KS3 Maths Level by Level Pack A: Level 4

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Key Stage 3 Mathematics

Level by Level

Pack A: Level 4

Stafford Burndred

ISBN 1 899603 22 0

Published by Pearson Publishing Limited 1997

© Pearson Publishing 1995

A licence to copy the material in this pack is granted to the purchaser strictly within theirschool, college or organisation. The material must not be reproduced in any other formwithout the express permission of Pearson Publishing.

Pembrokeshire e-Portal Licence exp 31Aug10

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

Place value

765 432 – This means seven hundred and sixty-five thousand, four hundred and thirty-two.

Ascending order means going up.(small to large)

Descending order means going down.(large to small)

1 000 000 This is one million500 000 This is half of a million250 000 This is a quarter of a million

Questions

1 Write the following numbers in words:

a 5020 _____________________________________________________________

b 36 240 _____________________________________________________________

2 Place the following numbers in ascending order:

5372 6843 1998 9081 8762

___________________________________________________________________________

3 Place the following numbers in descending order:

3827 4654 2838 4009 2816

___________________________________________________________________________

Answers1 a Five thousand and twenty

b Thirty-six thousand, two hundred and forty

2 1998, 5372, 6843, 8762, 9081

3 4654, 4009, 3827, 2838, 2816

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

KS3 Mathematics Pack A: Level 4 Number and Algebra


7 6 5 4 3 2

Seven hundred thousands

Five thousands Three tens

Two unitsSix ten thousands

Four hundreds

Place value

Exercises

1 What is the next whole number after one hundred thousand? Write your answer infigures. _____________________________________________________________________

2 What is the last whole number before twenty-five thousand? Write your answer infigures. _____________________________________________________________________

3 Write a quarter of a million in figures. __________________________________________

4 Write the following numbers in words:

a 72 368 ______________________________________________________________

b 4726 ______________________________________________________________

c 203 652 ______________________________________________________________

d 752 473 ______________________________________________________________

e 829 878 ______________________________________________________________

5 In the following lists of numbers put a circle around the smallest number andunderline the largest:

a 732 1011 899 6732 3005 8049

b 12 736 2385 1729 5621 10 999 2003

c 689 372 4593 78 736 4999 18 213 582 731

d 1001 2022 80 030 4000 3040 50 201

e 2386 4752 3913 6862 1479 5368

6 Place the following numbers in ascending order, ie smallest first:

a 573 862 731 472 861

______ ______ ______ ______ ______

b 301 804 600 899 901

______ ______ ______ ______ ______

c 2004 3809 6112 5328 7401

______ ______ ______ ______ ______

d 7203 5008 2999 6800 3711

______ ______ ______ ______ ______

e 8729 986 797 3284 7010

______ ______ ______ ______ ______




Multiplication facts

You must learn these multiplication tables:

1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 5 1 x 6 = 6

2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12

3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18

4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24

5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30

6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36

7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42

8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 40 8 x 6 = 48

9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45 9 x 6 = 54

10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50 10 x 6 = 60

1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 1 x 10 = 10

2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20

3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30

4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40

5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50

6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60

7 x 7 = 49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 70

8 x 7 = 56 8 x 8 = 64 8 x 9 = 72 8 x 10 = 80

9 x 7 = 63 9 x 8 = 72 9 x 9 = 81 9 x 10 = 90

10 x 7 = 70 10 x 8 = 80 10 x 9 = 90 10 x 10 =100

If you multiply a whole number by 10 add one nought.For example, 24 x 10 = 240

If you multiply a whole number by 100 add two noughts.For example, 82 x 100 = 8200

If you divide a whole number by 10 remove one nought.For example, 360 ÷ 10 = 36

If you divide a whole number by 100 remove two noughts.For example, 7200 ÷ 10 = 72

