Maths Answers

Summer Year 6

Week 1

Ø Ordering fractions and decimals

1. 3/5 7/10 3/4 16/20

2. 1/4 3/8 1/2 9/16

3. 3/5, 2/3 and 7/12

4. 0.15, 0.51, 1.5, 5.01, 5.1, 15.0

5. 0.71 and 0.9

6. 0.3, 0.09, 0.55 and 0.12

7. 29.73

8. 51.37

Ø Ordering fractions and decimals H

1. 3/5 7/10 ¾ 16/20

2. ¼ 3/8 ½ 9/16

3. 3/5, 2/3 and 7/12

4. 0.15, 0.51, 1.5, 5.01, 5.1, 15.0

5. 0.71 and 0.9

6. 0.3, 0.09, 0.55 and 0.12

7. 29.73

8. 51.37

9. 1 2/3 and 1.6

Ø Ordering fractions and decimals E

1. 3/5 7/10 ¾ 16/20

2. ¼ 3/8 ½ 9/16

3. 3/5, 2/3 and 7/10

4. 0.15, 0.51, 1.5, 5.01, 5.1, 15.0

5. 0.71 and 0.9

6. 0.3, 0.09, 0.55 and 0.12

7. Examples: 23.79 < 23.97 79.23 <79.32 23.79 < 97.32

8. 51.37

Ø Ordering numbers

1. 734, 737, 743, 747, 773, 774

2. 395, 394, 359, 354, 349, 345

3. Example: 75 <79 30 > 12 9 > 6

4. Example: 335 > 239 76 < 79 9 > 7

5. 775 925

6. -5 35

Ø Ordering numbers E

1. 346

2. 437, 473, 477

3. 345, 349, 354, 359, 394, 395

4. Example: 25 < 73 40 > 15

5. Example: 335 > 239 46 < 75

Ø Squares, factors and multiples

1. 16 + 25 = 41

2. 1, 2, 5, 10

3. Example: 18, 48 A number that ends in a 3 is an odd number, there are no odd numbers which are multiples of 6

4. 296, 341, 726, 1001

5. Example: No It is true that when you multiply any number by two, the answer is always even, so any even numbers that you multiplied by two to get even numbers are even numbers when halved. The sequence of halving even numbers is odd, even, odd, even, odd, even, (e.g. halve 2, 4, 6, 8, 10, 12), etc.

Multiples of 7 / Not multiples of 7
Even / 42
14 / 24
36
Not even / 63
35 / 17
31

7. 72

8. 89

9. 665 Any sensible working

Ø Squares, factors and multiples E

1. 1, 4, 9, 16, 25, 36 16 + 25 = 41

2. 1, 2, 5 and 10 (any 2 of)

3. Example: 18, 48 Because a number ending in 3 will be odd and no odd number can be a multiple of 2.

4. 295, 305, 340, 725, 1000

5. No Example: It is true that when you multiply any number by two, the answer is always even, so any even numbers that you multiplied by two to get even numbers are even numbers when halved. The sequence of halving even numbers is odd, even, odd, even, odd, even, etc (e.g. halve 2, 4, 6, 8, 10, 12). Example, 4, 8, etc.

Multiples of 5 / Not multiples of 5
Even / 40
10 / 24
36
Not even / 65
35 / 17
31

7. 72

8. 89

Ø Reading scales

1. 750ml, 14 cups

2. 4.2m, 3.3m, 2.1m

3. 5 javelins, 3m, 7.5m

4. 13 degrees

6. 375g

Ø Reading scales E

1. 500ml, 750ml, 12 cups

2. 4.2m, 3.3m, 0.4m

3. 5 javelins, 3m, 7.5m

4. 13 degrees

6. 325g

Ø Reading timetables

1. 1h 35min, 1:40pm

3. 8:45am, 10:45am, 1h 15min

4. 10am, examples: because there are 60 min in an hour and 35 is more than half of 60, OR 9:35 is after 9:30 which is halfway between 9am and 10am.

