Maths Answers
Autumn Year 6
Week 1:
Place value additions and subtractions (6-digit numbers)
430,000 + 6378 = 436,378 805,370 + 20,007 = 825,377
234,000 + 846 = 234,846 904,678 + 20,000 = 924,678
770,777 + 7000 = 777,777 504,027 + 30,600 = 534,627
734,523 - 523 = 734,000 827,410 - 27,000 = 800,410
652,235 - 50,000 = 602,235 272,896 - 72,000 = 200,896
645,345 - 640,000 = 5345 852,462 - 50,402 = 802,060
5-digit addition practice
1. 45,248 + 32,517 = 77,765
2. 52,382 + 24,045 = 76,427
3. 63,521 + 23,934 = 87,455
4. 38,413 + 27,305 = 65,718
5. 73,278 + 20,001 = 93,279
6. 45,379 + 23,365 = 68,744
7. 39,241 + 26,382 = 65,623
8. 45,382 + 23,618 = 69,000
9. 35,684 + 37,947 = 73,631
10. 56,937 + 24,285 = 81,222
Week 2:
Place value
2.304 + 0.05 = 2.354
2.37 + 0.002 = 2.372
2.074 + 0.5 = 2.574
23.78 +0.009 = 23.789
1.58 + 0.005 = 1.585
2.305 + 0.02 = 2.325
78.409 + 0.02 = 78.429
3.075 + 0.1 = 3.175
45.015 + 0.2 = 45.215
2 + 0.555 = 2.555
Function machines
2.75 x 10 = 27.5 4.5 ÷ 10 = 0.45
0.9 x 10 = 9 78 ÷ 10 = 7.8
17.4 x 10 = 174 0.4 ÷ 10 = 0.04
74.5 x 100 = 7450 70 ÷ 100 = 0.7
0.02 x 100 = 2 48 ÷ 100 = 0.48
2.58 x 100 = 258 9 ÷ 100 = 0.09
Function machines
0.478 x 100 = 47.8 42.7 ÷ 100 = 0.427
1.756 x 100 = 175.6 5.8 ÷ 100 = 0.058
0.008 x 100 = 0.8 0.5 ÷ 100 = 0.005
0.457 x 1000 = 457 8 ÷ 1000 = 0.008
2.634 x 1000 = 2634 5789 ÷ 1000 = 5.789
0.006 x 1000 = 6 37 ÷ 1000 = 0.037
Mystery decimals
1.139 rounds to 1.14 when rounded to the nearest 0.01.
2.312 rounds to 2.3 when rounded to the nearest 0.1.
6.254 rounds to 6 when rounded to the nearest whole.
Whole class practice
1. £45.75 + £24.28 = £70.03
2. £63.70 + £24.85 = £88.55
3. £43.78 + £24.65 = £68.43
4. £56.25 + £8.39 = £64.64
5. £38.56 + £25.79 = £64.35
6. £64.78 + £5.56 = £70.34
7. £34.35 + £23.31 + £12.25 = £69.91
8. £44.25 + £12.27 + £35.15 = £91.67
9. £32.45 + £21.79 + £34.50 = £88.74
10. £27.25 + £25.19 + £13.45 = £65.89
11. £26.78 + £34.56 + £4.39 = £65.73
12. £51.23 + £23.36 + £34.29 = £108.88
13. £75.35 + £25.27 + £43.09 = £143.71
14. £67.45 + £45.59 + £7.79 = £120.83
15. £95.38 + £56.31 + £48.31 = £200
16. E.g. £27.14 + £40.52 + £32.34 = £100.
Adding distances
Albert 6.47m + 2.28m = 8.75m
Bob 10.35m + 9.37m = 19.72m
Celia 12.18m + 11.56m = 23.74m
Daphne 11.72m + 13.43m = 25.15m
Edna 13.53m + 10.64m = 24.17m
Fred 12.38m + 11.29m = 23.67m
Gertrude 11.78m + 12.54m = 24.32m
Horace 6.49m + 3.73m = 10.22m
When rounded to the nearest metre, 24m was the most common distance crawled by the snails.
