Numeracy Support Booklet
2015 / 16
Numeracy
Page 1
Royds School
Contents
Skill
Page
Basic Calculations
Addition
Subtraction
Multiplication
Division
Involving Decimals
2
2
2
3
3
Simple Fractions
3
Simple Percentages
4
Simple Decimals
4
Metric Measure
5
Metric Weight
5
Rounding
6
Squares, Square Roots and Powers
6
BODMAS
6
Data Handling
7
Line Graphs
7
Weekly Numeracy Exercises
8 – 25
Numeracy
Page 2
Royds School
Numeracy – Support Booklet
Addition
364 + 278
3842 + 905
36472 + 87 + 758 + 9086
3 6 4
3 8 4 2
3 6 4 7
8
7 5
9 0 8
+
+ 2 7 8
+
9 0 5
6 4 2
4 7 4 7
1
1
1
2
7
8
6
4 6 4 0 3
1
1
3
2
Subtraction
92 – 38
3708 – 526
1
8
8026 – 345
9
7 1
1
6
1
9 2
– 3 8
3 7 0 8
5 2 6
–
8 0 2 6
–
3 4 5
5 4
3 1 8 2
7 6 8 1
Multiplication
694 × 4
157 × 93
592 × 836
6 9 4
×
4
1 5 7
×
9 3
2 7 7 6
4 7 1
5 6
1 4 1 3 0
2
3
1
1
2
1 4 6 0 1
5 9 2
× 8 3 6
5
4 9 4 9 1 2
1
1
Numeracy
1
325 5 2
1 7 7 6 0
7 1
4 7 3 6 0 0
Page 3
1
1
Royds School
Division
564 ÷ 3
32592 ÷ 7
1 8 8
3
2
2
5 6 4
749 ÷ 4
0 4 6 5 6
7
3
4
No Remainders
Add decimal point
and zeros
3
4
3 2 5 9 2
1 8 7. 2 5
4
3
2
1
2
7 4 9. 0 0
Decimals
29.1 + 6 + 104. 42
HTU . t h
+
2 9 . 1
6
1 0 4 . 4 2
30.6 – 9.58
2
1
5
53.28 × 9
1
3 0 . 6 0
–
9 . 5 8
5 3. 2 8
×
9
2 1 . 0 2
4 7 9. 5 2
2
1 3 9 . 5 2
2
7
1
Simple Fractions
1
of £20
4
2
of £35
5
5
of £18
6
One quarter → 20  4 = 5
One fifth → 35  5 = 7
Two fifths → 2  7 = £14
One sixth → 18  6 = 3
Five sixths → 5  3 = £15
Numeracy
Page 4
Royds School
Simple Percentages
50% 
1
2
25% 
1
4
75% 
3
4
10% 
1
10
20% 
1
5
40% 
2
5
50% of 30 = 15
25% of 20 = 5
40% of 30 = 12
60% of £60
45% of £80
34% of £90
10% = 6
60% = £36
10%
40%
5%
45%
10%
30%
1%
4%
34%
=8
= 32
=4
= £36
=9
= 27
= 0.90
= 3.60
= £30.60
Simple Decimals (tens, hundreds, thousands)
TH
H
T
U • t
h
th
tth
× 10
2 • 7
2
2.7 × 10 = 27
7 ••
TH
H
T
U
0
0.901 ÷ 10 = 0.0901
TH
H
T
U
4
6
0
4
t
0
h
•
•
th
•
•
•
t
h
th
9
0
1
0
9
0
tth
÷ 10
1
tth
÷ 100
460 ÷ 100 = 4.6
6
•
TH
H
T
U
0
0.056 × 10 000 = 560
Numeracy
5
6
0
•
t
h
th
0
5
6
tth
× 10 000
•
•
Page 5
Royds School
Metric Measure
1000
km
100
m
1000
10
cm
100
3km → m
750 cm → m
3 × 1000 = 3000 m
750 ÷ 100 = 7.5 m
mm
10
67mm → m
67 ÷ 10 ÷ 100 = 0.067 m
or
67 ÷ 10 = 6.7 cm
6.7 ÷ 100 = 0.067 m
Metric Weight
1000
tonnes
1000
kg
1000
1000
g
1000
mg
1000
5 tonnes → kg
8.7 kg → g
80 900 000mg → kg
5 × 1 000 = 5 000 kg
8.7 × 1 000 = 8 700 g
80 900 000 ÷ 1 000 ÷ 1 000 = 80.9 mg
or
Numeracy
Page 6
80 900 000 ÷ 1 000 = 80 900 g
80 900 ÷ 1 000 = 80.9 mg
Royds School
Working with Multiples of Ten
1.
