Introduction
The Key Stage 3 Mathematics series covers the National Curriculum for Mathematics (The
National Curriculum, DFE, January 1995, 0 11 270894 3). Detailed curriculum references areprovided. Each pack is designed to be flexible and can be used in a variety of ways:
• A complete course for Level 3 – The worksheets can be used to provide complete coverageof: Number and Algebra; Shape, Space and Measures; and Handling Data. The problem-solving tasks provide experience for the students in Using and Applying Mathematics.
• Individual lessons – The teacher can explain the tasks and provide the worked examples,either on the board, as overhead transparencies or as photocopied sheets for the students.Students should then attempt the exercises.
• Teacher’s lesson notes – The notes and examples are useful for new teachers and can formthe basis of lesson plans.
• Absent students – The notes, examples and exercises can be used by students during long-term absence or to help them catch up after absence.
• Teacher’s absence – If a teacher is absent, a double-sided worksheet (notes and examples onone side, exercises on the other) can be provided for students. This will allow the students tocontinue with learning the curriculum.
• Examination revision – The notes and examples can be issued to students shortly before theexamination for revision purposes.
The pack includes:
• Notes and worked examples
• Exercises
• Coursework tasks for AT1 – Using and Applying Mathematics
• Examination papers containing National Curriculum-type questions
• Using and Applying Mathematics problem-solving tasks
• Pupil’s record form
• Answers.
Using the notes and examples
Students should fold the worksheet so that the answers cannot be seen. They can then read thenotes, try the questions, and then check their answers.
Exam papers
The pack contains four exams. If all four examinations are set, the contents of Number andAlgebra, Shape, Space and Measures, and Handling Data will have been covered at Level 3. Thetests are designed to draw together work done in this pack.
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Each question is related to a specific part of the National Curriculum as indicated on the charton page 58.
It is also possible to use each exam paper as homework sheets in preparation for the end of KeyStage 3 tests.
Pupil’s record form
This allows the success of students to be recorded using the results on the exercises andexamination questions. Either a tick/cross system or a mark system may be used.
End of term activities
The game ‘Robot’ allows students to practice mental arithmetic skills in addition andmultiplication (page 36).
Using and Applying Mathematics
The puzzle ‘Fort Knox’ on page 14 can be extended to produce a problem solving task. ‘Whatconditions are required for all of the gold bars to be stolen?’ The answers to the puzzle aregiven on page 65.
Stafford BurndredJune 1997
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KS3 Mathematics Pack F: Level 3 Introduction
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Exam 1
1 Here are some numbers on cards:
a Write the numbers in words. __________________________________________
b The 2 means two lots of ten.
Complete these statements:
The 7 means ________ lots of ________
The 8 means ________ lots of ________
Rearrange the cards to make other numbers.
c What is the largest number you can make?
d What is the smallest number you can make?
2 This ruler is used to measure the pencil.
a What is the length of the pencil? _________________________________
b What is the length to the nearest 10 millimetres?___________________
c What is the length to the nearest 100 millimetres?__________________
0 10 20 30 40 50 60 70 80 90 100
Millimetres
7 2 8
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d This arrow shows 723 written to the nearest hundred is 700. Draw arrows toshow the value of the other numbers to the nearest hundred.
723 600
681 700
783 800
617
e Each of the boxes contains ten eggs.
i How many eggs can you see? _____________________________________
ii Write this number to the nearest ten. _______________________________
3 Sally has these coins. How much money does she have? ____________________
Paul has these coins. How much money does he have?______________________
4 Tom buys this bar of chocolate. He pays with a £5 note.
How much change does he receive? ______________________________________
£1 £1 2p 1p
£1 £1 50p 20p
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KS3 Mathematics Pack F: Level 3 Exam 1
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YUM
CHOCOLATE30p
5 What temperature is shown on this thermometer? __________________________
Here are some numbers. Draw a circle around the negative numbers:
–4 3 6 –1 8
6 Fill in the missing numbers to make these sums correct:
13 + 6 =
+ 2 = 8
15 – = 11
– 6 = 7
7 Today is Friday the 13th of July.
What was the date last Friday? ___________________________________________
What will the date be next Friday? ________________________________________
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Exam 2
1 We can make 8 like this:
Fill in the boxes to show the different ways we can make 12.
