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Sum
books
5 Northway Chester CH4 8BB
Exercises in KS3 Mathematics - Year 7 Basics
First Published 2003
Copyright R Joinson and
Sum
books
This package of worksheets is sold subject to the condition that it is photocopied for educational purposes only onthe premises of the purchaser
ISBN 09543580-4-X
Preface
These sheets were written in response to suggestions from teachers. They are aimedat the pupils who come into year 7 and find the present work difficult. The work coverslevels 2, 3 and part of 4 of the national curriculum and, compared to our other KS3sheets, have been written with a more open layout, simpler language and easierquestions.
R Joinson October 2003Chester
Contents
Adding 1 - 7Subtraction 1 - 8Dot Patterns - 9
Roman Numerals - 10Ordering - 11
Putting in Signs - 12Adding 2 - 13Adding 3 - 14
Subtracting 2 - 15Subtracting 3 - 16
Adding Decimals - 17Negative Numbers - 18
Number List - 19Subtracting Decimals - 20
Multiplying 1 - 21Multiplying 2 - 22
Dividing - 23Missing Numbers - 24
Missing Signs - 25Number Sequences - 26
Number Lines - 27Putting numbers into Order 1 - 28Putting numbers into Order 2 - 29
Making Numbers - 30Comparing - 31
Working in Stages - 32Counting on - 33
Halves and Quarters - 34Fractions - 35
Equivalent Fractions - 36Writing Fractions - 37Lists of Numbers - 38Approximations - 39Number Chains - 40
Money Problems 1 - 41Money Problems 2 - 42
Rules - 43Making Patterns - 44
Number Machines - 45Theatre Seats - 46
Position - 472D Shapes - 483D Shapes - 49Little Cubes - 50
Shapes Questions 1 - 51Shapes Questions 2 - 52
Angles 1 - 53
Angles 2 - 54Turning - 55
Similar Shapes 1 - 56Similar Shapes 2 - 57
Reflection Symmetry - 58Reflection - 59
More Reflection - 60Area and Perimeter - 61
Equal Areas - 62Making Rectangles - 63
Measurement - 64Reading Scales 1 - 65Reading Scales 2 - 66
Time 1 - 67Time 2 - 68
Digital Times a.m. - 69Digital Times p.m. - 70
Sorting 1 - 71Sorting 2 - 72Sorting 3 - 73
Finding Information 1 - 74Finding Information 2 - 75Information Tables 1 - 76Information Tables 2 - 77Information Tables 3 - 78
Calendar 1 - 79Calendar 2 - 80
Using Information 1 - 81Using Information 2 - 82
Pictograms - 83Bar Charts 1 - 84Bar Charts 2 - 85
Charts and Pictograms 1 - 86Charts and Pictograms 2 - 87
Frequency Tables 1 - 88Frequency Tables 2 - 89
Putting Data into Tables 1 - 90Putting Data into Tables 2- 91
Years - 92
©
Sum
books
2003
Key Stage 3
7
Adding 1
7bExercise 11) What number does the stand for?
2) What number does the stand for?
3) What number does the stand for?
Exercise 2Look at each of these.What number does the stand for?
+ =
3 + = 7
+ =
+ = 75
+ =
+ =35
1) 3 + 6 =
3) 5 + = 8
5) + 3 = 6
2) 1 + 7 =
4) 8 + = 9
6) + 3 = 9
7) 4 + = 9 8) + 4 = 8
©
Sum
books
2003
Key Stage 3
8
Subtraction 1
7bExercise 11) What number does the stand for?
2) What number does the stand for?
3) What number does the stand for?
Exercise 2Look at each of these.What number does the stand for?
– =
8 – = 4
– =
– = 45
– =
– =38
1) 7 – 6 =
3) 8 – = 5
5) – 1 = 6
2) 5 – 2 =
4) 8 – = 3
6) – 3 = 4
7) 9 – = 3 8) – 4 = 5
©
Sum
books
2003
Key Stage 3
9
Dot Patterns
7b
1) These dots are the numbers on a dice.
They show the numbers 1 to 6.
Draw dot patterns for the numbers 7, 8, 9 and 10.
2) The numbers on opposite sides of a dice always add up to 7.
Adding the dots gives another pattern for 7
Use these dots to draw two more patterns for 7.
+ =
+
=+
=
©
Sum
books
2003
Key Stage 3
10
Roman Numerals
7bHere are the first 12 Roman numerals.
1) What numbers do you think these mean?
XIII XIV XV
2) Now try these
XX XXV XXX
Answer these sums in Roman numerals.
3)
III + III
4)
II + V
5)
V + III
6)
V + V + I
7)
III + III + II
8)
IV + III + II
9)
V + III + IV
10)
X + II + III
11)
X – II
12)
XII – V
13)
XX – V
14)
XXX – XV
15)
XVI – IX
I II III IV V VI VII
VIII IX X XI XII
1 2 3 4 5 6 7
8 9 10 11 12
©
Sum
books
2003
Key Stage 3
11
Ordering
7bExercise 1
Exercise 2
In each of these lists a number is missing.
For each list write down the missing number.
1) 12, 13, 14, 15, 16, 17, ...., 19, 20, 21, 22, 23, 24, 25, 26
2) 37, 38, 39, ...., 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51
3) 58, 59, 60, 61, 62, ...., 64, 65, 66, 67, 68, 69, 70, 71, 72
4) 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, ...., 73, 74, 75, 76
5) 84, 85, 86, 87, 88, ...., 90, 91, 92, 93, 94, 95, 96, 97, 98
6) 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, ...., 55
14
2738
6
77
26
8964
55
73
6 14 26 . . . . . . . . .
93
39
Here are 12 numbers.
They have been jumbled up.
Write them down in order.
Finish it off. The list has been started.
©
Sum
books
2003
Key Stage 3
12
Putting in Signs
7bExercise 1Look at these.
4 + 5 = 9 7 – 3 = 4 6 + 3 = 9 8 – 4 = 4
Those below have got their + and – signs missing.Write them out again with the + or – sign in. 1) 4 ... 3 = 7 2) 5 ... 2 = 3 3) 9 ... 7 = 2 4) 7 ... 2 = 9 5) 6 ... 5 = 1 6) 5 ... 5 = 0 7) 2 ... 6 = 8 8) 4 ... 4 = 8 9) 6 ... 1 = 510) 14 ... 5 = 9 11) 13 ... 3 = 16 12) 25 ... 14 = 1113) 17 ... 7 = 10 14) 27 ... 10 = 37 15) 34 ... 26 = 60
Exercise 21) Jaspal has £7 in his pocket. He puts this with £11 in his money box. He works out how much money he has altogether. a) Does he + or – the two numbers? b) Write down a sum to show what he has to do. c) How much does he now have in his money box?
2) Rebecca has a piece of tape 32 centimetres long. She cuts 10 centimetres from it. She now has two pieces of tape. One piece is 10 centimetres long. She wants to work out the length of the second piece. a) Does she + or – the 32 and the 10? b) Write down a sum to show what she has to do. c) What is the length of the second piece of tape?
3) Ben has 22 cards. He gives 7 of them to his friend Sam. He works out how many cards he has left. a) Does he + or – the two numbers? b) Write down a sum to show what he has to do. c) How many cards has he left?
©
Sum
books
2003
Key Stage 3
13
Adding 2
7bDo not use a calculator
1) Add these together.
i) 19 + 7 j) 15 + 6 k) 13 + 16 l) 12 + 13
2) Add these together.
i) 14 + 24 j) 33 + 45 k) 27 + 38 l) 43 + 51
3) Add these together.
i) 7 + 12 + 42 j) 31 + 6 + 16 k) 35 + 8 + 23
416
+ + ++
+ + + +
526
6
59 6
16
13
8 14
45
3311
9
14
a) b) c) d)
e) f) g) h)
+ 26
27+ +
+
+
+
+
+23
38 34 47
45 23
54
3531
26
36
35 46
63a) b) c) d)
e) f) g) h)
+
+
+
+
+
+
+
+
169
35
71523
569
19
4 524
9 27
53
43
634
26 22
38
29
5
35 8
35
15 26
a) b) c) d)
e) f) g) h)
©Sumbooks 2003 Key Stage 3
14
Adding 3
7bDo not use a calculator
1) Add these together.
i) 126 + 17 j) 215 + 26 k) 275 + 37 l) 375 + 56
2) Add these together.
i) 286 + 174 j) 312+ 457 k) 394 + 822 l) 360 + 856
3) Add these together.
i) 25 + 674 + 346 j) 548 + 86 + 451 k) 348 + 97 + 23
14233
+ + ++
+ + + +
72483
27
291 73
362
215
56 117
324
423142
65
814
a) b) c) d)
e) f) g) h)
+ 374
274+ +
+
+
+
+
+176
794 674 839
318 476
358
548465
568
547
428 563
456a) b) c) d)
e) f) g) h)
+
+
+
+
+
+
+
+
54858
137
65572354
55427
104
58 75967
12 384
740
671
57673
856 758
595
648
54
665 53
347
432 453
a) b) c) d)
e) f) g) h)
©Sumbooks 2003 Key Stage 3
15
Subtracting 2
7bDo not use a calculator
1) Subtract these numbers.
i) 18 – 13 j) 25 – 21 k) 35 – 34 l) 46 – 22 m) 44 – 14 n) 42 – 39 o) 34 – 16 p) 54 – 12
2) Subtract these numbers.
i) 21 – 6 j) 34 – 5 k) 53 – 7 l) 47 – 9 m) 71 – 5 n) 34 – 12 o) 32 – 15 p) 73 – 15
3) There are 26 pupils in group 7A. 15 of them are girls. How many are boys?
4) A box contains 44 apples. 16 are removed. How many are left?
5) Megan travels from her home to London. It is 45 miles altogether. A bus carries her 17 miles towards London. How much further has she to travel?
–173
–
–
–
–
–
–
–
194
13 2
16 4
148
29 7
26 9
3317
a) b) c) d)
e) f) g) h)
– – – – 30
7 5413
4312
63 12
– – – – 43 15
67 34
63 19
81 22
a) b) c) d)
e) f) g) h)
©Sumbooks 2003 Key Stage 3
16
Subtracting 3
7bDo not use a calculator
1) Subtract these numbers.
i) 83 – 52 j) 47 – 29 k) 53 – 45 l) 67 – 52 m) 84 – 37 n) 91 – 26 o) 43 – 19 p) 52 – 34
2) Subtract these numbers.
i) 201 – 5 j) 412 – 7 k) 380 – 9 l) 514 – 6 m) 312 – 9 n) 486 – 24 o) 526– 37 p) 326 – 17
3) Subtract these numbers
–4812
–
–
–
–
–
–
–
6319
56 22
54 32
8317
93 37
45 29
6338
a) b) c) d)
e) f) g) h)
– – – – 200
9 600
20 500
15 605 22
– – – – 608 25
450 44
750 37
430 33
a) b) c) d)
e) f) g) h)
– – – – 321
37 486
23 395
17 580 37
– – – – 666 57
594 44
519 82
184 43
a) b) c) d)
e) f) g) h)
– – – – 718
77 426 56
386 65
554 89
i) j) k) l)
©Sumbooks 2003 Key Stage 3
17
Adding Decimals
7bDo not use a calculator
Add these together.
m) 4.5 + 3.4 n) 4.6 + 3.1
o) 5.4+ 3.9 + 3.0 p) 1.4 + 2.7 + 8.9
q) 4.5 + 4.9 + 9.5 r) 5.3 + 2.8 + 5.7
s) 4.7 + 7.6 + 3.8 t) 4.8 + 6.9 + 7.4
u) 3.7 + 5.4 + 8.6 v) 4.6 + 5.3 + 2.9
+
+ +
+ 3.1
+
+1.2 5.6 9.7
2.14.4
1.13.2
3.41.3
6.43.1
a) b) c)
d) e) f)
+ + +4.31.8
5.33.24.7
3.63.14.75.2
g) h) i)
+ + +4.30.8
5.34.88.4
7.62.55.85.3
j) k) l)
©Sumbooks 2003 Key Stage 3
18
Negative Numbers
7b
1)
2)
This is a number line.