348 × 30
2.
5430 ÷ 30
Step 1: Find 348 × 3
Step 1: Find 5430 ÷ 10
5430 ÷ 10 = 543
348
3
Step 2: Now do 543 ÷ 3
1044
181
3 543
Step 2: Now do 1044 × 10
1044 × 10 = 10 440
So, 5430 ÷ 30 = 181
So, 348 × 30 = 10 440
Rounding Decimals
1.
Round the following to 1 decimal place
a.
2.
3.42  3.4
b.
93.5821  93.6
c.
9.95  10.0
Round the following to the nearest penny (two decimal places)
a.
£5.229  £5.23
b.
£10.374  £10.37
c.
£0.025231  £0.03 or 3p
Squares, Square Roots and Powers
32 = 3 × 3 = 9
9 =3
Numeracy
52 = 5 × 5 = 25
25 = 5
Page 7
92 = 9 × 9 = 81
81 = 9
Royds School
43 = 4 × 4 × 4 = 64
3
35 = 3 × 3 × 3 × 3 × 3 = 243
64  4
BODMAS
When carrying out a calculation we give priority to certain operations. For example, on your
calculator type 5 + 2  3. Older calculators will give the answer 21, while newer calculators
give the correct answer of 11. This is because multiplication gets priority before addition. The
complete order is:
Brackets, Others, Division and Multiplication, Addition and Subtraction
a.
3+42
=3+8
= 11
b.
3 + 8  4  1 c.
=3+2–1
=4
27  32 + 2 d. 4  (7 – 5) + 3
= 27  9 + 2
=42+3
=3+2
=8+3
=5
= 11
Basic Data Handling
Recall
E.g
MEAN:
MEDIAN:
MODE:
RANGE:
Add up and divide by the number of results
The middle entry (or entries) of an ordered set of results
The most frequent entry, the one that appears the most
The spread of results, highest subtract lowest
Find the mean, median, mode and range of the following temperatures
22C, 24C, 22C, 18C, 25C, 26C, 25C, 22C
Mean :
(22  22  ...  22)
184
=
= 23C
8
8
Median : order
18C, 22C, 22C, 22C, 24C, 25C, 25C, 26C
=
(22  24)
= 23C
2
Mode :
Most common = 22C
Range :
26 – 18 = 8C
Numeracy
Page 8
Royds School
Line Graphs
Time
Temperature (C)
8am
14
10am
16
12pm
22
2pm
25
4pm
20
6pm
17
Class Temperature
30
Temperature (C)
25
x
x
20
x
x
x
15
x
10
10.30
13.00
15.30
18.00
20.30
Time (s)
Numeracy
Page 9
Royds School
Exercise 1
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
43 + 27
1.
408 + 78
1.
8948 + 983
2.
78 + 29
2.
69 + 8326
2.
84926 + 5978
3.
785 – 63
3.
374 – 158
3.
74926 – 4809
4.
52 – 18
4.
4264 – 273
4.
800371 – 737
5.
74 × 3
5.
746 × 5
5.
71342 × 8
6.
147 × 4
6.
2156 × 7
6.
837 × 47
Numeracy
Page 10
Royds School
Exercise 2
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
83 – 47
1.