2a Paula bought 6 bars of chocolate.
Each bar had 10 squares.
How many squares did she have?_________________________________________
b Paula, Jayne, David and Alan share the chocolate equally.
How many squares does each person receive? _____________________________
x = 12
x = 12
x = 12
x = 12
x = 12
x = 12
1 x 8 = 8
2 x 4 = 8
4 x 2 = 8
8 x 1 = 8
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3 Carly has these coins:
She wants to buy some lollipops.
How many lollipops can she buy?_________________________________________
4 Mr Green decides to buy a can of cola for each pupil in his class. There are 27students in his class.
Tins of cola are bought in boxes of 12.
How many boxes should he buy? _________________________________________
5 Use your calculator to answer this question.
Golf balls are packed in boxes of 12. A sports shop ordered 876 golf balls. Howmany boxes were needed?
Write down the calculator keys you pressed.
Show the answer displayed in your calculator.
Lollipops 4p each
10p 10p 10p 5p
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KS3 Mathematics Pack F: Level 3 Exam 2
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6 John adds these numbers in his head:
263 + 125First he adds the hundreds
Then he adds the tens
Then he adds the units
Total
How would he add these numbers in his head?
713 + 162Fill in the missing numbers:
First he adds the hundreds
Then he adds the tens
Then he adds the units
Total
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KS3 Mathematics Pack F: Level 3 Exam 2
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200 100 300+ =
60 20 80+ =
3 5 8+ =
300 80 8+ + 388=
700 100+ =
60+ =
+ =
+ + =
Exam 3
1 These shapes could be sorted into circles and triangles.
How many circles are there? _____________________________________________
How many triangles are there? ___________________________________________
John decides to put the shapes into four groups.
One group is shaded triangles.
Suggest three other groups:
a _____________________________________________________________________
b _____________________________________________________________________
c _____________________________________________________________________
2 These patterns have line symmetry. Draw a dotted line on each picture to show themirror line.
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KS3 Mathematics Pack F: Level 3 Exam 3
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The dotted line is a line of symmetry. Complete the picture.
3 Here are some units used for measuring:
Place the units in the correct groups. Some have been done for you.
Capacity
litre
Time
second
Length
millimetre
Weight (mass)
gram
litre
kilogram
millimetre
metre
minute
kilometre
centilitre
day
hour
centimetre
second
millilitre
gram tonne
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KS3 Mathematics Pack F: Level 3 Exam 3
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4 Here is some information. The arrow links the activity to the time taken.
Washing the dishes takes about 10 minutes. This is shown by the arrow. Draw arrowsto show the time other activities take.
Now put the times in order, shortest first.
_______________________________________________________________________________
Activity Time
Washing the dishes
5 seconds
Yawning
10 minutes
A TV advert
3 hours
Building a house
12 weeks
Travelling from London to Manchester
by train 30 seconds
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Exam 4
1 This is a price list in a café:
a What is the price of a large fish?_______________________________________
b Mr Ralph bought two large sausages, one small fish and two small chips.
What was the total cost?______________________________________________
c John bought one item. It cost 45p. What did he buy?____________________
d Anna bought two different items. The total cost was 90p. What did she buy?
____________________________________________________________________
2 This bar chart shows how the students in Miss Riley’s class arrived at school:
a How many students arrived by car? ___________________________________
b Complete these sentences:
i 3 students arrived by____________________________________________
ii 8 students arrived by____________________________________________
c How many students were in Miss Riley’s class? _________________________
0
1
2
3
4
5
6
7
8
BusCar
Nu
mb
er o
f p
up
ils
Bike Walk
Small Regular Large
60p 70pChips 90p
40p 65pSausage 80p
£1.30 £1.80Fish £2.20
30p 45pPeas 55p
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KS3 Mathematics Pack F: Level 3 Exam 4
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3 This pictogram shows the number of planes landing at an airport:
a How many planes landed on Monday? ________________________________
b How many planes landed on Tuesday? ________________________________
c How many planes landed on Wednesday? _____________________________
d 20 planes landed on Thursday. Complete the pictogram.
e 12 planes landed on Thursday. Complete the pictogram.
f Which day did most planes land at the airport?
