30 children in each class. 2. School dinners cost £11.25 for one week. 3. 37 children chose curry. 4. The total area of all 7 classrooms is 294m². 5. 30 children have not yet got their 25m swimming badge. 6. Children are in school for 31 ¼ hours during one week. 7. Each class will have £40 to spend.

Solving word problems (H)

1. There are 30 children in each non-reception class. 2. School dinners cost £427.50 for 190 days. 3. 60 children chose curry. 4. The area of the corridor is 18m². 5. 48 children have one swimming badge so far. 6. Children are in school for 375 hours during one term. 7. Each class will have £51 to spend.

Week 7:

Multiplying fractions

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

1/2 x 1/5 = 1/10 1/3 x 1/5 = 1/15 2/3 x 1/5 = 2/15 1/2 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 (E)

1/3 ÷ 2 = 1/6 1/4 ÷ 2 = 1/8 1/5 ÷ 2 = 1/10 1/3 ÷ 3 = 1/9 1/4 ÷ 3 = 1/12 2/5 ÷ 2 = 2/10 = 1/5 2/3 ÷ 2 = 2/6 = 1/3 3/4 ÷ 3 = 3/12 = 1/4 2/5 ÷ 4 = 2/20 = 1/10 2/3 ÷ 4 = 2/12 = 1/6 3/4 ÷ 2 = 3/8 4/5 ÷ 2 = 4/10 = 2/5

Dividing fractions (H)

© Hamilton Trust Year 5/6 Spring Maths Answers 1/3 ÷ 2 = 1/6 1/5 ÷ 3 = 1/15 1/6 ÷ 2 = 1/12 1/3 ÷ 3 = 1/9 2/5 ÷ 2 = 2/10 = 1/5 1/6 ÷ 3 = 1/18 2/3 ÷ 2 = 2/6 = 1/3 2/5 ÷ 4 = 2/20 = 1/10 5/6 ÷ 2 = 5/12 2/3 ÷ 4 = 2/12 = 1/6 3/5 ÷ 2 = 3/10 4/5 ÷ 2 = 4/10 = 2/5

1. 369 ÷ 3 = 123 2. 448 ÷ 4 = 112 3. 575 ÷ 5 = 115 4. 378 ÷ 3 = 126 5. 672 ÷ 6 = 112 6. 898 ÷ 8 = 112 r2 7. 791 ÷ 7 = 113 8. 643 ÷ 3 = 214 r1 9. 857 ÷ 4 = 214 r1 10. 563 ÷ 5 = 112 r3 11. 691 ÷ 6 = 115 r1 12. 936 ÷ 9 = 104

Long division

1 x 13 = 13 10 x 13 = 130 2 x 13 = 26 20 x 13 = 260 3 x 13 = 39 30 x 13 = 390 4 x 13 = 52 40 x 13 = 520 5 x 13 = 65 50 x 13 = 650 6 x 13 = 78 60 x 13 = 780

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

Short division (E)

1. 844 ÷ 4 = 211 2. 639 ÷ 3 = 213 3. 489 ÷ 4 = 122 r1 4. 368 ÷ 3 = 122 r2 5. 558 ÷ 5 = 111 r3 6. 872 ÷ 4 = 218 7. 575 ÷ 5 = 115 8. 524 ÷ 4 = 131

Short division (H)

1. 447 ÷ 4 = 111 r3 2. 447 ÷ 8 = 55 r7 3. 678 ÷ 4 = 169 r2 4. 678 ÷ 8 = 84 r6 5. 375 ÷ 6 = 62 r3 6. 375 ÷ 3 = 125 7. 856 ÷ 7 = 122 r2 8. 462 ÷ 9 = 51 r3 9. 674 ÷ 5 = 134 r4 10. 266 ÷ 4 = 66 r2 11. 437 ÷ 3 = 145 r2 12. 726 ÷ 9 = 80 r6

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

Long division (H)