Questions

1 What is the missing number:

a 3 x = 24 b ÷ 4 = 7 c 30 ÷ = 6

2 Work out the following:

a 36 x 10 = b 478 x 100 = c 3200 ÷ 100 =

Answers1 a 8, b 28, c 5

2 a 360, b 47 800, c 32




Multiplication facts

Exercises

1 Fill in the missing numbers. Do not use a calculator.

a 9 x 8 = b x 9 = 36 c x 8 = 24

d x 7 = 35 e 8 x = 56 f 24 ÷ = 3

g ÷ 5 = 3 h 36 ÷ = 4 i ÷ 9 = 6

2 Complete the following:

a 7 x 100 = b 28 x 100 = c 3400 ÷ 100 =

d What is the cost of 100 pencils at 8p each? _________

e What is the cost of 10 rulers at 27p each? _________

3 Mrs Green has 46 boxes of light bulbs. Each box contains 10 light bulbs. How many light bulbs does she have? _________

4 Boxes of crisps each contain 48 packets. The local supermarket has 100 boxes. How many packets is this? _________

5 How many pence are in £16? _________

6 Mrs White bought 10 chairs for £240.How much was each chair? _________

7 Mr Davis bought ten boxes of matches at 16p per box.How much did he pay? _________

8 Miss Machin bought 12 boxes of pens. Each box contained 10 pens and cost 80p.She sold the pens for 10p each.How much profit did she make? _________




Solving problems without a calculator

If the examination has this means you must not use a calculator.

If the examination question states ‘show your working’, you must show your working.If you do not you will lose marks.

Answering problems

Read the question carefully. Try to decide if it is an add, take away, multiply or dividequestion.

If the numbers are large and you do not know if you should add, take away, multiply ordivide try putting easier numbers in the question to help you decide.

Questions

1 Work out the following:

a 3 6 b 92 ÷ 4x 8___

c 8 2 7 d 4 7 2+ 1 8 9 - 1 3 9_______ _______

2 48 sweets were divided equally between 8 girls.How many sweets did each girl receive? _________

Answers1

2 48 ÷ 8 = 6




C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

3 6

x 8

2 8 8

4

2 3

4 9 2

4 7 2

- 1 3 9

3 3 3

8 2 7

+ 1 8 9

1 0 1 6

1 1

1

16dc

baYou must show the 4.

If you do not you

will lose marks.

You must show the 1.

You must show the

numbers you carry.

You must show

your method.

Solving problems without a calculator

Exercises

1 7 2 1 2 4 3 8 3 8 0 7 4 7 8 6+ 1 3 4 + 2 8 1 + 3 4 6 - 3 2 1_____ ______ ______ ______

5 7 8 3 6 5 0 3 7 7 2 8 6 7- 5 2 9 - 2 7 8 x 8 x 7_____ _____ ____ ____

9 7 4 10 81 ÷ 9 11 72 ÷ 8 12 91 ÷ 7x 8_____

13 7 boys each had 8 books. How many books did they have altogether? _________

14 8 cats each had 3 kittens. How many kittens were there? _________

15 A classroom had 32 chairs. They were placed in rows of 8. How many rows were there? _________

16 There were 9 trains in a station. Each train had 7 carriages.How many carriages were there? _________

17 A car park has enough spaces for 276 cars. If there are 87 empty spaces how manycars are in the car park? _________

18 One car can carry five people.How many cars are needed to carry 35 people? _________

19 42 tins were placed in seven boxes. How many tins were in each box? _________




C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

Addition and subtraction of decimals

Exercises

1 3 1 · 2 4 2 7 2 3 · 4 3 8 · 4 3 4 6 0

+ 4 3 · 1 2 + 4 6 · 8 + 2 · 4 + 3 · 4_________ ________ _______ _______

5 8·73 + 14 + 0·82

6 5·9 + 13·64 + 17

7 16·8 + 27·04 + 40

8 7 3 · 6 4 9 1 7 · 3 2 10 1 5 · 8 3 11 1 6

- 2 1 · 3 1 - 1 4 · 1 1 - 3 · 6 - 4 · 3 2_________ ________ ________ ________

12 4 · 6 3 13 4 8 · 2 9 14 1 8 15 1 6 · 4

- 1 · 0 2 - 3 · 7 1 - 1 · 3 - 1 · 3 7_______ ________ ______ ________

£ £ £ £

16 7 · 2 8 17 5 · 8 0 18 6 · 1 7 19 6 · 2 0

3 · 6 4 1 · 0 3 3 · 2 4 - 3 · 1 4

+ 5 · 4 7 + 3 · 2 7 + 8 · 1 4_______

_______ _______ _______

20 Mr Jones buys a book for £3.75 and a cassette for £6.99. He pays with a £20 note.How much change does he receive? _________

21 A plank of wood is 8.42 m long. 3.78 m is cut off. How much is left? _________

22 Michael has £18.37. He buys a tie for £2.99 and a shirt for £7.49.How much money does he have left? _________




C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

The boat problem

Once there was a man whohad to take a fox, a chickenand a sack of grain across ariver. He had a boat, but hecould only fit himself andone other object in theboat.