The numbers get bigger to the right, and smaller to the left.
Answer these questions.
a) What bigger number comes next to 5?
b) What smaller number comes next to –6?
c) Which number is smaller than 0 by 3?
d) Which number is bigger than –6 by 4?
e) Which number is half way between 1 and 5?
f) Which number is half way between 0 and –2?
g) Which number is half way between –2 and –6?
h) Which number is half way between 2 and –4?
B˚C
–10˚C
–D˚C
0˚C
5˚C
15˚C
20˚C
A˚C
30˚C This is a school thermometer.
Three numbers have been left off.
a) What number does A mean?
b) What number does B mean?
c) What number does D mean?
d) What temperature does the thermometer show?
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5
BiggerSmaller
©Sumbooks 2003 Key Stage 3
19
Number List
7bAll the answers are in this list.
1) Write down a multiple of 6
2) Write down an even number greater than 100.
3) Write down an odd number between 60 and 100.
4) Write down two numbers which add up to 150.
5) Write two numbers which give 160 when multiplied together.
6) Which two numbers have a difference of 20?
7) Which number is nearest in value to 150?
8) Which two numbers are missing ?
9) Put the numbers into order of size. Start with the smallest.
10) Write down a number that is a multiple of both 8 and 3.
11) Write down an odd number divisible by 5.
12) Which two numbers add up to 180?
13) What is added to 80 to give 148?
14) Which two numbers are missing ?
15) Which two numbers will divide into 200?
16) What is half of 160?
17) What is 23 one third of?
18) Write down all the even numbers less than 50.
19) How many numbers are bigger than 35?
80, 32, 48, 148, 67, 70, 20, 35, 68, 8, 47, 69
÷ = 10
– = 80
©Sumbooks 2003 Key Stage 3
20
Subtracting Decimals
7bDo not use a calculator
.
v) 7.4 – 3.2 w) 3.2 – 1.6 x) 5.7 – 4.3
4.6–
––
– –
–
–
–
–
7.43.1 2.3
5.73.6
5.84.3
5.32.2
5.95.7
6.84.6
5.32.6
5.42.6
a) b) c)
d)e) f)
g) h) i)
7.3–
––
– –
–
–
–
–
4.83.8 2.6
5.12.7
7.65.6
8.65.1
7.53.8
9.65.8
8.86.9
7.35.6
j) k) l)
m) n) o)
p) q) r)
–– –8.56.7
8.43.4
6.32.6
s) t) u)
©Sumbooks 2003 Key Stage 3
21
Multiplying 1
7bDo not use a calculator
Multiply these.
p) 9 × 3 q) 8 × 9 r) 6 × 8
s) 13 × 3 t) 18 × 4 u) 11 × 5
v) 32 × 3 w) 17 × 5 x) 23 × 5
y) 13 × 7 z) 16 × 6 a1) 17 × 7
b1) 23 × 4 c1) 37 × 2 d1) 43 × 2
×
× ×
× ×
× 222
154
173
14 6
216
224
j) k) l)
m) n) o)
×
×
×
×
×
× ×
×
× 42
33
54
5 7
92
76
102
128
135
a) b) c)
d) e) f)
g) h) i)
©Sumbooks 2003 Key Stage 3
22
Multiplying 2
7bDo not use a calculator
Multiply these.
p) 19 × 3 q) 25 × 9 r) 24 × 8
s) 26 × 7 t) 31 × 7 u) 26 × 9
v) 37× 8 w) 43 × 8 x) 83 × 4
y) 56 × 9 z) 67 × 8 a1) 71 × 7
b1) 72 × 9 c1) 61 × 8 d1) 57 × 6
×
× ×
× ×
× 565
638
419
53 6
219
448
j) k) l)
m) n) o)
×
×
×
×
×
× ×
×
× 23
6315
433
45 5
674
713
276
358
437
a) b) c)
d) e) f)
g) h) i)
©Sumbooks 2003 Key Stage 3
23
Dividing
7b
Do not use a calculator
1) Divide these.
a) 20 ÷ 2 b) 32 ÷ 2 c) 44 ÷ 2
d) 33 ÷ 3 e) 42 ÷ 3 f) 45 ÷ 3
g) 48 ÷ 4 h) 88 ÷ 4 i) 72 ÷ 4
j) 92 ÷ 2 k) 74 ÷ 2 l) 84 ÷ 3
m) 72 ÷ 3 n) 95 ÷ 5 o) 65 ÷ 5
p) 72 ÷ 6 q) 91 ÷ 7 r) 120 ÷ 6
s) 119 ÷ 7 t) 144 ÷ 8 u) 144 ÷ 9
v) 184 ÷ 8 w) 154 ÷ 7 x) 174 ÷ 6
2) All these have remainders.
a) 37 ÷ 3 b) 29 ÷ 2 c) 73 ÷ 5
d) 87 ÷ 4 e) 41 ÷ 3 f) 95 ÷ 2
g) 76 ÷ 5 h) 67 ÷ 2 i) 93 ÷ 4
j) 56 ÷ 3 k) 67 ÷ 5 l) 81 ÷ 4
m) 93 ÷ 6 n) 78 ÷ 8 o) 64 ÷ 7
p) 83 ÷ 5 q) 82 ÷ 9 r) 49 ÷ 6
s) 48 ÷ 7 t) 88 ÷ 9 u) 72 ÷ 7
v) 80 ÷ 7 w) 71 ÷ 8 x) 47 ÷ 9
©Sumbooks 2003 Key Stage 3
24
Missing Numbers
7bDo not use a calculator
Fill in all the missing numbers
1) If 29 – 5 = 24 then
a) 5 + ... = 29 b) 29 – ... = 5 c) 24 + ... = 29
2) If 7 × 9 = 63 then
a) 9 × ... = 63 b) 63 ÷ ... = 7 c) 63 ÷ ... = 9
3) If 17 + 33 = 50 then
a) 50 – ... = 33 b) 50 – ... = 17 c) 33 + ... = 50
4) If 8 × 10 = 80 then
a) 10 × ... = 80 b) 80 ÷ ... = 10 c) ... ÷ 10 = 8
5) If 80 ÷ 4 = 20 then
a) 80 ÷ ... = 4 b) ... × 4 = 80 c) ... × 20 = 80
6) All the answers are 4.
= 4
1 + ....
8 ÷ ....
.... × 2
Four times ....
Twice ....
8 – ....
Half of ....
A quarter of ....
©Sumbooks 2003 Key Stage 3
25
Missing Signs
7bDo not use a calculator
Fill in the missing signs, × , ÷ , + or –
a) 3 .... 2 = 5 b) 4 .... 3 = 7 c) 4 .... 3 = 1
d) 9 .... 5 = 4 e) 2 .... 6 = 12 f) 10 .... 2 = 5
g) 20 .... 10 = 2 h) 10 .... 2 = 12 i) 23 .... 2 = 21
j) 13 .... 8 = 21 k) 14 .... 5 = 9 l) 21 .... 3 = 7
m) 5 .... 5 = 25 n) 4 .... 9 = 36 o) 45 .... 9 = 5
p) 6 .... 6 = 36 q) 80 .... 10 = 8 r) 20 .... 4 = 80
s) 8 .... 8 = 64 t) 17 .... 23 = 40 u) 90 .... 9 = 10
v) 14 .... 2 = 28 w) 30 .... 2 = 15 x) 7 .... 7 = 49
y) All the answers are 10
= 10
80 ... 70
5 ... 2
27... 17
160 ... 16
20 ... 2
1 ... 10
5 ... 5
6 ... 4
©Sumbooks 2003 Key Stage 3
26
Number sequences
7bExercise 1
Finish these off. The numbers increase in value.
1) 15, 16, 17, 18, 19, 20, ..., ....
2) 1, 3, 5, 7, 9, 11, ..., ....
3) 2, 4, 6, 8, 10, 12, ..., ....
4) 3, 6, 9, 12, 15, 18, ..., ....
5) 10, 20, 30, 40, 50, 60, ..., ....
6) 5, 15, 25, 35, 45, 55, 65, ..., ....
7) 5, 10, 15, 20, 25, 30, ..., ....
Exercise 2
Finish these off. The numbers decrease in value.
1) 30, 29, 28, 27, 26, 25, ..., ....
2) 41, 40, 39, 38, 37, 36, ..., ....
3) 31, 29, 27, 25, 23, 21, ..., ....
4) 24, 22, 20, 18, 16, 14, ..., ....
5) 99, 88, 77, 66, 55, 44, ..., ....
6) 80, 70, 60, 50, 40, 30, ..., ....
7) 30, 27, 24, 21, 18, 15, ..., ....
Exercise 3
Fill in the missing numbers.
1) 31, 33, 35, 37, ..., ..., 43, 45.
2) 16, 18, 20, ..., ..., 26, 28, 30.
3) 35, 33, 31, 29, ..., ..., 23, 21.
4) 21, 24, 27, ..., ..., 36, 39, 42.
5) 65, 60, ..., ..., 45, 40, 35, 30.
6) 40, 36, 32, ..., ..., 20, 16, 12.
7) 24, 27, 30, 33, ..., ..., 42, 45.
©Sumbooks 2003 Key Stage 3
27
Number Lines
7bFill in the missing numbers.
0 0.2 0.4 0.7...... ............0.1
2.4 ...... 3.42.0 ......
3.4 3.8 ............ ......
a)
b)
c)
e)
f)
g)
...... ...... 0.6 0.90.7 ......0.50.3
0.8 1.0 ...... ......1.3 1.41.1......
...... 1.6 1.8 2.11.9 ............1.5
1.9 ...... 2.3 2.62.4 ......2.2......
......
d)
©Sumbooks 2003 Key Stage 3
28
Putting Numbers into Order 1
7bPut these into order.