815 – 342
1.
7082 – 4258
2.
73 × 5
2.
469 × 6
2.
485 × 27
3.
414 ÷ 3
3.
2106 ÷ 6
3.
61144 ÷ 8
4.
984 ÷ 4
4.
2156 ÷ 7
4.
36837 ÷ 5
5.
73.1 + 4.8
5.
59.39 + 104.2
5.
58.3 ÷ 4
6.
46.3 – 13.8
6.
81.4 – 37.36
6.
802.1 – 4.82 + 9
Numeracy
Page 11
Royds School
Exercise 3
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
584 – 108
1.
8153 × 7
1.
467 × 458
2.
1
2
of
£30
2.
1
6
of
£54
2.
2
of
3
£120
3.
1
4
of
£28
3.
1
of
5
£40
3.
3
7
£56
4.
1
of
5
£40
4.
3
4
of
£40
4.
7
of
12
5.
3
of
5
£10
5.
5
of
8
£24
5.
6.
50% of £8
6.
25% of £20
Numeracy
Page 12
6.
of
4
5
of
£48
£6
75% of £200
Royds School
Exercise 4
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
25% of £20
1.
20% of £20
1.
40% of £40
2.
10% of £70
2.
30% of £70
2.
35% of £40
3.
10% of £90
3.
70% of £30
3.
45% of £30
4.
20% of £50
4.
15% of £60
4.
12.5% of £80
5.
30% of £120
5.
65% of £40
5.
55% of £ 70
6.
2.7 × 10
6.
4.2 × 100
6.
4.8 ÷ 10
Numeracy
Page 13
Royds School
Exercise 5
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
30% of £60
2.
840 ÷ 100
2.
3.1 ÷ 100
2.
0.0803 × 1000
3.
3.5 × 10
3.
0.32 × 100
3.
0.024 ÷ 100
4.
4km → m
4.
500cm → m
4.
3.7km → m
5.
6g → mg
5.
400mg → g
5.
0.702kg → g
6.
90mm→ cm
6.
850cm → m
6.
122km → cm
7.
8000cm → m
7.
2080m → km
7.
703mm → cm
8.
1.2km → m
8.
401cm → m
8.
4.09km → m
9.
8.3tonnes → kg
9.
14mg → g
9.
10g → kg
10.
0.2m → cm
10.
0.5mm → cm
10.
0.601mg → g
Numeracy
1.
35% of £40
Page 14
1.
42% of £60
Royds School
Exercise 6
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
349 – 65
1.
4629 × 8
1.
3629 × 285
2.
4.58 + 9.6
2.
3800201 – 62894
2.
28746.91 ÷ 5
3.
8.52 × 10
3.
0.92 ÷ 100
3.
0.024 × 100000
4.
30 × 40
4.
300 × 70
4.
3.4 × 200
5.
1
4
£12
5.
2
5
5.
3
of
8
6.
20km→ m
6.
4200m → km
6.
522m → km
7.
8000cm → m
7.
480m → km
7.
9mm → cm
8.
6.4g → mg
8.
2608cm → m
8.
5.0903kg → mg
9.
2.3mm → cm
9.
940kg → g
9.
10.002cm → mm
Numeracy
of
of
£35
Page 15
£56
Royds School
10.
0.5m → cm
Numeracy
10.
10.4m → cm
Page 16
10.
0.601m → km
Royds School
Exercise 7
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
Round each of the following to the nearest penny.
1.
13.2p 
1.
58.6p 
1.
34.5p 
2.
17.6p 
2.
19.5p 
2.
69.9p 
3.
28.5p 
3.
£6.274 
3.
£43.324 
4.
£20.057 
4.
£13.4723 
4.
£6.1491 
5.
£28.395 
5.
£89.5378p 
5.
£25.99521 
Carry out each these mental calculations involving money.
6.
£2.40 + £3.10 + £1
6.
£7.80 – £2.30
6.
£6.60 + £3.40
7.