He must never leave the foxand the chicken togetherfor, unless he is with them,the fox will eat the chicken.He must never leave thechicken and the sack ofgrain together for, unless heis with them, the chickenwill eat the grain.

Fill in the pictures to show how the man takes everything across the river. Use a pencil,then you can rub out if you make a mistake.

The minimum number of journeys is 7.


KS3 Mathematics Pack A: Level 4 Using and Applying Mathematics


��

��

Start

Finish

River

��

��

Start

Finish

Calculation checks

Whole numbers are numbers to the left of the decimal point.

When writing a number correct to the nearest whole number you must look at the firstnumber after the decimal point.

If the first number after the decimal point is 5 or more (ie 5, 6, 7, 8, or 9) then thewhole number increases by 1.

If the first number after the decimal point is 4 or less (ie 0, 1, 2, 3, or 4) then the wholenumber stays the same.

376.824 written to the nearest whole number is 377.428.374 written to the nearest whole number is 428.

Question

Estimate the total amount of money:£3128 + £6280 +£5972 + £5310 + £8089 _________

AnswerIf the question asks for an estimate you must approximate each number. You must show all of your working.

£3128 is approximately £3000





Total £28 000

You must not add the numbers with a calculator and then approximate that answer. Look what happens:£3128 + £6280 +£5972 + £5310 + £8089 = £28 779

£28 779 is approximately £29 000

If you write the answer £29 000 without working you will obtain no marks.




3 6 8 . 4 7 2

whole numbers 4 is the first number after the decimal point

3 4 5

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7

Calculation checks

Exercises

1 Write the following correct to the nearest whole number.

a 3.2 _______ b 5.7 _______ c 6.4 _______

d 8.9 _______ e 7.5 _______ f 16.8 _______

g 42.6 _______ h 53.8 _______ i 47.29 _______

j 42.54 _______ k 37.3872 _______ l 47.9316 _______

m 127.3 _______ n 274.8 _______ o 569.37 _______

p 29.8 _______ q 39.53 _______ r 199.096 _______

s 48.9003 _______ t 89.711 _______ u 9.6 _______

2 The answers to some questions are shown. Three answers are wrong. Which ones?Show how you checked the answer.

a 38.5 x 621 = 239.088 __________________________________________________

b 7038 ÷ 51 = 138 __________________________________________________

c 4.98 x 21 = 1045.8 __________________________________________________

d 319 x 8.9 = 28391 __________________________________________________

e 604.5 ÷ 31 = 19.5 __________________________________________________

In each of the following questions underline which answer is the best estimate:

3 7987 + 1007 choose from a 7000 b 8000 c 9000 d 10 000

4 599 + 304 choose from a 700 b 800 c 900 d 1000

5 3108 + 3887 choose from a 8000 b 7000 c 6000 d 5000

6 7998 + 3999 choose from a 9000 b 10 000 c 11 000 d 12 000

7 997 + 3012 choose from a 4000 b 3500 c 3000 d 2000

8 597 - 199 choose from a 300 b 398 c 400 d 500

9 802 - 399 choose from a 300 b 400 c 403 d 450

10 1997 - 1302 choose from a 400 b 500 c 600 d 700

11 1604 - 896 choose from a 700 b 708 c 750 d 80




C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

Fractions and percentages

3/4 means three parts out of every four parts.

3/4 means three parts out of every four parts.

this glass is this glass is this glass is this glass is1/2 full 3/4 full 2/3 full 1/4 full

50% means 1/2

25% means 1/4

75% means 3/4

25% of this shape is shaded

Questions

1 Shade 5/8 of this shape:

2 Mark a point P which is 2/3of the way from A to B:

3 Shade 75% of this shape:

Answers




BA

BAP

Shade any five sections. Shade any three sections.

1 2 3

Fractions and percentages

Exercises

1 Shade 50% of this shape:

2 Shade 1/8 of this shape in red:

Shade 5/8 of this shape in blue:



5 Look at this line:

a Mark a point X which is halfway between P and Q.

b Mark a point Y which is 1/3 of the way from P to Q.

c Mark a point Z which is 3/4 of the way from P to Q.




QP

Number patterns 1

Square numbers

Triangle numbers

Breaking patterns

Try finding the difference between the numbers: 1, 4, 7, 10, 13, 16.Add 3 each time.

Multiples

The multiples of 3 are 3, 6, 9, 12, 15, etc.Any number in the 3 times table is a multiple of 3, eg 36, 42, 300.