Start with the smallest.
a) 5, 8, 3, 12, 9, 17
b) 28, 19, 3, 24, 7, 21
c) 17, 32, 15, 22, 28, 14
d) 44, 23, 37, 63, 18, 31
e) 45, 52, 41, 28, 42, 83
f) 32, 72, 27, 47, 28, 64
g) 93, 55, 34, 62, 84, 52
h) 52, 77, 49, 86, 39, 72
i) 84, 24, 100, 36, 107, 93
j) 65, 45, 23, 64, 156, 127
k) 38, 239, 174, 49, 59, 137
l) 294, 45, 274, 172, 16, 6
m) 329, 164, 248, 371, 451, 222
n) 423, 935, 36, 475, 631, 729
o) 483, 386, 757, 482, 626, 273
p) 452, 99, 152, 731, 683, 472
q) 740, 352, 845, 562, 67, 82
r) 563, 876, 935, 824, 83, 37
s) 674, 874, 284, 735, 929, 193
©Sumbooks 2003 Key Stage 3
29
Putting Numbers into Order 2
7bPut these into order.
Start with the smallest.
a) 7, 5, 8, 23, 4, 13
b) 57, 86, 9, 45, 5, 26
c) 43, 87, 153, 98, 357, 84
d) 647, 359, 693, 610, 59, 129
e) 0.5, 0.1, 0.6, 0.3, 0.2, 0.8
f) 0.9, 0.3, 0.7, 0.4, 0.6, 0.2
g) 0.8, 0.6, 1.3, 1.7, 1.2, 1.0
h) 1.9, 1.7, 0.4, 1.3, 2.0, 1.5
i) 2.8, 1.9, 2.1, 0.4, 3.7, 2.6
j) 3.5, 1.4, 2.8, 3.2, 0.4, 1.6
k) 0.7, 2.4, 6.8, 5.9, 4.7, 2.6
l) 4.4, 3.6, 2.9, 3.1, 6.0, 5.9
m) 6.7, 9.4, 5.8, 4.8, 7.5, 1.9
n) 3.7, 4.8, 2.8, 6.8, 3.9, 4.9
o) 9.3, 7.8, 6.4, 5.8, 7.9, 5.1
p) 8.4, 7.4, 3.9, 4.8, 8.5, 2.6
q) 9.4, 8.7, 8.5, 9.1, 3.5, 7.6
r) 8.5, 7.3, 6.8, 3.8, 9.4, 8.4
s) 8.4, 4.9, 9.5, 2.8, 7.9, 6.4
©Sumbooks 2003 Key Stage 3
30
Making Numbers
7b1) Here are 4 cards.
They can make other numbers.
Like this.
Use these 4 numbers to do these
a) Write down 10 numbers beginning with a 1.
b) Write down 10 numbers beginning with a 3.
c) Write down 10 numbers beginning with a 4.
d) Write down 10 numbers beginning with an 8.
2) Which numbers are missing?
3 8 4 1
3 8 148 1 8 4 3
381
4
1
..
..3
113 1.. 4
3 8 4 .. 34 ..4
©Sumbooks 2003 Key Stage 3
31
Comparing
7b< means ‘is less than’
2 < 4 Two is less than four
–5 < 0 Minus 5 is less than zero
> means ‘is bigger than’
5 > 3 Five is bigger than three
3 + 4 > – 3 Three add four is bigger than minus three
= means ‘is equal to’
3 + 7 = 10 Three plus seven is equal to 10
6 – 4 = 1 + 1 Six subtract four is equal to one add one
Put <, > or = between each of these.
a) 4 ........ 8 b) 3 ........ 1
c) 7 ........ 4 d) 7 ........ 8
e) 2 ........ 9 f) 3 + 4 .......5
g) 9 + 5 ........ 95 h) 8 ........ 7 + 4
i) 8 – 3 ........ 6 j) 9 – 2 ........ 4
k) 0 ........8 – 8 l) 6 ........ 3 + 4
m) –5 ........ 5 n) –6 ........ 0
o) –6 ........ 4 p) 7 ........ –3
q) 5 + 6 ........ 13 – 2 r) 7 + 4 ........ 3 – 1
s) 7 + 2 ........ 3 + 6 t) 6 ........ –3
u) 8 + 3 ........ 4 – 1 v) 9 – 4 ........ 8 + 2
w) 1 + 5 ........ –3 x) 8 + 8 ........ 9 + 7
y) 5 + 6 ........ 13 – 2 z) 7 + 4 ........ 3 – 1
©Sumbooks 2003 Key Stage 3
32
Working in Stages
7bDo not use a calculator
1) Ryan adds together 26 and 15 like this
Call 15 10 + 5
First add the 10 26 + 10 = 36
Then add the 5 36 + 5 = 41
Now do these additions in the same way.
Write down what you do, just like the example.
a) 23 + 14 b) 32 + 16 c) 29 + 17
d) 36 + 18 e) 41 + 23 f) 46 + 23
g) 45 + 22 h) 35 + 36 i) 38 + 43
j) 28 + 25 k) 42 + 18 l) 52 + 26
m) 33 + 32 n) 51 + 27 o) 37 + 24
2) Halla does 35 – 18 like this.
Start at 18 18 to 20 is 2
20 to 30 is 10
30 to 35 is 5
So 18 to 35 is 2 + 10 + 5 = 17
Now do these in the same way.
a) 31 – 18 b) 42 – 19 c) 43 – 22
d) 52 – 16 e) 37 – 21 f) 53 – 26
g) 63 – 24 h) 37 – 26 i) 44 – 28
©Sumbooks 2003 Key Stage 3
33
Counting on.
7b
Do not use a calculator
Josh works in a shop.
He sells a disc for £12.55.
The customer pays with a £20 note.
He gives the customer change like this.
£12.55 to £12.60 is 5p
£12.60 to £13.00 is 40p
£13.00 to £20 is £7.00
So Josh gives the customer £7.00 + 40p + 5p = £7.45
Do these in the same way.
Work out the change given.
a) A t-shirt costing £16.50 is bought with a £20 note.
b) A sports cap costing £4.53 is bought with a £10 note.
c) A book costing £5.43 is bought with a £10 note.
d) A radio costing £16.45 is bought with a £50 note.
e) A poster costing £7.34 is bought with a £10 note.
f) A pair of shoes costing £25.73 is bought with two £20 notes.
Do these In the same way.
g) £10 – £3.40 h) £20 – £7.53 i) £30 – £24.62
j) £20 – £18.64 k) £40 – £29.68 l) £50 – £32.47
m) £30 – £17.24 n) £20 – £9.96 o) £10 – £8.66
p) £60 – £34.27 q) £45 – £19.84 r) £35 – £23.76
©Sumbooks 2003 Key Stage 3
34
Halves and Quarters
7b1) What fraction of these is shaded in?
2)
Fill in the missing letter.
Diagram .... has about a quarter shaded in.
Diagram .... has about half shaded in.
Diagram .... has about three quarters shaded in.
3) This is a metre rule.
Point X is half way along it.
How many parts are there altogether?
How many parts are in half the ruler?
How many parts are in a quarter of the ruler?
How many parts are in three quarters of the ruler?
a) b) c)
d) e) f)
Diagram A Diagram B Diagram C
X
©Sumbooks 2003 Key Stage 3
35
Fractions
7b
1) What fraction of these has been shaded in?
2) What fraction of these has been shaded in?
a) b) c)
d) e) f) g)
h)i) j)
a) b) c)
d) e) f)
g) h) i)
©Sumbooks 2003 Key Stage 3
36
Equivalent Fractions
7b1) Which of these show ?
2) Which of these show ?
12---
24
26
13
36
25
410
a) b) c)
d) e) f)
13---
515
412
48
25
38
410
a) b) c)
d) e) f)
©Sumbooks 2003 Key Stage 3
37
Writing Fractions
7b1) What fraction of the designs are black?
2) Approximately what fraction is shaded?
a) b) c)
d) e) f)
g) h) i)
j) k) l)
a) b) c)
d) e) f)
©Sumbooks 2003 Key Stage 3
38
Lists of Numbers
7b1) Here is a list of numbers.
12 14 67 53 99 25 47 82 10
37 56 86 94 36 76 23 48 64
Put them in order, smallest first.
The list has been started for you.
10 12 14 23
2) Here is a list of numbers.
196 287 954 743 532 105 735 856 375
851 745 376 476 832 264 463 765 934
Put them in order, smallest first.
The list has been started for you.
105 196 264 287
3) Here is a list of numbers.
746 543 976 35 725 504 754 632 342
65 864 987 345 275 845 637 945 773
Some digits are underlined.
What are the values of the underlined digits.
The list has been started.
746 Six units
543 Four tens
976 Nine hundreds
35 Five units
725 Two tens
©Sumbooks 2003 Key Stage 3
39
Approximations
7b1) These numbers are rounded to the nearest 10.
The list has been started.
Finish it off.
63 rounded to the nearest 10 is 60
79 rounded to the nearest 10 is 80
264 rounded to the nearest 10 is 260
465 rounded to the nearest 10 is 470 (round up - be careful)
72 rounded to the nearest 10 is
476 rounded to the nearest 10 is
753
843
745 (be careful)
532
27
2) These numbers are to be rounded off to the nearest 100.
The list has been started for you.
Finish it off.
764 rounded to the nearest 100 is 800
86 rounded to the nearest 100 is 100
325 rounded to the nearest 100 is 300
750 rounded to the nearest 100 is 800 (round up - be careful)
364 rounded to the nearest 100 is
718 rounded to the nearest 100 is
487
638
845
974
253
450 (be careful)
©Sumbooks 2003 Key Stage 3
40
Number Chains
7b1) Write down the next two numbers.
2) In each questions above, say what you do each time.
The first two have been done for you.
a) Add 2 each time
b) Add 5 each time
20 25 30 3515
10 12 14 168
10 13 16 197
4 7 10 131
14 18 22 2610
9 14 19 244
26 22 18 1430
21 18 15 1224
0 1 2 3–1
2 1 0 –13
5 3 1 –17
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
©Sumbooks 2003 Key Stage 3
41
Money Problems 1
7b1) Billy goes to the shop. He buys a packet of crisps for 25p, and a bar of chocolate for 42p. a) How much does he spend altogether? b) How much change does he get from a £1 coin?
2) Holly wrote a cheque for six pounds and forty two pence. How did she write this amount in figures?
3) Liam spends £6.40. He buys two Christmas presents for his mum and dad. He spends the same amount on both of them. How much does he spend on each?
4) Emma buys two tickets for the cinema. They cost £5.20 each. How much does she spend altogether?
5) Jake buys 4 cinema tickets. They cost £5 each. What is their total cost?
6) Kamala has a £1 coin. She buys chocolate bars costing 30 pence each. a) How many can she buy? b) How much change will she have?
7) Arlan has a £10 note. He buys a train ticket for £5.32. How much change will he be given?
8) A box of corn flakes costs 74 pence. What is the cost of two boxes?
©Sumbooks 2003 Key Stage 3
42
Money Problems 2
7b1) Luke saves 20p coins. He has 85 of them. How much is this?
2) Put these amounts of money into order of size. Begin with the smallest. £3.45, 78p, £6.00, £8, 32p, £10.43, £16
3) Ellie buys a cinema ticket. She pays with a £10 note. She gets £6.70 change. How much did the ticket cost?
4) Jessica buys a bus ticket. It costs her 65p to get into town. It costs another 65p to get home again. Instead she could buy a return ticket for £1.15. How much will she save if she buys a return ticket?
