ks3 mathematics level by level pack f: level 3longhill.org.uk/resources/maths/year 7/ks3/level...

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.

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP Tel 01223 350555 Fax 01223 356484 1

KS3 Mathematics Pack F: Level 3 Introduction

Stockwell Park High School

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


KS3 Mathematics Pack F: Level 3 Introduction


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


KS3 Mathematics Pack F: Level 3 Exam 1


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




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




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




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




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




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.




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




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




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




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




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




National Curriculum references


KS3 Mathematics Pack F: Level 3 National Curriculum references


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)


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


KS3 Mathematics Pack F: Level 3 Pupil’s record form


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


KS3 Mathematics Pack F: Level 3 Answers


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




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)




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




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




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




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




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




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


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

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP Tel 01223 350555 Fax 01223 356484

KS3 Mathematics Pack F: Level 3


ks3 mathematics level by level pack f: level 3longhill.org.uk/resources/maths/year 7/ks3/level...

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