Factors

The factors of 12 are 1, 2, 3, 4, 6, 12.Any number which will divide exactly into 12 is a factor of 12.

Question

What are the next two numbers in each pattern? Describe the pattern.

a 3, 7, 11, 15, 19, ____, ____

___________________________________________________________________________

b 3, 12, 48, 192, 768, 3072, ___________, _____________

___________________________________________________________________________

Answera 23, 27. Add 4 to the previous number.

b The next two numbers are 12 288 and 49 152.The pattern is obtained by multiplying the previous number by 4.




1 (1 x 1)

4 (2 x 2)

9 (3 x 3)

16 (4 x 4)

25 (5 x 5)

1 3 6 10 15

Number patterns 1

Exercises

Find the next two numbers in each pattern. Explain the pattern in words.

1 1, 3, 5, 7, 9, 11, ___ , ___

________________________________________________________________________

2 50, 45, 40, 35, 30, 25, ___ , ___

________________________________________________________________________

3 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, ___ , ___

________________________________________________________________________

4 1, 1, 2, 3, 5, 8, 13, 21, 34, ___ , ___

________________________________________________________________________

Complete the next pattern. Explain the pattern.

5

________________________________________________________________________

6

________________________________________________________________________

7

________________________________________________________________________

8 Write 3 multiples of 6.

________________________________________________________________________

9 Write all the factors of 24.

________________________________________________________________________

10 Write all the factors of 18.

________________________________________________________________________




Number patterns 2

Exercises

Look at these numbers:

1 What do you have to do to the numbers in column 1 to make the numbers incolumn 2? __________________________________________________________________






7 Complete these number patterns:

a 5000 x 7 = 500 x 70 = x 700 = x

b 80 000 x 3 = 8000 x = x 300 = x

= x

c 10 + 0 = 8 + 2 = 6 + 4 = + = +

= +

d 256 x 1 = 64 x 4 = 16 x = x 64 = x

8 Explain how you worked out the pattern in question 7d.__________________________________________________________________________

Column 1 Column 2 Column 3 Column 4 Column 5

1 2 3 4 5 6 7

3 6 9

12 15 18 21

5 8

11 14 17 20 23

6 12 18 24 30 36 42

3 9

15 21 27 33 39




The soldiers problem

Two soldiers needed to cross a river. The river was too dangerous to swim and therewas no bridge. Nearby, two small girls were rowing a small boat. The soldiers asked ifthey could borrow the boat. The girls agreed, but explained that the boat was so smallthat it could only carry one adult or two children.

Explain how the two soldiers and two girls reached the other side of the river. Use apencil on the diagrams, then if you make a mistake you can rub it out.

Now investigate what happens if there are 3 soldiers, 4 soldiers, 5 soldiers, etc.

What do you notice about the number of moves? How do they increase?

Can you find a rule?


KS3 Mathematics Pack A: Level 4 Using and Applying Mathematics


FinishSoldierSoldier

GirlGirl

StartSoldierSoldier

GirlGirl

Two girls One soldierOne girlor or

Formulae expressed in words

This is a formula

Telephone bill = rental charge + cost of telephone calls

The telephone bill is calculated by adding the rental charge and the cost of thetelephone calls.

This is an instruction

Choose a number, double it, then add 3 to your answer.

If you choose the number 8:

Start number, double it, add 38 16 19

Questions

1 Use the telephone bill formula.

a What is the bill if the rental charge is £12 and the cost of the calls is £41?____________

b What is the cost of the telephone calls if the rental charge is £12 and thetelephone bill is £76? ____________

2 Use the number instructions with the following start numbers:

a 7 ______ b 12 ______ c 0 ______

d Find the start number if the result is 37. _________

Answers1 a Telephone bill = £53

b Cost of telephone calls = £64

2 a 17b 27c 3

d To find the start number, the formula must be reversed:Instead of adding 3, we take away 3.Instead of doubling, we halve the number.37 - 3 = 34half of 34 = 1717 is the start number




Formulae expressed in words

Exercises

1 The cost of a meal is calculated as follows:

Cost of the meal = cost of the food + cost of the electricity

Find the cost of the following meals:

a Cost of the food is £8.20, cost of the electricity is £1.23. ____________

b Cost of the food is £6.85, cost of the electricity is £0.87. ____________

Find the cost of the food for the following meals:

c Cost of the meal is £6.37, cost of the electricity is £0.81. ____________

d Cost of the meal is £8.43, cost of the electricity is £1.27. ____________

2 Add three to the start number, double your answer, then take away 1. What is theresult if you start with:

a 7 _________

b 4 _________

c 12 _________

d 25? _________

What was the start number if the result is:

e 15 _________

f 21 _________

g 33 _________

h 41? _________




Co-ordinates in the first quadrant

P is the point (3,2)

Start from 0.Go along 3 then go up 2.