5) Chen and Jamie buy a pack of chocolate bars. There are 5 bars in the pack. The pack costs £1.25. a) What is the cost of each bar? b) Chen has 2 bars. How much should he pay? c) Jamie has the other three bars. How much should he pay?
6) Entrance to the museum is £2.50. Beth goes with her school friends. They are charged £27.50. How many are in the group?
©Sumbooks 2003 Key Stage 3
43
Rules
7bFill in the missing numbers.
1)
1
23 54
2
34 65
3
45 6
4
2)
1
2
4 53
3
4
6 75
5
11
3)
5
3
97
11113
7
5
9
3 5
4)
6
4
14
82
1210
9
6
3
12
4
©Sumbooks 2003 Key Stage 3
44
Making Patterns
7b1) These patterns are made with tiles.
a) What is added to pattern 1 to make pattern 2?
b) What is added to pattern 2 to make pattern 3?
c) What is added to pattern 3 to make pattern 4?
d) How many tiles are needed for pattern 5?
e) Draw a picture of pattern 5.
2) These patterns are made with matchsticks.
a) What is added to pattern 1 to make pattern 2?
b) What is added to pattern 2 to make pattern 3?
c) What is added to pattern 3 to make pattern 4?
d) How many matchsticks are needed for pattern 5?
e) Draw pattern 5.
Pattern 1
Pattern 2
Pattern 3
Pattern 4
Pattern 1 Pattern 2 Pattern 3
©Sumbooks 2003 Key Stage 3
45
Number Machines
7b1) When 2 goes into this number machine, 6 comes out.
a) What comes out when 3 goes in?
b) What comes out when 7 goes in?
c) What comes out when 11 goes in?
2) What does the ? mean in each of these?
+42 6
+52 ?
+7? 13
+?9 11
x4 ?3
x5 25?
÷20 4 ?
©Sumbooks 2003 Key Stage 3
46
Theatre Seats
7b
This is the plan of the seats in a theatre.
The position marked is seat 9 row K.
This seat is called 9K.
a) How many rows are in the theatre?
b) How many seats are in the theatre?
c) Which seat is right behind 9K?
d) Lauren sits in seat 14E. Her mum and dad sit either side of her.
Which seats do they sit in?
e) Megan sits in seat 5E. Her three friends sit in the seats on her left.
Which seats are these?
f) There are 5 rows of seats in front of Matthew. To his left there are
six more seats in his row. Where is he sitting?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20ABCDEFGHIJKLMNOP
Front of the Theatre
©Sumbooks 2003 Key Stage 3
47
Position
7b1)
This is a letter F.
One corner is marked A.
Its position is 5 across and 3 up . (trace it with your finger)
This is called (5,3)
a) What are the other corners of the letter called?
b) Add 3 lines to make it into an E.
c) What are the 3 new corners called?
0 5 10 15 20
5
10
15
20
A
©Sumbooks 2003 Key Stage 3
48
2D Shapes
7bHere are the names of some shapes.
1) Trapezium
2) Rectangle
3) Pentagon
4) Triangle
5) Hexagon
6) Square
7) Octagon
8) Parallelogram
Here are the pictures of these shapes.
Match the shape with the name.
Here is the first one.
a) is a square
a) b) c)
d)e)
f)g) h)
©Sumbooks 2003 Key Stage 3
49
3D Shapes
7b
Here are the names of some shapes.
1) Cube
2) Cuboid
3) Triangular prism
4) Cylinder
5) Cone
6) Sphere
7) Pyramid
Here are the pictures of these shapes
Match the shape with the name.
Here is the first one.
a) is a triangular prism.
a) b) c)
f)
d)
g)
e)
©Sumbooks 2003 Key Stage 3
50
Little Cubes
7b
d) Hannah has 63 small cubes. How many sticks can she make?
e) Liam has 125 small cubes. How many sticks can he make?
f) Rebecca has 220 small cubes. How many layers can she make.
g) Amy has 16 layers. How many big cubes can she make?
h) Hari has 20 layers. How many big cubes can he make?
i) Ellie has 35 sticks. How many layers can she make?
k)l)
k)l)
k)l)
k)l)
k)l)
k)l)
This stick is made from 10 cubes
This layer is made from 10 sticks.
a) How many cubes are in it?
This big cube is made from 10 layers.
b) How many sticks are in it?
c) How many small cubes are in it?
©Sumbooks 2003 Key Stage 3
51
Shapes Questions 1
7b
Answer these questions.
Use the diagrams above to help you.
1) How many corners has a triangle?
2) How many corners has a rectangle?
3) How many sides has a hexagon?
4) How many sides has an octagon
5) How many corners has a pentagon?
6) How many sides has a rectangle?
7) How many corners has a square?
8) How many sides has a triangle?
9) How many sides has a square?
10) How many corners has an octagon?
11) How many sides has a pentagon?
12) How many corners has a hexagon?
13) How many sides has a trapezium?
14) How many corners has a parallelogram?
©Sumbooks 2003 Key Stage 3
52
Shapes Questions 2
7b
Answer these questions.
Use the diagrams above to help you.
1) How many edges has a cube?
2) How many corners has a triangular prism?
3) How many faces has a cuboid?
4) How many edges has a cone?
5) How many edges has a cylinder?
6) How many faces has a sphere?
7) How many edges has a pyramid?
8) How many faces has a cylinder?
9) How many corners has a cuboid?
10) How many faces has a pyramid?
11) How many faces has a cone?
12) How many corners has a cube?
©Sumbooks 2003 Key Stage 3
53
Angles 1
7b1) Here are 8 angles. Answer the questions about them.
(i) Which angle is the smallest?
(ii) Which angle is the largest?
(iii) Which angles are bigger than angle b?
(iv) Which angles are smaller than angle e?
(v) Which angle is nearest in size to angle b?
2)
a) b)c)
d)e)
f)
g)h)
In this triangle
Which angle is the largest?
Which angle in the smallest?
a b
c
©Sumbooks 2003 Key Stage 3
54
Angles 2
7b
Look at these shapes.
There are 33 angles marked with letters.
Say whether the angles are:-
A right angle
Bigger than a right angle
Smaller than a right angle
a b
c
d e
f
gh
i
j
kl
m n
op
q
r s
tu
v
w
x
y
z
A
B
CD
E
F
G
©Sumbooks 2003 Key Stage 3
55
Turning
7b
What will these T’s look like when turned? The first has been done for you.
12 turn clockwise
14
34
12
14
turn clockwise
turn clockwise
turn anti-clockwise
turn anti-clockwise
©Sumbooks 2003 Key Stage 3
56
Similar Shapes 1
7bLook at these shapes.
Some of them are similar.
They are the same shape but bigger or smaller
For example, shapes ‘a’ and ‘c’ are similar.
What other shapes are similar?
a) b)c)
d)
e)f)
g)
h)i)
j) k) l)
©Sumbooks 2003 Key Stage 3
57
Similar Shapes 2
7bLook at these shapes.
Some of them are similar.
They are the same shape but bigger or smaller
For example, shapes ‘e’ and ‘k’ are similar.
What other shapes are similar?
a) b) c)
d) e)f)
g) h) i)
j)k)
l)
©Sumbooks 2003 Key Stage 3
58
Reflection Symmetry
7bEach of these shapes has reflection symmetry.
Copy these shapes.
Draw on them a line of symmetry.
The first one has been done for you.
a) b)
c)d)
e) f)
g) h)
©Sumbooks 2003 Key Stage 3
59
Reflection
7bCopy these onto square dotty paper.Draw their reflections. The first has been done.
©Sumbooks 2003 Key Stage 3
61
Area and Perimeter
7b
1) Count the squares to find the area of these.
2) What is the perimeter of each shape?
5cm
4cm
6cm
6cm
7cm
10cm
a) b)
f)
g)
7cm
7cm
c)
7cm
6cm
e)
6cm
9cm
d)
©Sumbooks 2003 Key Stage 3
62
Equal Areas
7b
Shape 1 has the same area as shape i.
Which other shapes have the same areas?
1)
2)
3)
4)
5)
6)
7)
8)
9)
a)
b)
c)
d)
e)
f)
g)
h)
i)
©Sumbooks 2003 Key Stage 3
63
Making Rectangles
7b
Each diagram shows two sides of a rectangle or square.
Draw two more lines to complete them.
©Sumbooks 2003 Key Stage 3
64
Measurements
7b
Centimetre
Gram
Litre
Millilitre
Millimetre
Metre
Kilometre
Kilogram.
1) Which of these is used for the length of something?
2) Which of these is used for the weight of something?
3) Which of these is used for the capacity of something?
Use one of these words for each of questions 4 to 10.
4) What is used to measure an amount of petrol?
5) What is used to measure the distance from London to Cardiff?
6) What is used to measure the thickness of a pencil?
7) What is used to measure the length of your school?
8) What is used to measure the weight of a person?
9) What is used to measure the width of your desk?
10) What is used to measure the weight of a hamster?
11) Which is larger, 1 litre or 1 millilitre?
12) Which is larger, 1 metre or 1 kilometre?
13) Which is larger, 1 kilogram or 1 gram?
14) Which is larger, 1 centimetre or 1 millimetre?
15) 100 centimetres make 1 metre.
a) How many centimetres make half a metre?
b) How many centimetres make a quarter of a metre?
c) How many centimetres make two metres?
©Sumbooks 2003 Key Stage 3
65
Reading Scales 1
7b
What number is the arrow is pointing to?
10 20
50 60
520 530
10 20
a)
b)
c)
d)
e)
f)
g)
0
10 200
0 100
300200
©Sumbooks 2003 Key Stage 3
66
Reading Scales 2
7b
What number is the arrow pointing to?
0 100 200 300
0 50 100 150
0 20 40 60
a)
b)
c)
d)
e)
f)
g)
0 100 200 300
0 100 200 300
estimate
40 60 80 100
40 60 80 100
estimate
©Sumbooks 2003 Key Stage 3
67
Time 1
7b
Write down the times on these clocks.
1
2
3
4567
8
9
10
1112 1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
a) b) c)
d) e) f)
g) h) i)
j) k) l)
©Sumbooks 2003 Key Stage 3
68
Time 2
7bWhat is the time interval between these pairs of clocks?
The first has been done for you.
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
456
78
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112 1
2
3
4567
8
9
10
1112
From to
From to
From to
From to
From to
is 5 hours
a)
b)
c)
d)
e)
©Sumbooks 2003 Key Stage 3
69
Digital Times a.m.
7b
Write down these a.m. times in digital form.
The first has been done.
1
2
3
4567
8
9
10
1112 1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
a) b) c)
d) e) f)
g) h) i)
j) k) l)
11:45
©Sumbooks 2003 Key Stage 3
70
Digital Times p.m.
7b
Write down these p.m. times in digital form.
The first has been done.
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
1
2
3
4567
8
9
10
1112
a) b) c)
d) e) f)
g) h) i)
j) k) l)
14:50
©Sumbooks 2003 Key Stage 3
71
Sorting 1
7bJessica lists all the pupils in group 7G.Thomas Daniel Emily Olivia Sophie
Mathew Lauren Jessica Mohammed Ryan
Bethany Abigail Molly Kaylie Eleanor
Adam Liam Sharron Michael Alice
Jacob Grace Joseph Sarah
a) Write a list of the girls. Write a list of the boys. The lists have been started for you,
Girls Boys Emily Thomas Olivia Daniel
b) How many girls are in the group? How many boys are in the group?