£3.90 + £4.60
7.
£22.30  £1.40
7.
£19.00 + £16.40
8.
£10  £4.60
8.
£3.78 + £ 4.90 + £0.31
8.
£22  £2.30  £2
9.
£20 – 6.50
9.
£100 – 5.20
9.
£4.99 × 3
Numeracy
Page 17
Royds School
10.
£50 – £19.99
Numeracy
10.
£100 – 54.99
Page 18
10.
£100 – £0.99
Royds School
Exercise 8
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
Round each of the following to the nearest penny.
1.
39.2p 
1.
28.7p 
1.
39.5p 
2.
86.3p 
2.
11.4p 
2.
99.9p 
3.
28.7p 
3.
£9.636 
3.
£43.028 
Evaluate each of the following.
4.
42 =
4.
72 =
4.
122 =
5.
92 =
5.
22 =
5.
162 =
6.
16 =
6.
81 =
6.
100 =
7.
64 =
7.
121 =
7.
169 =
8.
23 =
8.
43 =
8.
25 =
9.
33 =
9.
34 =
9.
19 =
10.
625
can you arrange 8
10.
can you arrange 50
10.
£1 coins into a square?
£1 coins into a square?
£1 coins into a square?
Numeracy
Page 19
can you arrange
Royds School
Challenge ???
Numeracy
3
125 
Page 20
Royds School
Exercise 9
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
2+43
1.
62+5
1.
2+45–1
2.
9–32
2.
8 + 10  5
2.
(2 + 4)  3
3.
10 – 4  2
3.
3 + 42 – 2
3.
4  (5 – 2)2
4.
3 – 24  8
4.
8
4.
15 – 7  2 + 4
5.
1+2×3+4
6.
3  (6 – 5) + 2
6.
2 + 4  (5 – 2)
6.
(2 + 3)  (8 – 2)
7.
(8  6)  (15 – 13)
7.
4 – 25  5 + 1
7.
18  (3 + 6) – 2
Challenge
Numeracy
5.
1
2
of 12
2 × 32
5.
10 – 23 + 3
13 + 23  4 – 3  2
Page 21
Royds School
Exercise 10
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
4.3  100
1.
600  1000
1.
24000 ÷ 80
2.
340cm → m
2.
21.4g → mg
2.
0.209km → m
3.
8–6÷2
3.
3+4×2–7
3.
4  32 – (3 + 2)
4.
3+2×8
4.
82  10 × 4
4.
15 – 7  2 + 8 ÷ 2
5.
10 – 3 × 3 + 1
5.
2 × (7 – 3)2
5.
102 – (8 – 2)2 – 8
6.
3 + (9 – 5) × 2
6.
16 ÷ 2  (6 – 2)
6.
(2 × 32) ÷ (7 – 1)
7.
(4  6)  (8 ÷ 2)
7.
7.
82  16 × (18 ÷ 4 )
Challenge
Numeracy
81 – 32 + 8 ÷ 2
(2 + 3  4 + 6)  (6 – 8  2 + 3)
Page 22
Royds School
Exercise 11
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
4.3  100
1.
600  1000
1.
24000 ÷ 80
2.
380mm → cm
2.
61.2km → m
2.
1.209m → cm
3.
490 – 79
3.
523.2 × 8
3.
56284 × 94
4.
8.9 + 46.29
4.
68.2 – 6.532
4.
6238.3 ÷ 4
5.
4.13 × 4
5.
3 + 8.3 × 5
5.
9.2 + 5.9 × 8
6.
20% of £70
7.
3+4×5
7.
19 – 4 × 5
7.
32 – 16
8.
721 ÷ 3
8.
826 ÷ 5
8.
53 ÷ 4
Numeracy
6.
30% of £8
Page 23
6.
35% of £12
Royds School
Exercise 12
Without any working and in 12 minutes, write down the answer to as many of the sums
below as you can. Take a note of how many you get correct in the time allowed. Challenge a
parent!
1.