Questions

1 Give the co-ordinates of thefollowing points:

A ( , )

B ( , )

C ( , )

2 Mark these points on the graph:

X is the point (3,2)

Y is the point (5,4)

Z is the point (1,3)

Answers1 A (1,4) 2

B (2,1)

C (4,2)




0 1 2 3 4 5

1

2

3

4

5

0

Z

X

Y

0 1 2 3 4 5

1

2

3

4

5

0

A

C

B

0 1 2 3 4 5

1

2

3

4

5

0

P

up 2

along 3

Co-ordinates in the first quadrant

Exercises

1 Give the co-ordinates of the following points:

a A ( , ) b B ( , ) c C ( , )

d P ( , ) e Q ( , ) f R ( , )

2 ABCD form a square. Mark the point D on the diagram and give the co-ordinates. ( , )

3 PQRS form a rectangle. Mark the point S on the diagram and give the co-ordinates. ( , )

4 Give the co-ordinates of the mid-point of AC. ( , )

5 Give the co-ordinates of the mid-point of PR. ( , )

123456789

1011121314151617181920

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

RQ

P

A

B C




3-D models

Exercise

Net for a triangular prism


KS3 Mathematics Pack A: Level 4 Shape, Space and Measures

FLAP

FLAP

FLAP

FLAP

FLAP

Cut along the solid lines.

Fold along the dotted lines.

Stick together with glue.


Magic squares

This is a 3 x 3 magic square. All of the rows, all ofthe columns and both of the diagonals add up tothe same number – 15.

Cut out the numbers 1 to 16 at the bottom of thesheet and place them on the 4 x 4 square. Everyrow, every column and each of the diagonals mustadd up to the same number.

When you have solved this problem, try again witha 5 x 5 square using the numbers 1 to 25.


KS3 Mathematics Pack A: Level 4 Puzzle


161514131211109

87654321

4

9

7 6

15

83

2

151515

15

15

15

15

15

Common 2-D shapes

When attempting the last two questions on this page it may help to trace the shape ontracing paper and then turn the tracing paper to find where the new shape is formed.

Questions

1 ABCD is a rectangle. Complete the diagram.

2 EFGH is a square. Complete the diagram.

3 The shape JKLM is turned and moved. J'K' are shown. Complete the diagram andmark the points L'M'.

4 The shape PQRS is turned and moved. P'Q' are shown. Complete the diagram andmark the points R'S'.

Answers




A

B

C

E

F

G

L

M

K

J

S

Q

R

P

P'

Q'J'

K'

D

A

B

C

H

G

F

E L' M'

K'J' Q'

P'R'

S'

Common 2-D shapes

Exercises

1 WXYZ is a square. Complete the diagram.

2 HIJK is a rectangle. Complete the digram.

3 The shape ABCDE is turned over and moved. A'B' are shown. Complete thediagram and mark the points C'D'E'.

4 The shape PQRSTU is turned over and moved. P'Q'R' are shown. Complete thediagram and mark the points S'T'U'.

5 LM is one side of a square LMNO. Complete the diagram.




A

B

C

E

X

W

L

M

J

R'

P'

Q'

Y

D

B'

A'

I

H

R

U

PQ

S

T

Congruent shapes

If two shapes are identical then they are congruent.Look at these two rectangles:

The rectangles have the same length and breadth.Therefore the shapes are congruent.

Shapes are congruent if one shape can be cut out and fitted exactly onto the othershape. An easy way to check is to use tracing paper. Trace the first shape, and see if itwill fit exactly onto the other shape. You can turn the shape or flip the shape.

These triangles are congruent.If you flip the left triangle it will fit onto the other triangle exactly.

Question

Here are four shapes. Which two are congruent? _______________

AnswerA and D are congruent. (If you trace shape A you will find that it fits onto shape D exactly.)




2 cm

4 cm

7 cm

2 cm

4 cm

7 cm

2 cm 2 cm

A

B

C

D

Congruent shapes

Exercise

Look at these shapes. Write down all of the pairs of congruent shapes.