___________________________________________________________________
Monday
Tuesday
Wednesday
Thursday
Friday
Represents 10 planes
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4 This table shows the number of computers in schools:
Show this information in this bar graph. Arden School has been drawn for you.
Complete this pictogram.
Arden School
represents 10 computers
Bolden School
Calden School
Delby School
Exton School
0
5
10
15
20
25
30
35
40
ArdenSchool
Nu
mb
er o
f co
mp
ute
rs
Arden School
Bolden School
Calden School
Delby School
Exton School
40
30
25
12
18
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KS3 Mathematics Pack F: Level 3 Exam 4
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National Curriculum references
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Pupils show understanding of place value in numbersup to 1000 and use this to make approximations
They have begun to use decimal notation
They have begun to use negative numbers in contextssuch as money, temperature and calculator displays
Pupils use mental recall of addition and subtractionfacts to 20 in solving problems involving largernumbers
They use mental recall of the 2, 5 and 10 multiplicationtables and others up to 5 x 5 in solving whole numberproblems involving multiplication or division, includingthose that give rise to remainders
Pupils use calculator methods where numbers includeseveral digits
They have begun to develop mental strategies anduse them to find methods for adding and subtractingnumbers with at least two digits
Pupils classify 3-D and 2-D shapes in various waysusing mathematical properties such as reflectivesymmetry
They use non-standard units and standard metric unitsof length, capacity, mass and time in a range ofcontexts
Pupils extract and interpret information presented insimple tables and lists
They construct bar charts and pictograms where thesymbol represents a group of units. To communicateinformation they have gathered, and they interpretinformation presented to them in these forms
Place value 1 1Approximations 1 2
Decimals: Money 1 3Using a calculator 1 4
Negative numbers 1 5
Addition and subtraction facts 1 61 7
Tables 2 12 2
Whole number problems includingremainders 2 3
2 4
Calculator skills 2 5
Addition and subtraction(Mental arithmetic) 2 6
2-D and 3-D shapes 3 1Reflective symmetry 3 2
Measures 3 3Time 3 4
Tables and lists 4 1
Bar charts 4 2Pictograms 4 3Pictograms, bar charts and tables 4 4
Exam
Que
stio
nLevel 3
Number and Algebra Topic title
Shape, Space and Measures
Handling Data
Pupil’s record form
Name: _____________________________ Form:___________________
Teacher: ____________________________ Exam marks: ____________
Exercises Exam Exam questionscompleted answered
Number and Algebra
Place value 1 1
Approximations 1 2
Decimals: Money 1 3
Using a calculator 1 4
Negative numbers 1 5
Addition and subtraction facts 1 6
1 7
Tables 2 1
2 2
Whole number problems includingremainders 2 3
2 4
Calculator skills 2 5
Addition and subtraction 2 6
(mental arithmetic)
Shape, Space and Measures
2-D and 3-D shapes 3 1
Reflective symmetry 3 2
Measures 3 3
Time 3 4
Handling Data
Tables and lists 4 1
Bar charts 4 2
Pictograms 4 3
Pictograms, bar charts and tables 4 4
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KS3 Mathematics Pack F: Level 3 Pupil’s record form