Week 3:
Whole class practice
£32.79 + £11.35 = £44.14, £50 - £44.14 = £5.86
£31.56 + £11.35 = £42.91, £50 - £42.91 = £7.09
£26.95 + £11.35 = £38.30, £50 - £38.30 = £11.70
£26.95 + £18.75 = £45.70, £50 - £45.70 = £4.30
£26.95 + £20.45 = £47.40, £50 - £47.40 = £2.60
£23.65 + £11.35 = £35, £50 - £35 = £15
£23.65 + £18.75 = £42.40, £50 - £42.40 = £7.60
£23.65 + £20.45 = £44.10, £50 - £44.10 = £5.90
£20.45 + £11.35 = £33.80, £50 - £33.80 = £16.20
£20.45 + £18.75 = £39.20, £50 - £39.20 = £10.80
£18.75 + £11.35 = £30.10, £50 - £30.10 = £19.90
£11.35 + £18.75 + £20.45 = £50.55, £100 - £50.55 = £49.45
£11.35 + £18.75 + £23.65 = £53.75, £100 - £53.75 = £46.25
£11.35 + £18.75 + £26.95 = £57.05, £100 - £57.05 = £42.95
£11.35 + £18.75 + £31.56 = £61.66, £100 - £61.66 = £38.34
£11.35 + £18.75 + £32.79 = £62.89, £100 - £62.89 = £37.11
£11.35 + £18.75 + £45.79 = £75.89, £100 - £75.89 = £24.11
£11.35 + £20.45 + £23.65 = £55.45, £100 - £55.45 = £44.55
£11.35 + £20.45 + £26.95 = £58.75, £100 - £58.75 = £41.25
£11.35 + £20.45 + £31.56 = £63.36, £100 - £63.36 = £36.64
£11.35 + £20.45 + £32.79 = £64.59, £100 - £64.59 = £35.41
£11.35 + £20.45 + £45.79 = £77.59, £100 - £77.59 = £22.41
£11.35 + £23.65 + £26.95 = £61.95, £100 - £61.95 = £38.05
£11.35 + £23.65 + £31.56 = £66.56, £100 - £66.56 = £33.44
£11.35 + £23.65 + £32.79 = £67.79, £100 - £67.79 = £32.21
£11.35 + £23.65 + £45.79 = £80.79, £100 - £80.79 = £19.21
£11.35 + £26.95 + £31.56 = £69.86, £100 - £69.86 = £30.14
£11.35 + £26.95 + £32.79 = £71.09, £100 - £71.09 = £28.91
£11.35 + £26.95 + £45.79 = £84.09, £100 - £84.09 = £15.91
£11.35 + £31.56 + £32.79 = £75.70, £100 - £75.70 = £24.30
£11.35 + £31.56 + £45.79 = £88.70, £100 - £88.70 = £11.30
£11.35 + £32.79 + £45.79 = £89.93, £100 - £89.93 = £10.07
£18.75 + £20.45 + £23.65 = £62.85, £100 - £62.85 = £37.15
£18.75 + £20.45 + £26.95 = £66.15, £100 - £66.15 = £33.85
£18.75 + £20.45 + £31.56 = £70.76, £100 - £70.76 = £29.24
£18.75 + £20.45 + £32.79 = £71.99, £100 - £71.99 = £28.01
£18.75 + £20.45 + £45.79 = £84.99, £100 - £84.99 = £15.01
£18.75 + £23.65 + £26.95 = £69.35, £100 - £69.35 = £30.65
£18.75 + £23.65 + £31.56 = £73.96, £100 - £73.96 = £26.04
£18.75 + £23.65 + £32.79 = £75.19, £100 - £75.19 = £24.81
£18.75 + £23.65 + £45.79 = £88.19, £100 - £88.19 = £11.81
£18.75 + £26.95 + £31.56 = £77.26, £100 - £77.26 = £22.74
£18.75 + £26.95 + £32.79 = £78.49, £100 - £78.49 = £21.51
£18.75 + £26.95 + £45.79 = £91.49, £100 - £91.49 = £8.51
£18.75 + £31.56 + £32.79 = £83.10, £100 - £83.10 = £16.90
£18.75 + £31.56 + £45.79 = £96.10, £100 - £96.10 = £3.90
£18.75 + £32.79 + £45.79 = £97.33, £100 - £97.33 = £2.67
£20.45 + £23.65 + £26.95 = £71.05, £100 - £71.05 = £28.95
£20.45 + £23.65 + £31.56 = £75.66, £100 - £75.66 = £24.34
£20.45 + £23.65 + £32.79 = £76.89, £100 - £76.89 = £23.11
£20.45 + £23.65 + £45.79 = £89.89, £100 - £89.89 = £10.11
£20.45 + £26.95 + £31.56 = £78.96, £100 - £78.96 = £21.04
£20.45 + £26.95 + £32.79 = £80.19, £100 - £80.19 = £19.81
£20.45 + £26.95 + £45.79 = £93.19, £100 - £93.19 = £6.81
£20.45 + £31.56 + £32.79 = £84.80, £100 - £84.80 = £15.20
