Maths Answers
Summer Year 5
Week 1
Ø Temperature
1. Thursday
2. Tuesday
3. 8°C
4. 5°C
5. 6°C
6. 7°C
7. 13°C
Ø Temperature E
Marking the thermometer:
Temperature drops:
Monday 8°C
Tuesday 9°C
Wednesday 7°C
Thursday 8°C
Friday 5°C
Ø Entering calculations into the calculator
1. 58 x 6 – 12 – 9 – 3 = 324
2. (4.2 x 2.9) x (24.99 + 3.99)
24.99 + 3.99 = 28.98, 4.2 x 2.9 = 12.18, 28.98 x 12.18 = £352.98 (352.9764)
3. ((24.99 x 6) + (£15.75 x 12) + 65.90) ÷ 12
24.99 x 6 = 149.94, 15.75 x 12 = 189, 149.94 + 189 + 65.90 = 404.84 404.84 ÷ 12 = £33.74 (33.73666)
4. £59 – (£16.75 + (£7.50 x 4))
4 x 7.50 = 30, 30 + 16.75 = 46.75, 59 – 46.75 = £12.25
5. (£24.97 + £9.68 + £12.65) ÷ 2
24.97 + 9.68 + 12.65 = 47.30, 47.30 ÷ 2 = Each family will pay £23.65
(£24.97 + £9.68) - £12.65
24.97 + 9.68 = 34.65, 34.65 – 12.65 = 22, 22 ÷ 2 = The second family should give £11.00 to the first family
Ø Entering calculations into the calculator E
1. 58 x 6 – 12 – 9 = 327
2. (4.2 x 2.9) x 24.99
4.2 x 2.9 = 12.18, 24.99 x 12.18 = £304.38 (304.3782)
3. (24.99 ÷ 2) + 15.75
24.99 ÷ 2 = 12.495, 15.75 + 12.495 = £28.25 (28.245)
4. 59 – (7.50 x 6)
6 x 7.50 = 45, 59 – 45 = £14
5. (24.97 + 12.65) ÷ 2
24.97 + 12.65 = 37.62, 37.62 ÷ 2 = £18.81
Week 2
Ø Multiplying and dividing by 10
72 x 10 = 720 x 10 = 7200
523 x 10 = 5230 x 10 = 52300
523 ÷ 10 = 52.3 ÷ 10 = 5.23
72 ÷ 10 = 7.2 ÷ 10 = 0.72
56 x 10 = 560 x 10 = 5600
547 ÷ 10 = 54.7 ÷ 10 = 5.47
Ø Multiplying and dividing by 10 H
72 x 10 = 720 x 10 = 7200
523 x 10 = 5230 x 10 = 52300
523 ÷ 10 = 52.3 ÷ 10 = 5.23
720 ÷ 10 = 72 ÷ 10 = 7.2
56 x 10 = 560 x 10 = 5600
5470 ÷ 10 = 547 ÷ 10 = 54.7
Ø Multiplying and dividing by 100
7 x 100 = 700 x 100 = 70000
23 x 100 = 2300 x 100 = 230000
5200 ÷ 100 = 52 ÷ 100 = 0.52
7250 ÷ 100 = 72.5 ÷ 100 = 0.725
5 x 100 = 500 x 100 = 50000
5400 ÷ 100 = 54 ÷ 100 = 0.54
Ø Multiplying and dividing by 100 H
23 x 100 = 2300 x 100 = 230000
7 x 100 = 700 x 100 = 70000
7250 ÷ 100 = 72.5 ÷ 100 = 0.725
5300 ÷ 100 = 53 ÷ 100 = 0.53
0.0005 x 100 = 0.05 x 100 = 5
5400 ÷ 100 = 54 ÷ 100 = 0.54
Ø Chef’s Information
100 boxes of duck eggs at £2 each - £200
100 portions of salmon at £4 each - £400
100 large boxes of oyster mushrooms at £12 each - £1200
100 bottles of champagne at £23 each - £2300
100 litres of Devon cream at £3 each - £300
100 kilograms of butter £1.50 per kilogram - £150
Ø Multiplying and dividing by 10 and 100
Example answers:
435 ÷ 10 = 43.5 435 ÷ 100 = 4.35 435 ÷ 100 = 4.35
43.5 ÷ 10 = 4.35 4.35 x 10 = 43.5 4.35 x 10 = 43.5
4.35 x 100 = 435 43.5 x 100 = 4350 43.5 x 10 = 435
435 ÷ 100 = 4.35 4350 ÷ 100 = 43.5 435 ÷ 100 = 4.35
4.35 x 10 = 43.5 END 43.5 x 10 = 435 END 4.35 x 10 = 43.5 END
435 ÷ 100 = 4.35 435 ÷ 10 = 43.5 435 ÷ 10 = 43.5
4.35 x 10 = 43.5 43.5 x 10 = 435 43.5 x 10 = 435
43.5 ÷ 10 = 4.35 435 x 100 = 43500 435 x 100 = 43500
4.35 ÷ 10 = 0.435 43500 ÷ 10 = 4350 43500 ÷ 100 = 435
0.435 x 10 = 4.35 4350 x 10 = 43500 END 435 x 10 = 4350 END
4.35 ÷ 10 = 0.435
0.435 x 10 = 4.35 END
435 ÷ 100 = 4.35
4.35 x 10 = 43.5
43.5 ÷ 10 = 4.35
4.35 ÷ 10 = 0.435
0.435 x 10 = 4.35
4.35 ÷ 10 = 0.435
0.435 x 10 = 4.35
4.35 ÷ 100 = 0.0435
0.0435 x 10 = 0.435 END
Ø Common multiples
(factors from 2 to 9 only, * not very useful)
45 is a common multiple of: 3, 5 and 9
56 is a common multiple of: 2, 4, 7 and 8