13 + 9
2.
34 – 21
3.
45
4.
27 + 14
5.
24 – 7
6.
76
7.
40  5
8.
45 + 27
9.
64  8
10.
68 – 47
11.
4 + 19 + 21
12.
21  4
13.
424  2
14.
14  3
15.
36 – 19
16.
93  3
17.
124 + 61
18.
132 – 34
19.
16  4
20
235 + 68
21.
246 – 99
22.
72  8
23
56  7
24.
126  3
25.
34  100
26.
86.1  100
27.
2410  100
28.
30  40
29.
200  60
30.
34  20
31.
25  300
32.
1600  20
33.
4500  50
34.
50  43  2
35.
4  74.3  25
36.
300  1.3
37.
18 + 36 – 11
38.
241 – 42 + 5
39.
56 + 144 – 34
40.
8 + 16 + 61 + 10
41.
45  4
42.
27  8
43.
240  5
44.
3600  40
45.
134 + 78
46.
£3.99  4
47.
£5.98  6
48.
340  17
49.
56000  800
50.
20  200  20  3
Numeracy
Page 24
Royds School
Number correct _________________
Numeracy
Page 25
Royds School
Exercise 13
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
584 – 108
1.
8153 × 7
1.
467 × 458
2.
1
2
2.
1
6
2.
2
of
3
3.
20% of £110
3.
85% of £60
4.
£8.45 × 3
4.
89 × 84
5.
2
5
5.
4
9
£36
5.
6.
5.8 km → m
6.
95cm → m
6.
7.
0.8 m → cm
Numeracy
of
of
£30
£30
7.
of
of
£54
3.
52.5% of £160
4.
9.03km → m
Page 26
7.
£120
8093 × 289
3
4
of
£17
3.7m + 83cm
80.1cm + 0.034km
Royds School
Numeracy
Page 27
Royds School
Exercise 14
Without any working and in 12 minutes, write down the answer to as many of the sums
below as you can. Take a note of how many you get correct in the time allowed. Challenge a
parent!
1.
15 + 7
2.
37 – 24
3.
56
4.
36 + 15
5.
54 – 8
6.
68
7.
24  6
8.
27 + 28
9.
42  8
10.
88 – 47
11.
4 + 18 + 32
12.
23  3
13.
363  3
14.
15  3
15.
53 – 19
16.
84  4
17.
104 + 67
18.
122 – 23
19.
17  4
20
266 + 39
21.
368 – 99
22.
32  8
23
56  2
24.
153  3
25.
74  100
26.
53.7  100
27.
2810  100
28.
20  40
29.
200  70
30.
43  20
31.
22  400
32.
1800  20
33.
45000  50
34.
50  76  2
35.
4  23.6  25
36.
200  1.4
37.
13 + 48 – 11
38.
237 – 39 + 4
39.
42 + 158 – 76
40.
9 + 24 + 35 + 10
41.
38  6
42.
36  7
43.
340  5
44.
3200  40
45.
234 + 78
46.
£2.99  6
47.
£5.97  4
48.
3800  19
49.
81000  900
50.
30  200  20  30
Numeracy
Page 28
Royds School
Number correct ____________________
Numeracy
Page 29
Royds School
Exercise 15
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
Round each of the following to the nearest penny.
1.
15.8p 
1.
89.2p 
1.
101.5p 
2.
63.9p 
2.
29.6p 
2.
89.8p 
3.
7.5p 
3.
£6.274 
3.
£23.7549 
4.
£50.063 
4.
£16.1783 
4.
£6.4592 
Carry out each these mental calculations involving money.
5.
£5.40 + £1.10 + £2
5.
£17.80 – £6.70
5.
£3.70 + £3.45
6.
£1.80 + £4.90
6.
£25.30  £2.40
6.
£16.00 + £14.40
7.
£10  £7.80
7.
£3.05 + £ 1.90 + £2.05
7.
£20  £8.60  £5
8.