£20.45 + £31.56 + £45.79 = £97.80, £100 - £97.80 = £2.20
£20.45 + £32.79 + £45.79 = £99.03, £100 - £99.03 = £0.97
£23.65 + £26.95 + £31.56 = £82.16, £100 - £82.16 = £17.84
£23.65 + £26.95 + £32.79 = £83.39, £100 - £83.39 = £16.61
£23.65 + £26.95 + £45.79 = £96.39, £100 - £96.39 = £3.61
£23.65 + £31.56 + £32.79 = £88, £100 - £88 = £12
£26.95 + £31.56 + £32.79 = £91.30, £100 - £91.30 = £8.70
Subtracting pairs of 5-digit numbers
75,369 - 35,826 = 39,543 83,580 - 26,317 = 57,263
64,329 - 32,876 = 31,453 72,463 - 48,725 = 23,738
50,756 - 38,249 = 12,507 76,371 - 24,393 = 51,978
62,341 - 46,586 = 15,755 83,036 - 34,152 = 48,884
Subtracting pairs of 4-digit numbers
3458 - 1275 = 2183 9215 - 5853 = 3362
4569 - 2625 = 1944 5813 - 2368 = 3445
5890 - 4575 = 1315 6238 - 3645 = 2593
7572 - 3647 = 3925 7421 - 5489 = 1932
Choosing a method of subtraction (H)
50,000 - 47,895 = 2105 48,948 - 23,413 = 25,535 40,002 - 39,789 = 213
51,200 - 37,456 = 13,744 86,472 - 34,258 = 52,214 95,230 - 94,785 = 445
65,387 - 32,415 = 32,972 72,010 - 49,994 = 22,016 95,724 - 24,379 = 71,345
72,100 - 68,993 = 3107 45,383 - 21,876 = 23,507 56,011 - 55,795 = 216
34,123 - 27,832 = 6291 58,320 - 24,529 = 33,791 70,004 - 37,645 = 32,359
Choosing a method of subtraction (E)
7803 - 5420 = 2383 5674 - 2715 = 2959 7124 - 5463 = 1661
8009 - 3475 = 4534 9874 - 3250 = 6624 5237 - 4301 = 936
7025 - 6967 = 58 8150 - 6344 = 1806 6000 - 4372 = 1628
6005 - 5997 = 8 51,200 - 37,456 = 13,744 86,472 - 34,258 = 52,214
50,000 - 47,895 = 2105 48,948 - 23,413 = 25,535 40,002 - 39,789 = 213
Week 4:
Quadrilateral sorting tree
Multiplication table
x / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12
2 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / 20 / 22 / 24
3 / 3 / 6 / 9 / 12 / 15 / 18 / 21 / 24 / 27 / 30 / 33 / 36
4 / 4 / 8 / 12 / 16 / 20 / 24 / 28 / 32 / 36 / 40 / 44 / 48
5 / 5 / 10 / 15 / 20 / 25 / 30 / 35 / 40 / 45 / 50 / 55 / 60
6 / 6 / 12 / 18 / 24 / 30 / 36 / 42 / 48 / 54 / 60 / 66 / 72
7 / 7 / 14 / 21 / 28 / 35 / 42 / 49 / 56 / 63 / 70 / 77 / 84
8 / 8 / 16 / 24 / 32 / 40 / 48 / 56 / 64 / 72 / 80 / 88 / 96
9 / 9 / 18 / 27 / 36 / 45 / 54 / 63 / 72 / 81 / 90 / 99 / 108
10 / 10 / 20 / 30 / 40 / 50 / 60 / 70 / 80 / 90 / 100 / 110 / 120
11 / 11 / 22 / 33 / 44 / 55 / 66 / 77 / 88 / 99 / 110 / 121 / 132
12 / 12 / 24 / 36 / 48 / 60 / 72 / 84 / 96 / 108 / 120 / 132 / 144
Mystery angles
Week 5:
Common multiples
45 is a common multiple of 3, 5 and 9
56 is a common multiple of 3 and 5
28 is a common multiple of 2, 4 and 7
18 is a common multiple of 2, 3, 6 and 9
60 is a common multiple of 2, 3, 4, 5 and 6
54 is a common multiple of 2, 3, 6 and 9
35 is a common multiple of 5 and 7
80 is a common multiple of 2, 4, 5 and 8
16 is a common multiple of 2, 4 and 8
30 is a common multiple of 2, 3, 5 and 6
49 is a multiple of 7
63 is a common multiple of 3, 7 and 9
40 is a common multiple of 2, 4, 5 and 8
14 is a common multiple of 2 and 7
42 is a common multiple of 2, 3, 6 and 7
24 is a common multiple of 2, 3, 4, 6 and 8
15 is a common multiple of 3 and 5