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 common 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 common 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
Week 3
Ø Using the grid method
32 x 27
x / 30 / 220 / 600 / 40 / 640
7 / 210 / 14 / 224
864
52 x 24
x / 50 / 220 / 1000 / 40 / 1040
4 / 200 / 8 / 208
1248
34 x 48
x / 40 / 830 / 1200 / 240 / 1440
4 / 160 / 32 / 193
1633
75 x 32
x / 70 / 530 / 2100 / 150 / 2250
2 / 140 / 10 / 150
2400
45 x 45
x / 40 / 540 / 1600 / 200 / 1800
5 / 200 / 25 / 225
2025
42 x 68
x / 40 / 260 / 2400 / 120 / 2520
8 / 320 / 16 / 336
2856
Week 4
Ø Reading timetables
1. Jackie’s next train is at 14:45 from London Paddington and she will arrive in Reading
at 15:11.
2. Sandip needs to catch the 15:13 train from Swindon.
3. Billy needs to catch the 14:41 train from Reading.
4. It takes 26 min to travel by train from London to Reading.
5. The shortest journey is from Reading to Didcot Parkway, which takes 15 min.
6. It takes 1h 22min to travel from London to Bristol Parkway when the train does not
stop at Didcot Parkway.
7. It takes 3 min longer when the train does stop at Didcot Parkway.
8. Various answers.
Week 5
Ø Equivalent percentages
Swimming 50%
Cycling 25%
Football 25%
Bananas 40%
Apples 30%
Oranges 30%
Dogs 50%
Cats 30%
Rabbits 20%
Ø Equivalent percentages H
Swimming 50%
Cycling 30%
Football 20%
Bananas 40%
Apples 30%
Oranges 30%
Dogs 50%
Cats 20%
Rabbits 30%
Ø Comparing percentages
Burley Common: 50 oak, 20 ash, 15 beech, 15 willow trees
Merttens Meadow: 30 oak, 30 hazel, 60 willow, 30 beech trees
Chidgey Common: 80 oak, 60 beech, 20 ash, 40 sweet chestnut trees
Holes Hollow: 30 oak, 12 hazel, 18 willow, 36 beech, 24 ash trees
Oak = Chidgey Common
Ash = Holes Hollow
Beech = Chidgey Common
Willow = Merttens Meadow
Hazel = Merttens Meadow
Sweet Chestnut = Chidgey Common
Ø Comparing percentages E
Burley Common: 50 oak, 20 ash, 15 beech, 15 willow trees
Merttens Meadow: 60 oak, 60 hazel, 120 willow, 60 beech trees
Chidgey Common: 80 oak, 60 beech, 20 ash, 40 sweet chestnut trees
Holes Hollow: 50 oak, 20 hazel, 40 willow, 30 beech, 60 ash trees
Oak = Chidgey Common
Ash = Holes Hollow
Beech = Chidgey Common
Willow = Merttens Meadow
Hazel = Merttens Meadow
Sweet Chestnut = Chidgey Common
Ø Ratio and proportion
1/3
3/4
2/5
There are four blue squares for every one red (4 to 1)
There are three red squares for every one blue (3 to 1)
There are two blue squares for every one red (2 to 1)
Ø Ratio, proportion and percentages
Total number of children / Cycling / Swimming / Ratio of cyclingto swimming
10 / 50%
5 children / 50%
5 children / 1 to 1
10 / 3/10
3 children / 7/10
7 children / 3 to 7
20 / ¾
15 children / ¼
5 children / 3 to 1
20 / 80%
16 children / 20%
4 children / 4 to 1
30 / 2/3
20 children / 1/3
10 children / 2 to 1
40 / 75%
30 children / 25%
10 children / 3 to 1
Ø Ratio, proportion and percentages E
Total number of children / Cycling / Swimming / Ratio of cycling to swimming10 / 50%
5 children / 50%
5 children / 1 to 1
10 / 3/10
3 children / 7/10
7 children / 3 to 7
20 / ¾
15 children / ¼
5 children / 3 to 1
20 / 80%
16 children / 20%
4 children / 4 to 1
30 / 2/3
20 children / 1/3
10 children / 2 to 1
40 / 75%
30 children / 25%
10 children / 3 to 1
Week 7
Ø Multiplication digital root circles
Week 9
Ø Finding a difference
4GB memory stick 0.51 + 2.00 + 0.25 = £2.76