23 + (9 – 6)2 – 9
9.
( 4 + 2 × 3) ÷ 25
Show your working.
8.
42 × 3
8.
9.
20 – 7 × 3
9.
Numeracy
81 + 2 × (9 – 5)
(9 – 5)2 × 2
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Royds School
Exercise 16
Without any working and in 12 minutes, write down the answer to as many of the sums
below as you can. Take a note of how many you get correct in the time allowed. Challenge a
parent!
1.
15 + 7
2.
36 – 24
3.
73
4.
25 + 18
5.
64 – 7
6.
95
7.
35  5
8.
38 + 27
9.
42  6
10.
46 – 28
11.
6 + 18 + 33
12.
32  3
13.
864  2
14.
18  4
15.
56 – 17
16.
104  2
17.
125 + 68
18.
356 – 58
19.
16  6
20
255 + 48
21.
456 – 99
22.
48  8
23
54  6
24.
306  3
25.
67  100
26.
56.4  100
27.
8750  100
28.
50  30
29.
30  600
30.
24  200
31.
32  300
32.
2400  20
33.
4500  90
34.
50  72  2
35.
25  35.3  4
36.
200  4.3
37.
29 + 26 – 21
38.
345 – 46 + 7
39.
26 + 244 – 74
40.
7 + 25 + 43 + 20
41.
56  4
42.
47  6
43.
340  5
44.
2700  90
45.
564 + 78
46.
£5.99  5
47.
£1.98  7
48.
2600  13
49.
48000  80
50.
20  100  40  3
Numeracy
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Royds School
Number correct _________________
Numeracy
Page 32
Royds School
Exercise 17
Work through all questions in one of the columns below. Ensure you look at the notes and
set out your working correctly.
1.
139 – 75
1.
205626 × 7
1.
229 × 787
2.
7.98 + 8.5
2.
780201 – 42524
2.
2806.49 ÷ 5
3.
8.2 × 10
3.
0.702 ÷ 100
3.
0.0204 × 100000
4.
30 × 60
4.
800 × 60
4.
4.8 × 2000
5.
1
4
£20
5.
3
of
5
5.
5
of
8
6.
26km→ m
6.
8200m → km
6.
904m → km
7.
30000cm → m
7.
740m → km
7.
0.4mm → cm
8.
7.4kg → g
8.
2608m → km
8.
0.0903kg → g
9.
7.3m → cm
9.
1140g → kg
9.
10.02cm → mm
Numeracy
of
£45
Page 33
£48
Royds School
10.
0.6km → m
Numeracy
10.
17.4m → cm
Page 34
10.
8.01m → km
Royds School
Exercise 18
Without any working and in 12 minutes, write down the answer to as many of the sums
below as you can. Take a note of how many you get correct in the time allowed. Challenge a
parent!
1.
17 + 7
2.
38 – 25
3.
63
4.
25 + 36
5.
68 – 9
6.
38
7.
28  4
8.
48 + 34
9.
36  6
10.
55 – 27
11.
5 + 17 + 23
12.
72  3
13.
8626  2
14.
17  5
15.
74 – 48
16.
132  2
17.
546 + 37
18.
377 – 79
19.
23  6
20
235 + 48
21.
753 – 99
22.
48  12
23
72  8
24.
906  3
25.
85  100
26.
26.4  100
27.
8490  100
28.
50  70
29.
40  600
30.
31  300
31.
23  400
32.
2200  20
33.
3200  80
34.
2  37  50
35.
25  29.3  4
36.
200  3.4
37.
36 + 28 – 17
38.
328 – 29 + 3
39.
48 + 242 – 57
40.
5 + 38 + 23 – 10
41.
67  4
42.
48  6
43.
270  5
44.
21000  70
45.
534 + 188
46.
£7.99  4
47.
£4.97  3
48.
6800  340
49.
480000  600
50.
40  200  20  6
Numeracy
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Royds School
Number correct _________________
Numeracy
Page 36
Royds School