1 x 24 = 24 10 x 24 = 240 2 x 24 = 48 20 x 24 = 480 3 x 24 = 72 30 x 24 = 720 4 x 24 = 96 40 x 24 = 960 5 x 24 = 120 50 x 24 = 1200 6 x 24 = 144 60 x 24 = 1440

1. 828 ÷ 24 = 34 r 12 2. 630 ÷ 24 = 26 r 6 3. 988 ÷ 24 = 41 r 4 4. 435 ÷ 24 = 18 r 3

© Hamilton Trust Year 5/6 Spring Maths Answers 1 x 27 = 27 10 x 27 = 270 2 x 27 = 54 20 x 27 = 540 3 x 27 = 81 30 x 27 = 810 4 x 27 = 108 40 x 27 = 1080 5 x 27 = 135 50 x 27 = 1350 6 x 27 = 162 60 x 27 = 1620

5. 597 ÷ 27 = 22 r 3 6. 938 ÷ 27 = 34 r 20 7. 693 ÷ 27 = 25 r 18 8. 711 ÷ 27 = 26 r 9

Week 8:

Area of triangles

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

Find the perimeter

8 + 8 + 6 + 2 + 2 + 6 = 32cm 9 + 9 + 5 + 6 + 4 + 3 = 36cm 8 + 8 + 6 + 3 + 1 + 2 + 3 + 3 = 34cm 8 + 2 + 3 + 2 + 3 + 2 + 8 + 2 + 3 + 2 + 3 + 2 = 40cm

Find volumes of cuboids (E)

10 x 3 x 4 = 120cm³ 6 x 5 x 3 = 90cm³ 4 x 4 x 3 = 48cm³ 8 x 3 x 5 = 120cm³ 6 x 6 x 6 = 216cm³ 7 x 8 x 4 = 224cm³

Find volumes of cuboids (H)

10 x 3 x 4 = 120cm³ 6 x 5 x 3 = 90cm³ 4 x 4 x 3 = 48cm³ 8 x 3 x 5 = 120cm³ 6 x 6 x 6 = 216cm³ 7 x 8 x 4 = 224cm³ 60 ÷ 20 = 3cm 120 ÷ 20 = 6cm

Week 9:

Using place value to add and subtract

1. 456,728 + 3000 = 459,728 2. 748,672 - 40,000 = 708,672 3. 237,045 + 203 = 237,248 4. 945,378 - 2005 = 943,373 5. 349,281 + 20,500 = 369,781 6. 973,452 - 800,300 = 173,152 7. 424,789 + 1 = 424,790 8. 472,480 - 1 = 472,479

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.

Ordering six-digit numbers

Round to the Round to the nearest 10,000 nearest 100,000 Belfast 268,100 270,000 300,000 Birmingham 994,900 990,000 1,000,000 Bristol 440,100 440,000 400,000 Cardiff 305,900 310,000 300,000 Edinburgh 438,900 440,000 400,000 Glasgow 632,800 630,000 600,000 Leeds 448,000 450,000 400,000 Leicester 340,100 340,000 300,000 Liverpool 477,600 480,000 500,000 Manchester 442,800 440,000 400,000 Newcastle-upon-Tyne 202,200 200,000 200,000 Plymouth 249,200 250,000 200,000 Swansea 172,200 170,000 200,000 Your own city/town/village if you wish!

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.

1. 57,348 - 3762 = 53,586 2. 84,823 - 6248 = 78,575 3. 45,240 - 2758 = 42,482 4. 83,602 - 7478 = 76,124 5. 52,033 - 5674 = 46,359 6. 86,535 - 8645 = 77,890 7. 73,452 - 5276 = 68,176 views on Sunday. 8. 17,177 - 8345 = 8832. The plane has 8832km further to go. 9. 12,364 - 1534 - 4245 = 6585. The hot-air balloon is now at an altitude of 6585 feet. 10. 35,478 - 3448 - 5999 = 26,031. The lottery winner has £26,031 left.