72 is a common multiple of 2, 3, 4, 6, 8 and 9
36 is a common multiple of 2, 3, 4, 6 and 9
25 is a multiple of 5
32 is a common multiple of 2, 4 and 8
64 is a common multiple of 2, 4 and 8
28 is a common multiple of 2, 4 and 7
100 is a common multiple of 2, 4 and 5
21 is a common multiple of 3 and 7
12 is a common multiple of 2, 3, 4 and 6
48 is a common multiple of 2, 3, 4, 6 and 8
27 is a common multiple of 3 and 9
50 is a common multiple of 2 and 5
81 is a common multiple of 3 and 9
Comparing fractions
1. 1/2 and 2/5 = 5/10 and 4/10
2. 1/3 and 2/5 = 5/15 and 6/15
3. 2/3 and 4/5 = 10/15 and 12/15
4. 1/4 and 2/5 = 5/20 and 8/20
5. 3/4 and 4/5 = 15/20 and 16/20
6. 5/6 and 7/9 = 45/54 and 42/54 (15/18 and 14/18)
7. 5/6 and 3/4 = 20/24 and 18/24 (10/12 and 9/12)
8. 1/3 and 2/7 = 7/21 and 14/21
1. 1/5, 1/3, 4/15 = 3/15, 5/15, 4/15, therefore 1/5, 4/15, 1/3
2. 1/2, 2/3, 5/6 = 3/6, 4/6, 5/6, therefore 1/2, 2/3, 5/6
3. 1/2, 3/4, 2/3 = 6/12, 9/12, 8/12, therefore 1/2, 2/3, 3/4
4. 1/2, 4/5, 3/4 = 10/20, 16/20, 15/20, therefore 1/2, 3/4, 4/5
5. 1/2, 5/6, 7/9 = 9/18, 15/18, 14/18, therefore 1/2, 7/9, 5/6
Finding non-unit fractions of amounts (H)
1. 3⁄7 of 63 = 27
2. 7⁄8 of 64 = 56
3. 4⁄9 of 63 = 28
4. 3⁄5 of 175 = 105
5. 2⁄5 of 235 = 94
6. 5⁄6 of 144 = 120
7. 2⁄7 of 154 = 44
8. 2⁄3 of 192 = 128
9. 3⁄4 of 128 is 96
10. 2⁄3 of 81 is 54
11. 4⁄5 of 125 is 100
12. 5⁄6 of 132 is 110
Finding non-unit fractions of amounts (E)
1. 1⁄6 of 48 is 8
2. 5⁄6 of 48 is 40
3. 1⁄8 of 72 is 9
4. 5⁄8 of 72 is 45
5. 1⁄7 of 42 is 6
6. 4⁄7 of 42 is 24
7. 1⁄5 of 145 is 29
8. 3⁄5 of 145 is 87
9. 1⁄3 of 138 is 46
10. 2⁄3 of 138 is 92
11. 1⁄6 of 132 is 22
12. 5⁄6 of 132 is 110
Week 6:
Rounding 5-digit numbers
22,479 rounds to 22,000
24,235 rounds to 24,000
27,832 rounds to 28,000
45,506 rounds to 45,500
45,726 rounds to 45,700
45,273 rounds to 45,300
32,506 rounds to 32,510
32,499 rounds to 32,500
32,533 rounds to 32,530
Multiplying 4-digit numbers by 1-digit numbers
1. 3 x 2493 = 7479
2. 3 x 8241 = 24,723
3. 4 x 2854 = 11,416
4. 4 x 6178 = 24,712
5. 6 x 4728 = 28,368
6. 6 x 7236 = 43,416
7. 7 x 2143 = 15,001
8. 7 x 5942 = 41,594
9. 8 x 1487 = 11,896
10. 8 x 6048 = 48,384
Written multiplication (E)
1. 3 x 478 = 1434
2. 6 x 538 = 3228
3. 5 x 876 = 4380
4. 6 x 226 = 1356
5. 3 x 1242 = 3726
6. 4 x 2321 = 9284
7. 5 x 2014 = 10,070
8. 6 x 1157 = 6942
Oscar’s online gifts
Headphones 3 x £23.67 = £71.01
Cycling Computers 3 x £28.43 = £85.29
Hoodies 3 x £45.29 = £135.87
Smartphones 3 x £29.78 = £89.34
RC Helicopters 3 x £32.45 = £97.35
E.g. 3 x £26.37 = £79.11
Greta’s online gifts
Mobile Socks 3 x £6.43 = £19.29
Hats 3 x £8.24 = £24.72
Art Sets 3 x £4.65 = £13.95
Hoppers 3 x £7.24 = £21.72
Water Blasters 3 x £9.32 = £27.96
Kites 3 x £5.75 = £17.25
Week 7:
Rounding up and down (E)
1. 346 ÷ 4 = 86 r2 86 full cartons can be packed
2. 100 ÷ 7 = 14 r2 100 days is 14 weeks and 2 days
3. 135 ÷ 3 = 45 The plumber needs to order 45 lengths
4. 2m = 200cm, 200 ÷ 5 = 40 40 nails can be made
5. 427 ÷ 3 = 142 r1 The factory can cut 142 lengths
6. £365 ÷ 4 = £91.25 They each win £91 to the nearest pound