Battery recharger 0.01 – 3.00 + 0.49 = -£2.50 £2.50
£13.00 - £10.50 - 1p + 1p = £2.50
100 Blank CDs 0.01 + 2.00 + 0.75 = £2.76
£21.75 - £19.00 + 1p = £2.76
Walkie talkies 0.21 – 6.00 + 0.25 = -£5.54 £5.54
Headphones 0.11 + 4.00 + 0.49 = £4.60
External 320GB hard drive 0.25 + 17.00 + 0.49 = £17.74
Greatest difference External 320GB hard drive
Least difference Battery recharger
One shop www.techy.co.uk
Ø Finding a difference E
4GB memory stick 0.51 + 0.25 = 76p
Battery recharger 0.51 – 3.00 + 0.99 = -£1.50 £1.50
£12.49 - £11.00 + 1p = £1.50
100 Blank CDs 0.01 + 1.00 + 0.75 = £1.76
£20.75 - £19.00 + 1p = £1.76
Walkie talkies 0.75 – 6.00 + 0.79 = -£4.46 £4.46
Headphones 0.01 + 4.00 + 0.49 = £4.50
£32.49 - £28.00 + 1p = £4.50
External 320GB hard drive 0.25 + 7.00 + 0.49 = £7.74
Greatest difference External 320GB hard drive
Least difference 4GB memory stick
One shop www.techy.co.uk
Ø Athletic differences
Javelin 0.3 + 1 + 0.2 = 1.5m
Long jump 0.03 + 0.1 + 0.04 = 0.17m
Standing jump 0.05 + 0.2 + 0.06 = 0.31m
High jump 0.07 + 0.1 + 0.08 = 0.25m
100m -0.7 -0.02 = -0.9s 0.9s
200m – 0.4 -1 – 0.2 = -1.6 1.6s
Ø Athletic differences E
Javelin 0.3 + 0.2 = 0.5m
Long jump 0.03 + 0.04 = 0.07m
Standing jump 0.05 + 0.2 + 0.02 = 0.27m
High jump 0.01 + 0.1 + 0.03 = 0.14m
100m -0.2 -0.2 = -0.4s 0.4s
200m – 0.4 – 0.1 = -0.5 0.5s
Week 11
Ø Solving word problems (* choose to use calculator)
1. *24 x 2.272 = 54.528, 3 x 4.544 = 13.632, 13.632 + 54.528 = 68.16 litres
2. 23.50 ÷ 2 = 11.75, 23.50 x 2 = 47, 23.50 + 11.75 + 47 = £82.25
3. ¼ of 120 is 30, 30 ÷ 2 = 15 books about cars
4. *6.32 x 3.86 = 24.40, 5.69 x 4.72 = 26.86 So the second classroom has the biggest floor area
5. 42 ÷ 6 = 7, 7 + 12 = 19 She will have packed 19 boxes when she’s finished 19 x 6 = (20 x 6) – 6 = 120 – 6 = 114 eggs packed
6. (10 x 3) + (50 x 2) + (30 x 1) = 30 + 100 + 30 = 160 lambs
Ø Solving word problems E (* choose to use calculator)
1. *4 x 2.272 = 9.088, 4 x 4.544 = 18.176, 9.088 + 18.176 = 27.26 litres
2. 24.80 ÷ 2 = 12.40, 24.80 x 2 = 49.60, 24.80 + 12.40 + 49.60 = £86.80
3. ¼ of 80 is 20, 20 ÷ 2 = 10 books about cars
4. *6.32 x 3.86 = 24.40, 5.69 x 4.72 = 26.86 So the second classroom has the biggest floor area
5. 24 ÷ 6 = 4, 4 + 10 = 14 She will have packed 14 boxes when she’s finished 14 x 6 = (10 x 6) + (4 x 6) = 60 + 24 = 84 eggs packed
6. (25 x 3) + (50 x 2) + (25 x 1) = 75 + 100 + 25 = 200 lambs
Ø Counting triangles
9 and 10 triangles
Ø Counting triangles H
18 and 21 triangles
Week 12
Ø Comparing percentages
1. 10% of £45 = £4.50 20% of £30 = £6.00
2. 25% of 84m = 21m 50% of 50m = 25m
3. 10% of 250ml = 25ml 1% of 2000ml = 20ml
4. 10% of £320 = £32.00 25% of £1200 = £300.00
5. 50% of 426m = 213m 10% of 2500m = 250m
6. Bike 1 has been reduced by the most money (£25.00 as opposed to £20.00) The new prices are £225.00 for Bike 1 and £380.00 for Bike 2
7. Mike made a profit of £180.00 on the Ford, he lost £125.00 on the Peugeot so overall, he made a profit of £55.00
Ø Comparing percentages H
1. 10% of £45 = £4.50 20% of £30 = £6.00
2. 25% of 84m = 21m 50% of 50m = 25m
3. 10% of 250ml = 25ml 1% of 2l = 20ml
4. 10% of £320 = £32.00 25% of £1200 = £300.00
5. 50% of 426m = 213m 10% of 2km = 200m
6. Bike 1 has been reduced by the most money (£24.90 as opposed to £21.00) The new prices are £224.10 for Bike 1 and £399.00 for Bike 2