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Answers
Place value (page 4)1 Seventy-eight 2 Four hundred and eighty-nine
3 Eight hundred and six 4 Three hundred and ninety-nine
5 300 6 568
7 754 8 260
9 966 10 400
11 4 12 4
13 40 14 40
15 400 16 389
17 999 18 132 318 416 902
19 87 222 303 535 20 892 810 684 529
21 943 913 391 139 22 1000 999 687 98
Approximations (page 5)1 20 2 50 3 60
4 40 5 120 6 270
7 470 8 580 9 240
10 200 11 100 12 200
13 0 14 100 15 100
16 700 17 600 18 700
19 700 20 900
21 a 380 b 400
22 a £830 b £800
23 1000
24 a 440 b 400
25 a 380 b 400
Decimals: Money (page 8)1 £2.35 2 £3.40 3 £3.04
4 £4.01 5 £2.23 6 £3.32
7 £0.33 or 33p 8 £1.08 9 £5.83
10 £6.62 11 £9.50 12 £8.42
13 £2.89 14 £11.06 15 £3.50
16 £3.40 17 £1.76 18 £4.30
Using a calculator (page 10)1 £1.79 2 £3.66 3 £2.72
4 £0.93 or 93p 5 £1.64 6 £0.63 or 63p
7 £2.62 8 £2.19 9 £3.70
10 £0.03 or 3p 11 £4.15 12 £4.64
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13 £4.13 14 £4.66 15 £4.80
16 £2.14 17 £2.69 18 £3.32
19 £1.67 20 £3.35
21 The items cost £5.49. Mr Smith only has £5.
22 £4.05 23 £143.92 24 £299.80
25 £22.95 26 £23.99 27 £9.95
28 £64.95 29 £0.18 or 18p 30 £0.23 or 23p
Negative numbers (page 12)1 4 2 –2 3 –1
4 0 5 5 6 3
7 –1 8 1 9 –4
10 –4 11 –3 –1 2 4 8 12 –6 –3 –2 –1 4
13 –12 –7 –1 0 3 14 –1° 15 1°
16 –2° 17 –3° 18 2°
19 –4° 20 0° 21 Saturday
22 Temperature of –3° shown
Negative numbers (page 13)1 Balloon 2 Anchor
3 Swimmer 4 Treasure chest
5 Fish 6 Seagull
7 Shark 8 Parachute
9 Diver 10 Penguin
11–15 Check pictures on worksheet
Addition and subtraction facts (page 16)1 11 2 17 3 8
4 7 5 18 6 7
7 17 8 6 9 19
10 15 11 18 12 11
13 8 14 15 15 8
16 2 17 25 18 11
19 8 20 13 21 11
22 11 23 17 24 15
25 11th June 26 20th April
Tables (page 18)1 12 eggs 2 £80 3 9
4 7 5 16 6 9
7 7 8 £3 9 £16
10 8 11 6 12 10
13 4
14 Two times six is 6 larger 15 £40
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Whole number problems involving remainders (page 20)1 9 2 2 3 4
4 5 5 8 6 3
7 5 8 8 9 8
10 9 11 8 12 6
Calculator skills (page 22)1 816 2 77 3 16
4 754 5 153 6 882
7 483 8 444
Addition and subtraction (page 24)1 56 2 75 3 78
4 77 5 78 6 27
7 32 8 26 9 72
10 65 11 74 12 55
13 72 14 77 15 96
16 38 17 29 18 5
19 36 20 13 21 92
22 40 23 26 24 58
25 23 26 88 27 66
28 17 29 36 30 98
31 86 32 41 33 15
34 857 35 588 36 214
37 56 38 170 39 793
40 430
2-D and 3-D shapes (page 26)1 a B, D, F, G b A, C, E c C, D, G
d A, B, E, F e B
2 a 1, 2, 3, 5, 8 b 1, 2, 4, 6 c 3, 7
d 1, 2, 3 e Shapes with four straight sides
Reflective symmetry (page 28)
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1 2
3 4
5 6
7 8
Measures (page 30)1 E Tape measure 2 C Ruler 3 B Clock
4 A Kitchen scales 5 H Bathroom scales 6 D Measuring jug
7 G Stopwatch 8 F Thermometer 9 Litres
10 Tonnes 11 Metres 12 Centimetres
13 Kilograms 14 Kilometres 15 Tonnes
Time (page 32)1 Nine o’clock 2 Twenty past ten 3 Five to three
4 Twenty-five to twelve
5-12 Correct times
13 9.10 14 Five to nine 15 5.40
16 Quarter past four 17 8.30
Tables and lists (page 34)1 60p 2 70p 3 £1.10
4 £1.80 5 85p 6 £1.00
7 75p 8 £2.40 9 £1.05
10 60p 11 90p 12 £1.20
13 80p 14 50p 15 £1.40
16 Small cola 17 Giant burger 18 Extra large cola
19 Small burger 20 Medium burger 21 Giant fries
22 Extra large fries 23 Extra large burger 24 Large cola
25 Large fries 26 Small cola 27 Giant burger
28 £2.35 29 £3.95 30 £2.20
Tables and lists (page 35)1 2 3
Bar charts (pages 38 and 39)1 a 2 b 5 c 6
d 5 e 3 f 21
g Swimming h Netball
2 a 12 b 5 c 3
d 7 e 27 f Pop
g Heavy rock
3 a 6 b 9 c 3
d 10 e Perch f Tench
g 28
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Type of horse
Shire
Falabella
Shetland
Race Horse