Subtraction practice (E)

1. 64,784 - 21,529 = 43,255 2. 75,548 - 43,273 = 32,275 3. 86,347 - 33,720 = 52,627 4. 72,583 - 45,251 = 27,332 5. 56,421 - 24,175 = 32,246 6. 92,765 - 48,308 = 44,457 7. 45,287 - 38,145 = 7142. There is a difference of 7142 between their populations. 8. 63,564 - 52,382 = 11,182. The car drove 11,182 miles in the last year.

Equivalent percentages

Swimming 50% Cycling 30% Football 20%

Bananas 40% Apples 30% Oranges 30%

Dogs 50% Cats 20% Rabbits 30%

Week 10:

Multiply and divide by 10, 100 and 1000

1. 4326 ÷ 100 = 43.26 6. 783 ÷ 100 = 7.83 2. 4326 ÷ 1000 = 4.326 7. 4.535 x 100 = 453.5 3. 7840 ÷ 100 = 78.4 8. 4.535 x 1000 = 4535 4. 7840 ÷ 1000 = 7.84 9. 0.786 x 1000 = 786 5. 783 ÷ 1000 = 0.783 10. 0.786 x 100 = 78.6

11. 789,234 ÷ 1000 = 789.234 12. 234 x 100 = 23,400

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.

Athletic differences

Javelin: 10.2 - 8.7 = 1.5m Long jump: 3.04 - 2.87 = 0.17m Standing jump: 1.76 - 1.45 = 0.31m High jump: 1.48 - 1.23 = 0.25m 100m: 16.7 - 15.8 = 0.9s 200m: 36.4 - 34.8 = 1.6s

Solve these equations (E)

1. a = 5 2. b = 7 3. c = 12 4. d = 20 5. e = 5 6. f = 3

7. 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.

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

9. 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.

10. g = 1 h = 16, g = 2 h = 8, g = 4 h = 4, g = 8 h=2, g = 16 h = 1.

Solve these equations (H)

7. 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.

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

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

10. a = 7 b = 3

11. c = 8 d = 2

12. e = 8 f = 4

Bamboos can grow at an amazing rate!

Day Height Growth since the previous day 1 2.9m 2 3.5m 0.6m 3 3.75m 0.25m 4 4.01m 0.26m 5 4.59m 0.58m 6 5.25m 0.66m 7 6.1m 0.85m 8 7.05m 0.95m

Subtracting decimals

1. 7.3 - 6.79 = 0.51 2. 8.45 - 7.8 = 0.65 3. 5.24 - 3.7 = 1.54 4. 9.4 - 5.78 = 3.62 5. 8.7 - 6.45 = 2.25 6. 7.5 - 5.29 = 2.21 7. 10.67 - 5.3 = 5.37 8. 12.8 - 9.27 = 3.53

Sequences

1. 40, 400, 4n 2. 41, 401, 4n + 1 3. 50, 500, 5n 4. 49, 499, 5n - 1

1. Carla has £12.11 left. 2. Sam has grown 0.07m (7cm) in the last year. 3. The length is 0.67m (67cm) longer than the width. 4. Grandma has 0.26m (26cm) of material left. 5. Auntie Sarah will have 0.38m (38cm) of wood left. 6. Grandad gets £20.06 change. 7. The off-peak ticket is £18.21 cheaper than the peak rail ticket. 8. Each of the friends would get £3.79 change each.

Word Problems (H)

1. Carla has £12.09 left. 2. Sam has grown 0.07m (7cm) and Elena has grown 0.05m (5cm). Sam has grown most in the last year. 3. The perimeter is 15.74m so Dieter is 1.74m out. 4. Grandma has 1.96m (196cm) of material left. 5. Auntie Sarah will have 0.32m (32cm) of wood left. 6. Grandad gets £12.56 change. 7. It is £11.46 cheaper to buy two singles than the peak return ticket. 8. Each of the friends would get £1.88 change each.