Jessica now draws two blocks. One block for the boys and one for the girls These are Jessica’s blocks. c) Say why she is wrong.
Draw two correct blocks.
Boys Girls
©Sumbooks 2003 Key Stage 3
72
Sorting 2
7bHere are some pictures of shapes.They have 3 sides, 4 sides or 5 sides.Some are shaded and some are not.
a) How many 3 sided shapes are shaded?b) Put your answer in the table below. Finish off the table
3 sided shapes
4 sided shapes
5 sided shapes
Shaded Not shaded
©Sumbooks 2003 Key Stage 3
73
Sorting 3
7bThe pupils in 7G are weighed.
Here is a list of their weights. They are in kilograms.
51, 50, 56, 46, 51, 52,
54, 57, 52, 59, 48, 55,
45, 41, 53, 47, 50, 50,
48, 45, 43, 55, 47, 52
a) Now write them down in order of size. Start with the smallest.
b) How many pupils weigh less than 45 kg?
c) Put this number in the table below. Finish off the table.
d) Now draw blocks to show this. The first block has been drawn for you.
Less than 45 kg
From 45 to 49 kg
From 50 to 54 kg
Over 54 kg
Numberof pupils
Less than45kg
From 45kgto 49kg
From 50kgto 54kg
Over54kg
2
4
6
8
10
©Sumbooks 2003 Key Stage 3
74
Finding Information 1
7bJames did a survey in group 7E.
He wrote down the colour of their eyes.
This is what he got.
1) How many girls had blue eyes?
2) How many girls had green eyes?
3) How many boys had brown eyes?
4) How many boys are in the group?
5) How many girls are in the group?
6) What is the total in the group?
Chloe did a survey in group 7F.
These are the results she got.
7) How many boys are in 7F?
8) How many girls are in 7F?
9) Which group has the most pupils, 7E or 7F?
Blue eyes
Brown eyes
Green eyes
Number of girls
Number of boys
5 4
6 7
3 2
Blue eyes
Brown eyes
Green eyes
Number of girls
Number of boys
6 4
5 3
1 3
©Sumbooks 2003 Key Stage 3
75
Finding Information 2
7bThe Park Cafe Menu
Bread and butter...................................................................£1.15
Main course
Fish pie..................................................................................£4.15
Ploughman’s Lunch...............................................................£3.65
Pizza......................................................................................£3.25
Beef Sandwich.......................................................................£2.90
Curry......................................................................................£3.90
Puddings
Ice cream...............................................................................£1.35
Fruit Salad..............................................................................£1.70
Piece of Cake.........................................................................£1.30
Drinks
Lemonade..............................................................................£0.60
Cola........................................................................................£0.85
Orange juice...........................................................................£0.75
Use the menu to answer these questions
1) What is the price of bread and butter?
2) What is the price of a pizza?
3) What is the most expensive food on the menu?
4) Charlotte buys these
A ploughman’s lunch.
A lemonade.
How much does she spend altogether?
5) Lewis buys a cola. He pays with a £1 coin. How much change does
he get?
6) Fruit Salad costs more than ice cream. How much more?
©Sumbooks 2003 Key Stage 3
76
Information Tables 1
7b The A483 road begins in Swansea and ends in Chester.
This table shows some of the towns it goes through.
The number is the distance of that town from Swansea.
For example - Oswestry is 113 miles from Swansea.
a) How far is Wrexham from Swansea?
b) How far is Wrexham from Chester?
c) What is the distance from Chester to Swansea?
d) Owen travels from Llandeilo to Newtown. How far does he travel?
e) Megan travels 120 miles from Swansea. Which two towns is she
between?
f) How far is Builth Wells from Wrexham?
Swansea
Llandeilo
Builth Wells
Newtown
Welshpool
Oswestry
Wrexham
Chester
Distancefrom
Swanseain miles
Town
0
22
58
85
98
113
127
139
©Sumbooks 2003 Key Stage 3
77
Information Tables 2
7b
The table below shows the temperature and rainfall for a week in July.
1) What was the temperature on Wednesday?
2) What was the temperature on Saturday?
3) What was the rainfall on Monday?
4) What was the rainfall on Friday?
5) Which day had the most rainfall?
6) Which day was the hottest?
7) Which two days had no rainfall?
8) Which two days had the same temperature?
9) On which day was the temperature lower than the day before?
10) What was the total rainfall for the week?
11) What is the difference between the highest and lowest temperatures.
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Monday
Temperaturein degrees C
Rainfall
in millimetres
18
21
25
16
18
19
20
2
0
9
12
3
2
0
©Sumbooks 2003 Key Stage 3
78
Information Tables 3
7bHere is a bus timetable from Town Centre to Victoria Road.
For example, the 09:50 bus from the Town Centre arrives at Victoria
Road at 10:12.
a) A bus leaves Town Centre at 10:15. At what time will it arrive at
Victoria Road?
b) How long does the bus take to travel from Town Centre to Victoria
Road?
c) Ellie has to get to Victoria Road for 10:30.
What is the latest bus she can catch from Town Centre?
d) The next bus on the time table leaves Town Centre at 11:15.
At what time will it arrive at Victoria road?
e) The 10:15 from Town Centre is delayed by road works.
It arrives at Victoria Road at 10.43.
For how long was it delayed?
f) The next day the 09:15 was delayed by 4 minutes.
At what time did it arrive at Victoria Road?
g) The last bus of the day leaves Town Centre at 21:50.
i) What is this time on the 12 hour clock?
ii) What time is this on the 12 hour clock?
iii)At what time, on the 24 hour clock, will it arrive at Victoria Road?
City Buses – Town Centre to Victoria Road
Town Centre departs
Victoria Road arrives
09:15 09:50 10:15 10:50
09:37 10:12 10:37 11:12
©Sumbooks 2003 Key Stage 3
79
Calendar 1
7bThis is the calendar for January and February.
Use it to answer these questions
a) On what day of the week is January 15th?
b) What date comes before January 1st?
c) How many days are there in February?
d) How many Fridays are there in February?
e) How many Fridays are there in January?
f) What is the 5th day after February 6th?
g) What is the date of the 4th Friday in January?
h) What is the 10th day after January 28th?
i) How many days are there from January 25th to February 3rd?
SMTWTFS
12
3456789
10111213141516
17181920212223
242526
282930
31
27
SMTWTFS
123456
789
10111213
14151617181920
212223242526
28
27
January
February
©Sumbooks 2003 Key Stage 3
80
Calendar 2
7b
This is the calendar for August to November.
Use it to answer these questions.
a) On what day of the week is September 16th?
b) What is the date of the 2nd Tuesday in November?
c) Which month has the most Tuesdays?
d) How many days are there from October 30th until November 12th?
e) On what day of the week is the last day of July?
f) On what day of the week is December 1st?
g) How many weeks are there from August 5th until November 4th?
h) On 16th August Laura makes an appointment to see her dentist.
The dentist says ‘It will be 3 weeks today’.
What is the date of her appointment?
SMTWTFS
12
3456789
10111213141516
17181920212223
242526
282930
31
27
SMTWTFS
123456
789
10111213
14151617181920
212223242526
282930
27
SMTWTFS
1234
567891011
12131415161718
19202122232425
26
28293031
27SMTWTFS 1
2345678
9101112131415
16171819202122
23242526
2829
30
27
August September
October November
©Sumbooks 2003 Key Stage 3
81
Using Information 1
7bHere are the distances between towns in Great Britain.
Two have been highlighted for you.
The distance between Aberdeen and Cardiff is 858 kilometres.
The distance between London and Norwich is 184 kilometres.
a) What is the distance between Cardiff and Newcastle?
b) What is the distance between Aberystwyth and Norwich?
c) How far is Birmingham from London?
d) Which two towns are furthest apart?
e) Which two towns are closest?
f) Which two towns are 576 kilometres apart?
g) Which two towns are 577 kilometres apart?
h) Hannah travels from Aberdeen to Birmingham.
Then she goes from Birmingham to London.
How far is her journey?
i) Which town is furthest from Norwich?
380177
753696858201577878379784
197188537
363467
172476161192336280
641326248512428
408624172576
345283385
460184 411
Aberd
een
Abery
stwyth
Birming
ham
Cardif
fEdin
burg
h
Liver
pool
Lond
on
Newca
stle
Norwich
©Sumbooks 2003 Key Stage 3
82
Using Information 2
7b
Here is a list of TV programmes.
5:00pm Cartoon
5:15pm Local News 5:25pm Athletics 7:00pm Comedy Film 8:45pm National News 9:05pm History Programme 9:50pm Documentary 10:35pm Football 12:10am Adventure Film
Use the list to answer these questions.
a) At what time did the National News begin?
b) How long did the National News last?
c) At what time did the Comedy Film start?
d) How long did the Comedy Film last?
e) The Adventure film is the same length as the Comedy Film.
At what time did it finish?
f) Sam normally goes to bed at 9.30. He watches the History Programme.
How many extra minutes does he stay up?
g) The programme before the Cartoon lasted for 50 minutes.
At what time did it begin?
h) At what time on the 24 hour clock did the History programme start?
i) At what time on the 24 hour clock did the Adventure film start?
j) Lucy started watching the TV at 5.15.
She watched it for three and a half hours.
Which programmes did she see?
©Sumbooks 2003 Key Stage 3
83
Pictograms
7bThe pictogram shows the people who go to a village fair.
Each person represents 10 people.
Answer these questions.
a) How many men went to the fair?
b) Which group were there most of?
c) How many girls went to the fair?
d) What do you think this represents?
e) Approximately how many boys went to the fair?
f) How many adults went to the fair?
g) How many people went to the fair altogether?
h) How many more girls than boys went to the fair?
Women
Men
Boys
Girls
©Sumbooks 2003 Key Stage 3
84
Bar Charts 1
7b Alex does a survey in his group.
He asks them what they like to do best.
He shows the data on this block diagram.
a) How many pupils prefer listening to music?
b) What was the most popular thing to do?
c) What was the least popular thing to do
d) What did four people like doing?
e) How many pupils did Alex ask?
f) Finish off this sentence.
Twice as many pupils ..... ..... as ..... ..... .....
1
2
3
4
5
6
7
8
Reading Playing Listening Watching Using a
9
10
outside to music TV computer
©Sumbooks 2003 Key Stage 3
85
Bar Charts 2
7b
A shop sells electrical items.
This bar chart shows what it sells in 1 week.
Use the diagram to answer the questions.
a) What was the most popular item sold?
b) What was the least popular item?
c) How many stereos were sold?
d) How many TVs were sold?
e) How many TV recorders were sold?
f) How many computers were sold?
g) How many radios were sold?
h) What was the total number of items sold?
4 8 12 16 20 24 28
TV
Stereo
TV Recorder
Computer
Radio
©Sumbooks 2003 Key Stage 3
86
Charts and Pictograms 1
7b
This table shows the number of people who bought food in a cafe.