Weight (Mass)
700 kg
80 kg
190 kg
400 kg
Tom
Suzy
Ben
Height
3 m
5 m
6 m
Kenny
Tom
Paul
Distance
40 m
35 m
55 m
4 a 15 (approx) b 50 c 65 (approx)
d 30 e Tea f Orange juice
g 160 (approx)
Pictograms (page 41 and 42)1 a 6 b 4 c 5
d 7 e f
2 a 400 b 300
c 250 (any answer near to this)
d Any answer over 100 and under 150
e Any answer over 250 and under 300
f
g
Pictograms, bar charts and tables (pages 43 to 45)1 a b
2 Monday 10
Tuesday 5
Wednesday accept 6 or 7
Thursday accept 8 or 9 do not accept fractions, eg 61/2
Friday accept 1 or 2
(check students graphs to see results.)
3 a 18 b 9 c 5
d 4 e
4 a Monday 3 symbols
Tuesday 21/2 symbols
Wednesday slightly less than 2 symbols
Thursday slightly more than 2 symbols
Friday slightly less than 1 symbol
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0 1 2 3 4 5 6 7 8 9
Number of yachts
Co
lou
rs
Red
Green
White
Blue
Black
Green
White
Blue
Black
Red
Red
Blue
Green
b
Fort Knox (page 14)There are several correct routes.
(Note: All bars can be stolen in vaults 1, 2 and 4.)
1 1 ➞ 2 ➞ 3 ➞ 6 ➞ 9 ➞ 8 ➞ 5 ➞ 4 ➞ 7. Gold bars stolen 45
2 1 ➞ 6 ➞ 7 ➞ 2 ➞ 3 ➞ 8 ➞ 9 ➞ 4 ➞ 5 ➞ 10 ➞ 15 ➞ 14 ➞ 13 ➞ 12 ➞ 11. Gold bars stolen 120
3 1 ➞ 5 ➞ 6 ➞ 7 ➞ 3 ➞ 4 ➞ 8 ➞ 12 ➞ 11 ➞ 10 ➞ 9 ➞ 13 ➞ 14 ➞ 15 ➞ 16. Gold bars stolen 134
4 1 ➞ 6 ➞ 7 ➞ 2 ➞ 3 ➞ 8 ➞ 9 ➞ 4 ➞ 5 ➞ 10 ➞ 15 ➞ 14 ➞ 13 ➞ 12 ➞ 11 ➞ 16 ➞ 17 ➞ 18 ➞ 19 ➞ 20 ➞ 25 ➞ 24 ➞ 23 ➞ 22 ➞ 21. Gold bars stolen 325
Exam 1 (page 46)1 a Seven hundred and twenty-eight (1 mark)b 7 lots of 100 (1 mark)
8 lots of 1 (1 mark)c 872 (1 mark)d 278 (1 mark)
2 a 78 mm (1 mark)b 80 mm (1 mark)c 100 mm (1 mark)d 681➞ 700 (1 mark)
783 ➞ 800 (1 mark)617➞ 600 (1 mark)
e i 42 (1 mark)ii 40 (1 mark)
3 Sally £2.70 (1 mark)Paul £2.03 (1 mark)
4 £4.70 (1 mark)
5 -3 (1 mark)-4 3 6 -1 8 (1 mark each) (2 marks)
6 19 (1 mark)6 (1 mark)4 (1 mark)13 (1 mark)
7 6th of July (1 mark)20th of July (1 mark)
Total 25 marks
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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Friday
Thursday
Wednesday
Tuesday
Monday
Exam 2 (page 49)
1 (1 mark)
(1 mark)
(1 mark)
(1 mark)
(1 mark)
(1 mark)
2 a 60 (2 marks)b 15 (2 marks)
3 8 (2 marks)
4 3 (2 marks)
5(2 marks)(1 mark)
6 (1 mark)
(2 marks)
(2 marks)
(3 marks)
Total 25 marks
Exam 3 (page 52)1 5 circles (1 mark)7 triangles (1 mark)
Shaded circles (1 mark)Unshaded circles Any order. Accept other sensible groups (1 mark)Unshaded triangles (1 mark)
2 (1 mark each) (3 marks)
112
26
34
43
62
121
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78 6 ÷ 137
2 =
10 +
+
+
+
3
800
=
=
+
=
2
70
70
5
5
800
= 875
3 Capacity Centilitre (1 mark)Millilitre (1 mark)
Time Minute (1 mark)Hour (1 mark)Day (1 mark)
Length Centimetre (1 mark)Metre (1 mark)Kilometre (1 mark)
Weight (Mass) Kilogram (1 mark)Tonne (1 mark)
4 Yawning 5 seconds (1 mark)TV advert 30 seconds (1 mark)Building a house 12 weeks (1 mark)Train 3 hours (1 mark)
5 seconds, 30 seconds, 10 minutes, 3 hours, 12 weeks (3 marks)
Total 25 marks
Exam 4 (page 55)1 a £2.20 (1 mark)
b £4.10 (3 marks)c Regular peas (1 mark)d Small chips, small peas (2 marks)
2 a 4 (1 mark)b i Bike (1 mark)
ii Walking (1 mark)c 21 (1 mark)
3 a 40 (1 mark)b Accept 26, 27, 28 or 29 (1 mark)c Accept 21, 22, 23 or 24 (1 mark)
d (1 mark)
e (1 mark)
f Monday (1 mark)
4
(4 marks)
(1 mark)
(1 mark)
(1 mark)
(1 mark)
Total 25 marks
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0
5
10
15
20
25
30
35
40
ArdenSchool
BoldenSchool
CaldenSchool
DelbySchool
ExtonSchool
Arden School
Bolden School
Calden School
Delby School
Exton School
Contents
Introduction .................................................................................................................................... 1