5. 45min, 9:40

6. 1h 40min, 4:35pm

Ø Reading timetables E

1. 1h 35min, 1:45pm

3. 8:45am, 10:45am, 1h 15min

4. 10am, examples: because there are 60 min in an hour and 35 is more than half of 60, OR 9:35 is after 9:30 which is halfway between 9am and 10am.

5. 45min, 9:40am

6. 40min, 4:35pm

Week 2

Ø Addition

1. 1715 Examples: 1305 5 + 3 + 7 = 15

63 60 + 40 = 100

+ 347 1300 + 300 = 1600

1715 1715

1 1

2. 0.02 and 9.98

3. 45p = 20p + 20p + 5p

72p = 50p + 20p + 2p

26p = 20p + 5p + 1p

90p = 50p + 20p +20p

4. £31.50 Example: Ben collects £12

Jess collects £(12 - 4) = £8

Sapna collects £(8 + 3.50) = £11.50

5. 735 Example: 479

+ 256

120

600

735

6. £16.43 Examples: 11.95 £12 + £2.50 + £2.00 – 7p = £16.43

2.49

+ 1.99

220

1400

16.43

Ø Addition E

1. 1652 Examples: 1305 5 + 7 = 12

+ 347 0 + 40 = 40

1652 1300 + 300 = 1600

1 1652

2. 9.8 and 0.2

3. 45p = 20p + 20p + 5p

62p = 50p + 10p + 2p

12p = 5p + 5p + 1p

4. £31 Example: Ben collects £12

Jess collects £(12 - 4) = £8

Sapna collects £(8 + 3) = £11

5. 735 Example: 479

+ 256

120

600

735

6. £15.98 Examples: 11.50 £11.50 + £2.50 + £2.00 – 2p = £15.98

2.49

+ 1.99

180

1400

15.98

Ø Subtraction

1. £2.03 Example: Coins add up to £2.97

£5 - £2.97 = £2.03

2. 36.17 Example: 4.2 x 4.7 = 19.74

19.74 x 4.5 = 88.83

125 – 88.83 = 36.17

3. £4.51 £4.99 + 1p = £5

£10.50 + £5 = £15.50

£20 - £15.50 = £4.50

£4.50 + 1p = £4.51

4. 165 Example: 2009 - 1884

1844 + 6 = 1850

1850 + 50 = 1900

1900 + 100 = 2000

2000 + 9 = 2009

100 + 50 + 9 + 6 = 165

5. 3.66 Example: 8.79 + 0.01 = 8.8

8.8 + 0.2 = 9.0

9 + 3 = 12

12 + 0.45 = 12.45

3 + 0.45 + 0.2 + 0.01 = 3.66

Ø Finding a difference E

1. £2.03 Example: Coins add up to £2.97

£5 - £2.97 = £2.03

2. 35 Example: 20 x 4.5 = 90

125 – 90 = 35

3. £4.51 £4.99 + 1p = £5

£10.50 + £5 = £15.50

£20 - £15.50 = £4.50

£4.50 + 1p = £4.51

4. 22 Example: 2009 - 1987

1987 + 3 = 1990

1990 + 10 = 2000

2000 + 9 = 2009

10 + 9 + 3 = 22

5. 10.6 Example: 3.9 + 0.1 = 4

4 + 10 = 14

14 + 0.5 = 14.5

10 + 0.5 + 0.1 = 10 .6

Ø Find a mystery number

1. 52 + 25 = 77 72 – 47 = 25

2. 20p Example: 2 pens = £2, so 1 pen = £1

Pen + pencil = £1.20

£1.20 - £1 = 20p

3. Lin has 9, Chan has 7 stickers Example: 16 – 2 = 14

14 ÷ 2 = 7

7 + 2 = 9

7 + 9 = 16

4. Gurpit had £6.00, Sapna had £6.50 Example: If same £12.50 ÷ 2 = £6.25

Sapna gave Gurpti 25p, so

Sapna had £6.25 + 25p = £6.50

And Gurpti had £6.25 – 25p = £6.00

5. Largest m + n = 29 + 19 = 48

Smallest m + n = 21 + 11 = 32

Ø Find a mystery number E

1. Wide variety of answers possible