Answer these questions.
1) What was the most popular drink?
2) How many sandwiches were sold?
3) How many drinks were sold?
4) Which food sold seven portions?
Draw a pictogram to show the data.
Use a stick figures like this for 2 people.
Use half a stick figure like this for 1 person.
Ensure that your diagram is very neat.
Type of food Number of people
Sandwich
Soup
Cake
Coffee
Tea
14
7
6
18
12
©Sumbooks 2003 Key Stage 3
87
Charts and Pictograms 2
7b
Ellie does a survey.
She checks 50 people in year 7.
She asks ‘What poster would you like in your bedroom?’
Here are her results.
a) Put in the frequency numbers.
b) How many pupils chose a pop star?
c) Use these numbers to draw a pictogram.
Use one stick person to represent 2 people.
Use half a stick person to represent 1 person
The pictogram has been started for you for you.
Type of Poster
Pop Star
Sports Person
Holiday Scene
Cartoon Character
Film Star
Tally Frequency
Pop Star
Sports Person
Holiday Scene
©Sumbooks 2003 Key Stage 3
88
Frequency Tables 1
7b
Oliver does a survey.
He asks some boys their favourite sport.
This is what he puts down.
Look at the table then answer the questions.
a) How many people said cricket?
b) Finish off the frequency column.
c) Which sport is the most popular?
d) How many answered tennis?
e) How many answered rugby?
f) What was the total number asked?
g) What does mean?
h) Give 2 reasons why some answered ‘None of These’
Football
Cricket
Tennis
Rugby
Swimming
None of these
FrequencyTallySport
Total
5
10
8
©Sumbooks 2003 Key Stage 3
89
Frequency Tables 2
7b
Cameron does a survey of some pupils.
He asks what they would like to do for a day out.
He recorded the data on a frequency table.
a) How many wanted to go to the museum?
b) How many wanted to go to the swimming baths?
c) Write down all the numbers in the frequency column.
d) Add together all the frequencies.
Put your answer in the ‘Total’ box.
e) How many people did Cameron ask?
f) What was the most popular day out?
g What was the least popular day out?
h) Which did six people choose?
Tally Frequency
Seaside
Museum
Place to visit
Cinema
Swimming baths
None of these
Leisure park
Total
©Sumbooks 2003 Key Stage 3
90
Putting Data into Tables 1
7b
Ben does a survey of the pupils in his class.
He asks them how they get to school.
He gives them this choice,
Taxi (T), Bike (Bi), Car (C), Bus (Bu), Walk (W), None of these (N).
This is his list of results.
C, Bu, W, Bu, N, W, C, T, W, Bu, W, Bu, Bi, Bi,
N, C, C, Bi, Bu, T, W, Bu, Bi, C, Bu, Bu, N, Bi
He puts this data into a tally chart.
a) The first 8 tallies have been put in.
Finish off the tallies.
b) Put in all the frequencies.
Use the table to answer these questions.
c) How many pupils come to school in a car?
d) How many pupils are there in the class?
e) What is the most popular way to get to school?
Type of Transport
Taxi
Bike
Car
Bus
Walk
None of These
FrequencyTally
©Sumbooks 2003 Key Stage 3
91
Putting Data into Tables 2
7b
The ages of the children who go to swimming club are:-
10, 11, 10, 12, 14, 11, 10, 13, 10, 11, 14,
11, 13, 12, 11, 11, 11, 10, 12, 13, 12, 11
a) Copy this frequency table into your book.
b) Fill in the tally column.
c) Fill in the frequency column.
d) Add up the frequencies and fill in the total.
Now use the table to answer these questions
e) How many members are aged 11?
f) How many members are there altogether?
g) How many members are under 13?
h) How many members are over 12?
i) What do you get if you add together answers g and h?
Age Tally Frequency
10
11
12
13
14
Total
©Sumbooks 2003 Key Stage 3
92
Years
7bMatch these dates with the events from the twentieth century.
1966, 1936, 1924, 1918, 1985, 1947,
1953, 1990, 1912, 1969, 1901, 1997
1920
1930
1940
1950
1960
1970
1980
1990
2000
1910
1900 Queen Victoria dies
Titanic sinks
First World War ends
First radio station
School leaving age raised to 15
Coronation of Queen Elizabeth II
England win the World CupFirst man lands on the moon
First episode of Eastenders
Nelson Mandella released from prison
Tony Blair becomes Prime Minister
First TV station
93
Answers
Adding 1 - Page 7
Exercise 1 1) 4 2) 2 3) 8
Exercise 2 1) 9 2) 8 3) 3 4) 1 5) 3 6) 6 7) 5 8) 4
Subtracting - Page 8
Exercise 1 1) 4 2) 9 3) 5
Exercise 2 1) 1 2) 3 3) 3 4) 5 5) 7 6) 7 7) 6 8) 9
Dot Patterns - Page 9
1) Exercises
2) Examples
Roman Numerals - Page 10
1) 13, 14, 15 2) 20, 25, 30 3) VI 4) VII 5) VIII
6) XI 7) VIII 8) IX 9) XII 10) XV 11) VIII 12) VII
13) XV 14) XV 15) VII
Ordering - Page 11
Exercise 1 6, 14, 26, 27, 38, 39, 55, 64, 73, 77, 89, 93
Exercise 2 1) 18 2) 40 3) 63 4) 72 5) 89 6) 54
Putting in Signs - Page 12
Exercise 1 1) + 2) – 3) – 4) + 5) – 6) – 7) +
8) + 9) – 10) – 11) + 12) – 13) – 14) + 15) +
Exercise 2 1) a) + b) 7 + 11 c) £18
2) a) – b) 32 – 10 c) 22cm
3) a) – b) 22 – 7 c) 15
Adding 2 - Page 13
1) a) 20 b) 18 c) 35 d) 51 e) 65 f) 41 g) 28 h) 27
i) 26 j) 21 k) 29 l) 25
2) a) 89 b) 59 c) 54 d) 80 e) 53 f) 92 g) 80 h) 82
i) 38 j) 78 k) 65 l) 94
3) a) 88 b) 70 c) 64 d) 71 e) 89 f) 92 g) 78 h) 81
i) 61 j) 53 k) 66
Adding 3 - Page 14
1) a) 247 b) 287 c) 548 d) 351 e) 364 f) 479 g) 931
h) 504 i) 143 j) 241 k) 312 l) 431
2) a) 830 b) 723 c) 941 d) 866 e) 842 f) 1152
g) 1237 h) 1267 i) 460 j) 769 k) 1216 l) 1216
3) a) 935 b) 1069 c) 1300 d) 1060 e) 1615 f) 1724
g) 1633 h) 1581 i) 1045 j) 1085 k) 468
Subtracting 2 - Page 15
1) a) 14 b) 15 c) 11 d) 12 e) 6 f) 22 g) 17 h) 16
i) 5 j) 4 k) 1 l) 24 m) 30 n) 3 o) 18 p) 42
2) a) 23 b) 41 c) 31 d) 51 e) 28 f) 33 g) 44 h) 59
i) 15 j) 29 k) 46 l) 38 m) 66 n) 22 o) 17 p) 58
3) 11 4) 28 5) 28 metres
Subtracting 3 - Page 16
1) a) 36 b) 44 c) 34 d) 22 e) 66 f) 56 g) 16 h) 25
i) 31 j) 18 k) 8 l) 15 m) 47 n) 65 o) 24 p) 18
2) a) 191 b) 580 c) 485 d) 583 e) 583 f) 406 g) 713
h) 397 i) 196 j) 405 k) 371 l) 508 m) 303 n) 462
o) 489 p) 309
3) a) 284 b) 463 c) 378 d) 543 e) 609 f) 550 g) 437
h) 141 i) 641 j) 370 k) 321 l) 465
Adding Decimals - Page 17
a) 6.8 b) 12.8 c) 6.5 d) 4.3 e) 4.7 f) 9.5 g) 13.0
h) 11.5 i) 11.4 j) 13.6 k) 20.8 l) 10.4 m) 7.9
n) 7.7 o) 12.3 p) 13.0 q) 18.9 r) 13.8 s) 16.1
t) 19.1 u) 17.7 v) 12.8
Negative Numbers - Page 18
1) a) 25ºC b) 10ºC c) –5ºC
2) a) 6 b) –7 c) –3 d) –2 e) 3 f) –1 g) –4 h) –1
Number List - Page 19
1) 48 2) 148 3) 67 or 69 4) 70 and 80 5) 8 and 20
6) 48 and 68 7) 148 8) 80 and 8
9) 8, 20, 32, 35, 47, 48, 67, 69, 68, 70, 80, 148 10) 48
11) 35 12) 32 and 148 13) 68 14) 148 – 68
15) 20 and 8 16) 80 17) 69 18) 8, 20, 32, 48 19) 8
Subtracting Decimals - Page 20
a) 4.3 b) 2.3 c) 2.1 d) 1.5 e) 3.1 f) 0.2 g) 2.2
h) 2.7 i) 2.8 j) 1.0 k) 4.7 l) 2.4 m) 2.0 n) 3.5
o) 3.7 p) 3.8 q) 1.9 r) 1.7 s) 1.8 t) 5.0 u) 3.7
v) 4.2 w) 1.6 x) 1.4
Multiplying 1 - Page 21
a) 8 b) 9 c) 20 d) 35 e) 18 f) 42 g) 20 h) 96
i) 65 j) 44 k) 60 l) 51 m) 84 n) 126 o) 88
p) 27 q) 72 r) 48 s) 39 t) 72 u) 55 v) 96 w) 85
x) 115 y) 91 z) 96 a1) 119 b1) 92 c1) 74 d1) 86
Multiplying 2 - Page 22
a) 138 b) 155 c) 129 d) 280 e) 225 f) 213 g) 162
h) 280 i) 301 k) 280 l) 504 m) 369 n) 318 o) 189
p) 352 q) 57 r) 225 s) 192 t) 182 u) 217 v) 234
w) 296 x) 344 y) 332 z) 504 a1) 536 b1) 497
c1) 648 d1) 488 e1) 342
Dividing - Page 23
1) a) 10 b) 16 c) 22 d) 11 e) 14 f) 15 g) 12 h) 22
i) 18 j) 46 k) 37 l) 28 m) 24 n) 19 o) 13 p) 12
q) 13 r) 20 s) 17 t) 18 u) 16 v) 23 w) 22 x) 29
2) a) 12r1 b) 14r1 c) 14r3 d) 21r3 e) 13r2 f) 47r1
g) 15r1 h) 33r1 i) 23r1 j) 18r2 k) 13r2 l) 20r1
m) 15r3 n) 9r6 o) 9r1 p) 16r3 q) 9r1 r) 8r1
t) 6r6 u) 9r7 v) 10r2 w) 11r3 x) 8r7 y) 5r2
.... ... ...... .. .... ......... ...
....
.. .