Week 11:

Part A Part B

1. 3 x 4251 = 12,753 1. 3 x £12.67 = £38.01 2. 6 x 2784 = 16,704 2. 6 x £23.72 = £142.32 3. 2469 x 3 = 7407 3. £45.14 x 4 = £180.56 4. 5843 x 7 = 40,901 4. £38.46 x 6 = £230.76 5. 8 x 4235 = 33,880 5. 7 x £64.23 = £449.61 6. 7 x 8679 = 60,753 6. 8 x £75.69 = £605.52

Short division

1. 364 ÷ 3 = 121 r1 5. 754 ÷ 5 = 150 r4 2. 487 ÷ 4 = 121 r3 6. 934 ÷ 4 = 233 r2 3. 582 ÷ 5 = 116 r2 7. 847 ÷ 6 = 141 r1 4. 456 ÷ 3 = 152 8. 968 ÷ 8 = 121

Short division (E)

1. 733 ÷ 3 = 244 1/3

© Hamilton Trust Year 5/6 Spring Maths Answers 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

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)

Adding four-digit and five-digit numbers

1. 3478 + 9423 + 2856 = 15,757 9423 + 2856 + 5637 = 17,916 2856 + 5637 + 3478 = 11,971 5637 + 3478 + 9423 = 18,538

2. 23,874 + 54,237 = 78,111 23,874 + 19,347 = 43,221 23,874 + 72,341 = 96,215 54,237 + 19,347 = 73,584 54,237 + 72,341 = 126,578 19,347 + 72,341 = 91,688

3. 23,874 + 3478 = 27,352 23,874 + 9423 = 33,297 23,874 + 2856 = 26,730 23,874 + 5637 = 29,511 54,237 + 3478 = 57,715 54,237 + 9423 = 63,660 54,237 + 2856 = 57,093 54,237 + 5637 = 59,874

© Hamilton Trust Year 5/6 Spring Maths Answers 19,347 + 3478 = 22,825 19,347 + 9423 = 28,770 19,347 + 2856 = 22,203 19,347 + 5637 = 24,984 72,341 + 3478 = 75,819 72,341 + 9423 = 81,764 72,341 + 2856 = 75,197 72,341 + 5637 = 77,978

Long division

544 ÷ 17 = 32 544 ÷ 18 = 30 4/18 (30 2/9) 673 ÷ 17 = 39 10/17 673 ÷ 18 = 37 7/18 673 ÷ 21 = 32 1/21 754 ÷ 21 = 35 19/21 832 ÷ 21 = 39 13/21 832 ÷ 26 = 32 936 ÷ 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 = 52 986 ÷ 17 = 58 986 ÷ 18 = 54 14/18 (54 7/9) 992 ÷ 17 = 58 6/17 992 ÷ 18 = 55 2/18 (55 1/9)

Mental addition and subtraction (E)

1. 4580 + 205 = 4785 6. 4783 - 480 = 4303 11. 7845 - 1999 = 5846 2. 8040 + 508 = 8548 7. 8536 - 2004 = 6532 12. 3425 + 400 = 3825 3. 3452 + 2005 = 5457 8. 4563 + 2000 = 6563 13. 3425 + 399 = 3824 4. 4293 + 4300 = 8593 9. 4563 + 1999 = 6562 14. 7845 - 200 = 7645 5. 8572 - 502 = 8070 10. 7845 - 2000 = 5845 15. 7845 - 199 = 7646

Mental addition and subtraction (H)

1. 64,378 + 3001 = 67,379 6. 74,874 + 2999 = 77,873 2. 78,745 - 21,000 = 57,745 7. 43,473 + 398 = 43,871 3. 45.063 + 2300 = 47,363 8. 87,532 - 29,999 = 57,533 4. 78,462 - 8002 = 70,460 9. 63,467 - 1998 = 61,469 5. 45,364 + 19,999 = 65,363 10. 54,879 - 495 = 54,384

Long division

1 x 15 = 15 2 x 15 = 30 3 x 15 = 45 4 x 15 = 60 5 x 15 = 75

1 x 23 = 23 2 x 23 = 46 3 x 23 = 69 4 x 23 = 92 5 x 23 = 115

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

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