2. 50p Example: 2 pens = £2, so 1 pen = £1

Pen + pencil = £1.50

£1.50 - £1 = 50p

3. Lin has 9, Chan has 7 stickers Example: 16 – 2 = 14

14 ÷ 2 = 7

7 + 2 = 9

7 + 9 = 16

4. Gurpit had £5.50, Sapna had £6.50 Example: If same £12 ÷ 2 = £6

Sapna gave Gurpti 50p, so

Sapna had £6 + 50p = £6.50

And Gurpti had £6 – 50p = £5.50

5. Largest m + n = 29 + 19 = 48

Smallest m + n = 21 + 11 = 32

Ø Angles and rotations

1. 3 x 90º = 270º

3. x, a, x

6. 180º- 40º = 140º, 140º ÷ 2 = 70º, so a = 70º

Ø Angles and rotations E

2. 2 x 90º = 180º

3. x, a, x

Ø Shape and symmetry

1. Pentagons – c, d, e

Right angles – three of a, d, e or f

3. b, c, d

6. a, c

Shape / Number of flat surfaces / Number of curved surfaces
cone / 1 / 1
cylinder / 2 / 1
cuboid / 6 / 0
pyramid / 5 / 0

Week 3

Ø Interpreting graphs

1. Swimming

Playing computer games, Reading

2. 15cm

15 seconds (quarter of a minute)

3. 50, 275, 875

4. 5

Sunday, Tuesday, Thursday

5. x, a, x, x

6. 60

Yes, an explanation example: The total number of children at Hamilton School is 230. 135 chose milk chocolate. 115 is half of 230. 135 is more than 135.

Ø Interpreting graphs E

1. 4

Dog

3. 5

Sunday, Tuesday, Thursday

4. 350

250

5. 20

Ø Multiplication

1. £4.10 Example: 4 x 60p = 240p

2 x 85p = 170p

410p

£7.90 Example: 10 x 85p = 850p

850 – 60p = 790p

2. 5291 Example:

3700

1480

+ 111

5291

3. 7 Example: 4 lots of 25 = 100

3 lots of 25 = 75

4. 31 Example: 999 is the largest 3-digit number

225 is about a quarter of 1000 (999 + 1)

So a number twice as big (and therefore 4 [2 x 2] times as large when multiplied should be about the largest. Try 30 (30 x 30 = 900), then 31 (31 x 31 = 961) and 32 (32 x 32 = 1024)

5. 8.82

6. 360 Example: 10 x 6 = 60 90 x 4 = 360

5 x 6 = 30

x / 30 / 7
100 / 3000 / 700 / 3700
40 / 1200 / 280 / 1480
3 / 90 / 21 / 111

7. £3.95 Example: 3 x 60 = 180, 180 – 3 = 177

2 x 110 = 220, 220 – 2 = 218

177

+ 218

300

395

8. £5 Example: 40 x 10 = 400

20 x 5 = 100

500p

9. 271.8 Example: 40 x 6 = 240

5 x 6 = 30

0.3 x 6 = 1.8

271.8

Ø Multiplication E

1. £2.60 Example: 4 x 40p = 160p

2 x 50p = 100p

260p

£4.40 Example: 10 x 50p = 500p

500 – 60p = 440p

2. 858 Example: 100 x 6 = 600

40 x 6 = 240

3 x 6 = 18

858

3. 9 Example: 4 lots of 25 = 100

so 8 lots of 25 = 200

1 lot of 25 = 25

8 + 1 = 9

4. 31 Example: 999 is the largest 3-digit number

225 is about a quarter of 1000 (999 + 1)

So a number twice as big (and therefore 4 [2 x 2] times as large when multiplied should be about the largest. Try 30 (30 x 30 = 900), then 31 (31 x 31 = 961) and 32 (32 x 32 = 1024)