94
Missing Numbers - Page 24
1) a) 5 + 24 = 29 b) 29 – 24 = 5 c) 24 + 5 = 29
2) a) 9 X 7 = 63 b) 63 ÷ 9 = 7 c) 63 ÷ 7 = 9
3) a) 50 – 17 = 33 b) 50 – 33 = 17 c) 33 + 17 = 50
4) a) 10 X 8 = 80 b) 80 ÷ 8 = 10 c) 80 ÷ 10 = 8
5) a) 80 ÷ 20 = 4 b) 20 X 4 = 80 c) 4 X 20 = 80
6) Half of 8, 1 + 3, 8 ÷ 2, 2 X 2, A quarter of 16,
Four times 1, Twice 2, 8 – 4
Missing Signs - Page 25
a) 3 + 2 b) 4 + 3 c) 4 – 3 d) 9 – 5 e) 2 X 6 f) 10 ÷ 2
g) 20 ÷ 10 h) 10 + 2 i) 23 – 2 j) 13 + 8 k) 14 – 5l) 21 ÷ 3 m) 5 X 5 n) 4 X 9 o) 45 ÷ 9 p) 6 X 6
q) 80 ÷ 10 r) 20 X 4 s) 8 X 8 t) 17 + 23 u) 90 ÷ 9
v) 14 X 2 w) 30 ÷ 2 x) 7 X 7 y) 5 + 5, 80 – 70,
5 X 2, 27 – 17, 6 + 4, 160 ÷ 16, 20 ÷ 2, 1 X 10
Number Sequences - Page 26
Exercise 1
1) 21, 22 2) 13, 15 3) 14, 16 4) 21, 24 5) 70, 80
6) 75, 85 7) 35, 40
Exercise 2
1) 24, 23 2) 35, 34 3) 19, 17 4) 12, 10 5) 33, 22
6) 20, 10, 7) 12, 9
Exercise 3
1) 39, 41 2) 22, 24 3) 27, 25 4) 30, 33 5) 55, 50
6) 28, 24 7) 36, 39
Number Lines - Page 27
a) 0.3, 0.5, 0.6 b) 0.2, 0.4, 0.8 c) 0.9, 1.2, 1.5
d) 1.4, 1.7, 2.0 e) 2.0, 2.1, 2.5 f) 2.2, 2.8, 3.6
g) 3.0, 3.6, 4.4
Putting Numbers into Order 1 - Page 28
a) 3, 5, 8, 9, 12, 17 b) 3, 7, 19, 21, 24, 28
c) 14, 15, 17, 22, 28, 32 d) 18, 23, 31, 37, 44, 63
e) 28, 41, 42, 45, 52, 83 f) 27, 28, 32, 47, 64, 72
g) 34, 52, 55, 62, 84, 93 h) 39, 49, 52, 72, 77, 86
i) 24, 36, 84, 93, 100, 107 j) 23, 45, 64, 65, 127, 156
k) 38, 49, 59, 137, 174, 239 l) 6, 16, 45, 172, 274, 294
m) 164, 222, 248, 329, 371, 451
n) 36, 423, 475, 631, 729, 935
o) 273, 386, 482, 483, 626, 757
p) 99, 152, 452, 472, 683, 731
q) 67, 82, 352, 562, 740, 845
r) 37, 83, 563, 824, 876, 935
s) 193, 284, 674, 735, 874, 929
Putting Numbers into Order 2 - Page 29
a) 4, 5, 7, 8, 13, 23 b) 5, 9, 26, 45, 57, 86
c) 43, 84, 87, 98, 153, 357 d) 59, 129, 359, 610, 647, 693
e) 0.1, 0.2, 0.3, 0.5, 0.6, 0.8 f) 0.2, 0.3, 0.4, 0.6, 0.7, 0.9
g) 0.6, 0.8, 1.0, 1.2, 1.3, 1.7 h) 0.4, 1.3, 1.5, 1.7, 1.9, 2.0
i) 0.4, 1.9, 2.1, 2.6, 2.8, 3.7 j) 0.4, 1.4, 1.6, 2.8, 3.2, 3.5
k) 0.7, 2.4, 2.6, 4.7, 5.9, 6.8 l) 2.9, 3.1, 3.6, 4.4, 5.9, 6.0
m) 1.9, 4.8, 5.8, 6.7, 7.5, 9.4 n) 2.8, 3.7, 3.9, 4.8, 4.9, 6.8
o) 5.1, 5.8, 6.4, 7.8, 7.9, 9.3 p) 2.6, 3.9, 4.8, 7.4, 8.4, 8.5
q) 3.5, 7.6, 8.5, 8.7, 9.1, 9.4 r) 3.8, 6.8, 7.3, 8.4, 8.5, 9.4
s) 2.8, 4.9, 6.4, 7.9, 8.4, 9.5
Making Numbers - Page 30
1) Any 10 from these
a) 1, 13, 14, 18, 138, 183, 134, 143, 184, 148, 1384,
1348, 1843, 1834, 1483, 1438
b) 3, 38, 34, 31, 384, 348, 381, 318, 341, 314, 3841,
3814, 3184, 3148, 3481, 3418
c) 4, 43, 48, 41, 438, 483, 431, 413, 481, 418, 4381,
4318, 4831, 4813, 4138, 4183
d) 8, 83, 84, 81, 834, 843, 841, 814, 813, 831, 8431,
8413, 8341, 8314, 8143, 8134
2) 4, 18, 34, 41, 48
Comparing - Page 31
a) < b) > c) > d) < e) < f) > g) < h) < i) <
j) > k) = l) < m) < n) < o) < p) > q) = r) >
s) = t) > u) > v) < w) > x) = y) = z) >
Working in Stages - Page 32
1) a) 23 + 10 = 33 b) 32 + 10 = 42
33 + 4 = 37 42 + 6 = 48
c) 29 + 10 = 39 d) 36 + 10 = 46
39 + 7 = 46 46 + 8 = 54
e) 41 + 20 = 61 f) 46 + 20 = 66
61 + 3 = 64 66 + 3 = 69
g) 45 + 20 = 65 h) 35 + 30 = 65
65 + 2 = 67 65 + 6 = 71
i) 38 + 40 = 78 j) 28 + 20 = 48
78 + 3 = 81 48 + 5 = 53
k) 42 + 10 = 52 l) 52 + 20 = 72
52 + 8 = 60 72 + 6 = 78
m) 33 + 30 = 63 n) 51 + 20 = 71
63 + 2 = 65 71 + 7 = 78
o) 37 + 20 = 57
57 + 4 = 61
2) a) 18 to 20 is 2 b) 19 to 20 is 1 c) 22 to 30 is 8
20 to 30 is 10 20 to 40 is 20 30 to 40 is 10
30 to 31 is 1 40 to 42 is 2 40 to 43 is 3
2 + 10 + 1 = 13 1 + 20 + 2 = 23 8 + 10 + 3 = 21
d) 16 to 20 is 4 e) 21 to 30 is 9 f) 26 to 30 is 4
20 to 50 is 30 30 to 37 is 7 30 to 50 is 20
50 to 52 is 2 9 + 7 = 16 50 to 53 is 3
4 + 30 + 2 = 36 4 + 20 + 3 = 27
g) 24 to 30 is 6 h) 26 to 30 is 4 i) 28 to 30 is 2
30 to 60 is 30 30 to 37 is 7 30 to 40 is 10
60 to 63 is 3 4 + 7 = 11 40 to 44 is 4
6 + 30 + 3 = 39 2 + 10 + 4 = 16
Counting on - Page 33
a) £16.50 to £17 is 50p b) £4.53 to £4.60 is 7p
£17 to £20 is £3 £4.60 to £5.00 is 40p
£3 + 50p = £3.50 £5 to £10 is £5
£5 + 40p + 7p = £5.47
c) £5.43 to £5.50 is 7p d) £16.45 to £16.50 is 5p
£5.50 to £6 is 50p £16.50 to £17 is 50p
£6 to £10 is £4 £17 to £20 is £3
£4 + 50p + 7p = £4.57 £20 to £50 is £30
£30 + £3 + 50p + 5p = £33.55
95
e) £7.34 to £7.40 is 6p f) £25.73 to £25.80 is 7p
£7.40 to £8 is 60p £25.80 to £26 is 20p
£8 to £10 is £2 £26 to £30 is £4
£2 + 60p + 6p = £2.66 £30 to £40 is £10
£10 + £4 + 20p + 7p = £14.27
g) £3.40 to £4 is 60p h) £7.53 to £7.60 is 7p
£4 to £10 is £6 £7.60 to £8 is 40p
£6 + 60p = £6.60 £8 to £20 is £12
£12 + 40p + 7p = £12.47
i) £24.62 to £24.70 is 8p j) £18.64 to £18.70 is 6p
£24.70 to £25 is 30p £18.70 to £19 is 30p
£25 to £30 is £5 £19 to £20 is £1
£5 + 30p + 8p = £5.38 £1 + 30p + 6p = £1.36
k) £29.68 to £29.70 is 2p l) £32.47 to £32.50 is 3p
£29.70 to £30 is 30p £32.50 to £33 is 50p
£30 to £40 is £10 £33 to £40 is £7
£10 + 30p + 2p = £10.32 £40 to £50 is £10
£10 + £7 + 50p + 3p = £17.53
m) £17.24 to £17.30 is 6p n) £9.96 to £10 is 4p
£17.30 to £18 is 70p £10 to £20 is £10
£18 to £20 is £2 £10 + 4p = £10.04
£20 to £30 is £10
£10 + £2 + 70p + 6p = £12.76
o) £8.66 to £8.70 is 4p p) £34.27 to £34.30 is 3p
£8.70 to £9 is 30p £34.30 to £35 is 70p
£9 to £10 is £1 £35 to £40 is £5
£1 + 30p + 4p = £1.34 £40 to £60 is £20
£20 + £5 + 70p + 3p = £25.73
q) £19.84 to £19.90 is 6p £23.76 to £23.80 is 4p
£19.90 to £20 is 10p £23.80 to £24 is 20p
£20 to £40 is £20 £24 to £30 is £6
£40 to £45 is £5 £30 to 35 is £5
£5+£20+10p+6p = £25.16 £5+£6+20p+4p = £11.24
Halves and Quarters - Page 34
1) a) b) c) d) e) f)
2) C, A, B 3) 20, 10, 5, 15
Fractions - Page 35
1) a) b) c) d) e) f) g) h)
i) j)
2) a) b) c) d) e) f) g)
h) i)
Equivalent Fractions - Page 36
1) a and d 2) b and c
Writing Fractions - Page 37
1) a) b) or c) d) e) f) g) h) or
i) j) or k) l)
2) a) b) c) d) e) f)
Lists of Numbers - Page 38
1) 10, 12, 14, 23, 25, 36, 37, 47, 48, 53, 56, 64, 67, 76, 82,
86, 94, 99
2) 105, 196, 264, 287, 375, 376, 463, 476, 532, 735,
743, 745, 765, 832, 851, 856, 934, 954
3) 746 Six units
543 Four tens
976 Nine hundreds
35 Five units
725 Two tens
504 Five hundreds
754 Five tens
632 Two units
342 Three hundreds
65 Five units
864 Six tens
987 Nine hundreds
345 Five units
275 Seven tens
845 Four tens
637 Six hundreds
945 Five units
773 Seven hundreds
Approximations - Page 39
1) 60, 80, 260, 470, 70, 480, 750, 840, 750, 530, 30
2) 800, 100, 300, 800, 400, 700, 500, 600, 800, 1000,
300, 500
Number Chains - Page 40
1) a) 18, 20 b) 40, 45 c) 22, 25 d)16, 19 e) 30, 34
f) 29, 34 g) 10, 6 h) 9, 6 i) 4, 5 j) –2, –3 k) –3, –5
2) a) add 2 b) add 5 c) add 3 d) add 3 e) add 4 f) add 5
g) subtract 4 h) subtract 3 i) add 1 j) subtract 1
k) subtract 2
Money Problems 1 - Page 41
1) a) 67p b) 33p 2) £6.42 3) £3.20 4) £10.40 5) £20
6) a) 3 b) 10p 7) £4.68 8) £1.48
Money Problems 2 - Page 42
1) £17 2) 32p, 78p, £3.45, £6, £8, £10.43, £16 3) £3.30
4) 15p 5) a) 25p b) 50p c) 75p 6) 11