Number and Algebra
Place value ...................................................................................................................................... 3
Approximations ............................................................................................................................... 5
Decimals: Money............................................................................................................................. 7
Using a calculator ............................................................................................................................ 9
Negative numbers........................................................................................................................... 11
Puzzle: Fort Knox............................................................................................................................. 14
Addition and subtraction facts ........................................................................................................ 15
Tables .............................................................................................................................................. 17
Whole number problems involving remainders .............................................................................. 19
Calculator skills................................................................................................................................ 21
Addition and subtraction (mental arithmetic) ................................................................................. 23
Shape, Space and Measures
2-D and 3-D shapes ........................................................................................................................ 25
Reflective symmetry ........................................................................................................................ 27
Measures ......................................................................................................................................... 29
Time................................................................................................................................................. 31
Handling Data
Tables and lists ................................................................................................................................ 33
Game: Robot ................................................................................................................................... 36
Bar charts......................................................................................................................................... 37
Pictograms....................................................................................................................................... 40
Pictograms, bar charts and tables................................................................................................... 43
Exam papers................................................................................................................................... 46
National Curriculum references .................................................................................................... 58
Pupil’s record form ........................................................................................................................ 59
Answers .......................................................................................................................................... 60
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KS3 Mathematics Pack F: Level 3
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