5. 8.82

6. 360 Example: 10 x 6 = 60 90 x 4 = 360

5 x 6 = 30

7. £3.95 Example: 3 x 60 = 180, 180 – 3 = 177

2 x 110 = 220, 220 – 2 = 218

177

+ 218

300

395

8. £2.50 Example: 20 x 10 = 200

10 x 5 = 50

250p

9. 271.8 Example: 40 x 6 = 240

5 x 6 = 30

0.3 x 6 = 1.8

271.8

Ø Division

1. 19 Example: 10 lots of 4 = 40

9 lots of 4 = 36

40 + 36 = 76

2. 8 packs Example: 7 lots of 4 = 28 (not enough)

8 lots of 4 = 32 (2 left over)

3. 29r14 Example: 10 lots of 17 = 170

20 lots of 17 = 340

30 lots of 17 = 510

29 lots of 17 = 510 – 17 = 493

507 – 493 = 14

4. 9 Example: small yoghurts 4 lots of 25p = £1, so 20 lots of 25p = £5 (20)

large yoghurts 10 lots of 45p = £4.50, 1 lot of 45p = 45p, so 11 lots

of 45p = £4.95 (11)

20 – 11 = 9

5. 12 books Example: 10 lots of 6 = 60

2 lots of 6 = 12

72 stamps

10 + 2 = 12 books

6. 52 Example: 10 lots of 7 = 70

20 lots of 7 = 140

30 lots of 7 = 210

40 lots of 7 = 280

50 lots of 7 = 350

2 lots of 7 = 14, so 52 lots of 7 = 350 + 14 = 364

Ø Division E

1. 21 Example: 10 lots of 4 = 40

20 lots of 4 = 80

1 lot of 4 = 4, so 21 lots of 4 = 84

2. 8 packs Example: 7 lots of 4 = 28 (not enough)

8 lots of 4 = 32 (2 left over)

3. 25 Example: 10 lots of 20 = 200

20 lots of 20 = 400

5 lots of 20 = 100, so 25 lots of 20 = 500

4. 10 Example: small yoghurts 4 lots of 25p = £1, so 20 lots of 25p = £5 (20)

large yoghurts 10 lots of 50p = £5 (10), 20 – 10 =10

5. 12 books Example: 10 lots of 6 = 60

2 lots of 6 = 12

72 stamps

10 + 2 = 12 books

6. 32r4 Example: 10 lots of 5 = 50

20 lots of 5 = 100

30 lots of 5 = 150

2 lots of 5 = 10, so 32 lots of 5 = 150 + 10 = 160

164 – 160 = 4

Ø Find a mystery number

1. 45 x 52 = 2340

2. 23 x 4 = 92

3. 7.8 and 9.3

4. 6cm Example: Area = width x length

90 = 15 x length

2 lots of 15 = 30

4 lots of 15 = 60

6 lots of 15 = 90

5. 24 Example: 19 x 2 = 38

38 – 14 = 24

6. Smallest number: m x n = (11 x 6) = 66

Largest number: m x n = (19 x 9) = 171

7. 20 Example: 24 + 6 = 30

30 ÷ 3 = 10

10 x 2 = 20

Ø Find a mystery number E

1. 42 x 43 = 1806

2. 23 x 3 = 69

3. 7.8 and 9.3

4. 6cm Example: Area = width x length

60 = 10 x length

6 lots of 10 = 60

5. 30 Example: 24 x 2 = 48

48 – 18 = 30

6. Smallest number: m x n = (11 x 6) = 66

Largest number: m x n = (19 x 9) = 171

7. 60 Example: 24 + 6 = 30

30 x 2 = 60

Ø Word problems

1. £1.53 Example: 128 ÷ 2 = 64

64 + 89 = 153

2. 3 apples Example: 1 + 1 + 10 = 12 pieces of fruit for each banana

3 lots of 12 = 36, so 3 bananas, 3 apples and 30 strawberries are used