Rules - Page 43
12--- 1
4--- 3
4--- 1
4--- 3
4--- 1
2---
12--- 1
9--- 1
3--- 1
16------ 1
4--- 1
8--- 1
4--- 1
7---
15--- 1
6---
25--- 5
8--- 3
10------ 2
5--- 4
5--- 3
8--- 5
9---
57--- 7
12------
34--- 1
2--- 2
4--- 1
5--- 4
5--- 3
5--- 2
5--- 1
3--- 3
6--- 1
2---
16--- 2
6--- 1
3---
23--- 1
4---
34--- 1
5--- 3
4--- 1
4--- 1
2--- 1
3---
34
5 6 7
45
6 7 8
1) 2)
5
67 8 9
91011 12 13
357 9 11
1315 5
79 11 13
1517 3
69
12151821
4
812
16202428
3) 4)
96
Making Patterns - Page 44
1) a) 2 white tiles b) 2 black tiles c) 2 white tiles d) 9
2) a) 3 matchsticks b) 3 matchsticks c) 3 matchsticks d) 16
Number Machines - Page 45
1) a) 7 b) 11 c) 15 2) 7, 6, 2, 12, 5, 5
Theatre Seats - Page 46
a) 16 b) 320 c) 9L d) 13E and 15E e) 6E, 7E and 8E f) 14F
Position - Page 47
a) (8,3), (8,9), (14,9), (14,12), (8,12), (8,15), (16,15), (16,18),
(5,18)
c) (16,3), (16,6), (8,6)
2D Shapes - Page 48
a) is a square b) is a triangle c) is a rectangle
d) is a pentagon e) is a trapezium f) is a parallelogram
g) is a hexagon h) is an octagon
3D Shapes - Page 49
a) is a triangular prism b) is a cube c) is a cone
d) is a sphere e) is a pyramid f) is a cylinder
g) is a cuboid
Little Cubes - Page 50
a) 100 b) 100 c) 1000 d) 6 e) 12 f) 2 g) 1 h) 2 i) 3
Shapes Questions 1 - Page 51
1) 3 2) 4 3) 6 4) 8 5) 5 6) 4 7) 4 8) 3 9) 4 10) 8
11) 5 12) 6 13) 4 14) 4
Shapes Questions 2 - Page 52
1) 12 2) 6 3) 6 4) 1 5) 2 6) 1 7) 8 8) 3 9) 8
10) 5 11) 2 12) 8
Angles 1 - Page 53
1) (i) c (ii) g (iii) g and h (iv) a, c, d and f (v) e 2) a, b
Angles 2 - Page 54
a - smaller b - right c - smaller d - bigger e - bigger
f - bigger g - bigger h - bigger i - bigger j - smaller
k - smaller l - smaller m - right n - right o - right
p - right q - right r - bigger s - right t - right u - right
v - right w - right x - smaller y - bigger z - smaller
A - bigger B - smaller C - smaller D - right E - bigger
F - smaller G - bigger
Turning. - Page 55
Similar Shapes 1 - Page 56
b and j d and i e and g f and k h and l
Similar Shapes 2 - Page 57
a and c b and g d and j f and l h and i
Reflection Symmetry - Page 58
e)
e)
0 5 10 15 20
5
10
15
20
A
12 turn clockwise
14
34
12
14
turn clockwise
turn clockwise
turn anti-clockwise
turn anti-clockwise
a) b)
c)
d)
e) f)
g) h)
97
Reflections - Page 59
More Reflections - Page 60
Area and Perimeter - Page 61
1) a) 20 square centimetres b) 36 c) 49 d) 54 e) 30 f) 54
g) 26
2) a) 18 centimetres b) 24 c) 28 d) 30 e) 26 f) 42 g) 26
Equal Areas - Page 62
2 - h 3 - g 4 - c 5 - e 6 - a 7 - b 8 - d 9 - f
Making Rectangles - Page 63
Measurements - Page 64
1) millimetre, centimetre metre, kilometre 2) gram,kilogram 3) litre, millilitre 4) litre 5) kilometre6) millimetres 7) metre 8) kilograms 9) centimetres10) grams 11) 1 litre 12) kilometre 13) kilogram14) 1 centimetre 15) a) 50cm b) 25cm c) 200cm
Reading Scales 1 - Page 65
1) 14 b) 52 c) 527 d) 6 e) 22 f) 40 g) 250
Reading Scales 2 - Page 66
a) 140 b) 360 c) 255 d) 30 e) 76 f) 49 g) 130
Time 1 - Page 67
a) 2 o’clock b) 7 o’clock c) half past 1 or one thirty
d) quarter to 6 e) quarter past 9 f) 25 past 4 g) 20 to 7
h) 10 to 3 i) 5 past 7 j) 20 past 12 k) 25 to 12 l) 10 past 9
Time 2 - Page 68
b) 1 hour 15 minutes c) 25 minutes d) 45 minutes e) 25 minutes
Digital Times am - Page 69
a) 11:45 b) 03:30 c) 00:20 d) 05:00 e) 10:40 f) 06:50
g) 01:55 h) 04:25 i) 07:05 j) 09:35 k) 08:10 l) 02:15
Digital Times pm - Page 70
a) 14:50 b) 17:25 c) 19:00 d) 21:30 e) 23:10 f) 19:45
g) 13:15 h) 14:20 i) 15:35 j) 23:05 k) 21:40 l) 23:55
98
Sorting 1 - Page 71
a) Girls Boys
Emily Thomas
Olivia Daniel
Sophie Mathew
Lauren Mohammed
Jessica Ryan
Bethany Adam
Abigail Liam
Molly Michael
Kaylie Jacob
Eleanor Joseph
Sharron
Alice
Grace
Sarah
b) 14 girls and 10 boys
c) The girls block should be bigger than the boys block.
Sorting 2 - Page 72
a) 3
b)
Sorting 3 - Page 73
a) 41, 43, 45, 45, 46, 47, 47, 48, 48, 50, 50, 50,, 51, 51, 52,
52, 52, 53, 54, 55, 55, 56, 57, 59
b) 2
c)
d)
Finding Information 1 - Page 74
1) 5 2) 3 3) 7 4) 13 5) 14 6) 27 7) 10 8) 12 9) 7E
Finding Information 2 - 75
1) £1.15 2) £3.25 3) Fish pie 4) £4.25 5) 15p 6) 35p
Information Tables 1 - Page 76
a) 127 miles 2) 12 miles c) 139 miles d) 63 miles
e) Oswestry and Wrexham f) 69 miles
Information Tables 2 - Page 77
1) 16ºC 2) 20ºC 3) 0 4) 2mm 5) Wednesday
6) Tuesday 7) Monday and Saturday 8) Sunday and
Thursday 9) Wednesday 10) 28mm 11) 9ºC
Information Tables 3 - Page 78
a) 10:37 b) 22 minutes c) 09:50 d) 11:37 e) 6 minutes
f) 09:41 g) (i) 9:50pm (ii) 10:12pm (iii) 22:12
Calendar 1 - Page 79
a) Friday b) December 31st c) 28 days (29 each leap year)
d) 4 e) 5 f) February 11th g) January 22nd
h) February 7th i) 9
Calendar 2 - Page 80
a) Tuesday b) 11th c) September d) 13 e) Thursday
f) Monday g) 13 h) 6th September
Using Information 1 - Page 81
a) 512 kilometres b) 467 kilometres c) 192 kilometres
d) Aberdeen and London e) Liverpool and Birmingham
f) Edinburgh and Norwich g) Aberdeen and Liverpool
h) 696 + 192 = 888 kilometres i) Aberdeen
Using Information 2 - Page 82
a) 8:45 b) 20 minutes c) 7:00 d) 1 hour 45 minutes
e) 1:55 f) 20 minutes g) 4:10 h) 21:05 i) 00:10
j) Local news, Athletics and Comedy Film
Pictograms - Page 83
a) 40 b) girls c) 70 d) 5 boys e) 55 f) 85 g) 210 h) 15
Bar Charts 1 - Page 84
a) 5 b) Playing Outside c) Watching TV d) Using a
Computer e) 29 f) Twice as many pupils play outside as
listen to music
Bar Charts 2 - Page 85
a) TV b) TV Recorder c) 22 d) 27 e) 13 k) 23 g) 18 h) 103
Charts and pictograms 1 - Page 86
1) Coffee 2) 14 3) 30 3) Soup
3 sided shapes
4 sided shapes
5 sided shapes
shaded not shaded
3 1
3 5
3 3
Less than 45 kg
From 45 to 49 kg
From 50 to 54 kg
Over 54 kg
Numberof pupils
2
7
10
5
Less than45kg
From 45kgto 49kg
From 50kgto 54kg
Over54kg
2
4
6
8
10
Sandwich
Soup
Cake
Coffee
Tea
99
Charts and pictograms 2 - Page 87
a) 13, 14, 3, 9, 11 b) 13
c)
Frequency Tables 1 - Page 88
a) 8 b) 6, 8, 13, 50 c) Football d) 6 e) 8 f) 50
6) 5 people h) they don’t like sport or their favourite is
something else etc.
Frequency Tables 2 - Page 89
a) 4 b) 3 c) 6, 4, 12, 4, 3, 4 d) 33 e) 33 f) Cinema
g) Swimming h) Seaside
Putting Data into Tables 1 - Page 90
a) and b)
c) 5 d) 28 e) Bus
Putting Data into Tables 2 - Page 91a) to d)
e) 8 f) 22 g) 17 h) 5 i) the total
Years - Page 921966 - England win The World Cup
1936 - First TV station
1924 - First radio station
1918 - First World War ends
1985 - First episode of Eastenders
1947 - School leaving age raised to 15
1953 - Coronation of Queen Elizabeth II
1990 - Nelson Mandella released from jail
1912 - Titanic sinks
1969 - First man lands on the moon
1901 - Queen Victoria dies
1997 - Tony Blair becomes Prime Minister
Pop Stars
Sport
Holiday
Cartoon
Film
Type of Transport
Taxi
Bike
Car
Bus
Walk
None of These
FrequencyTally
2
5
5
8
5
3
Age Tally Frequency
10
11
12
13
14
Total
5
8
4
3
2
22