____________________ ____________________ ____________________

____________________ ____________________ ____________________

____________________ ____________________ ____________________




A

B

L

O

M

P Q

K

G

F

H

N

R

J

I

C

E

D

Rotational symmetry

A shape has rotational symmetry if it fits exactly onto its original outline more than oncein a complete turn. The number of times that it fits is called the order of rotationalsymmetry. If a shape only fits onto itself once we say that it has no rotational symmetry,or that it has order 1.

X marks the centre of rotation.

To find the centre of rotation: If a shape has an even number of sides, join oppositecorners. If a shape has an odd number of sides, join each corner to the centre of theopposite side.

Question

What is the order of rotational symmetry of this regular octagon? ____________

Mark the centre of rotational symmetry.

AnswerMake a tracing of the octagon. Turn the tracing through one complete turn ie 360°. It fits the original octagon exactly 8 times. Therefore the order of rotational symmetry is 8.




Shape Name a Square b Rectangle c Equilateral Triangle d Regular Pentagon e Regular Hexagon

a

b

c

d

e

Order of rotational symmetry

4

2

3

5

6

Rotational symmetry

Exercises

Look at these shapes. If a shape does not have rotational symmetry, write ‘none’. Ifit does have rotational symmetry, write the order and mark the centre of rotationwith an X.




A B

C

D

E

F G H I

J

K

L

M N

A _____

B _____

C _____

D _____

E _____

F _____

G _____

H _____

I _____

J _____

K _____

L _____

M _____

N _____

Reflection

The image you see in a mirror is a reflection. The image is exactly the same but it hasbeen flipped over.

Note: The object and the image are equal distances from the mirror line.

How to use tracing paper to reflect an object

Question

Draw the reflection of the triangle.

Answer

If you do not have a mirror, check your answer using the display on your calculator. Tilt the calculatortoward the object and place on the mirror line (the same way you would use a mirror). Look into the answerdisplay to see where the image should be. Remove the calculator and check your drawn image is in thesame place.




Mirror line

Image

Object

Image

Object

Flip the

tracing paper.

Trace the object and the

mirror line onto tracing paper.

Place the tracing of the mirror line

directly on top of the mirror line

on the paper. This will show where

the reflection image should be.

Image in calculator Image on paper

Reflection

Exercise

Reflect the following shapes in the mirror lines. Use tracing paper.




Measurement

Length

We use millimetres, centimetres, metres and kilometres.

This is a millimetre (1 mm):

This is a centimetre (1 cm):

A metre (1 m) is about one large pace.

A kilometre (1 km) is about one thousand large paces.

It takes about ten minutes to walk one kilometre.

Mass

A paper-clip has a mass of about one gram (1 g).

A bag of sugar has a mass of about one kilogram (1 kg).

A small car has a mass of about one tonne (1 t).

Capacity

A small spoon for medicine has a capacity of 5 millilitres (5 ml).

A teaspoon holds about one centilitre (1 cl).

An orange juice container holds about 1 litre (1 l).

Questions

1 What units would you use to measure the length of this piece of paper? Choosefrom millimetres, centimetres, metres, kilometres. ________________________

2 What is the missing number in the following sentence?

A bag of crisps has a mass of ______ grams.Choose from 5, 25, 500, 1000.

Answers1 Centimetres would be the most appropriate units. Millimetres would be acceptable.

2 25




SUGAR

FRESH

ORANGE

JUICE

Measurement

Exercises

1 This is a car speedometer. It shows the speed in kilometres per hour. What speed is shown? ______________

2 Mrs Morgan weighs herself on the bathroom scales. They show her weight inkilograms. How much does she weigh? _________________

3 You have a 30 cm ruler, a metre rule, a stop watch and a clock. Which would youuse to measure:

a the length of a room? __________________________

b the length of a pencil? __________________________

c the time taken to run 100 metres? __________________________

d the time taken to run a marathon? __________________________

4 Would you measure the mass of a full suitcase in grams, kilograms or tonnes?

_____________________________

5 This is Lofty the giraffe. He is slightly taller than a double-decker bus.Guess his height. ___________________




0

20

4

0

60

80 100 120 140

50 60

Perimeter, area and volume

Perimeter

The perimeter of a shape is the distance around the shape.

3 cm + 5 cm + 3 cm + 5 cm = 16 cm

Area (always measured in units2, eg mm2, cm2, m2)

To find the area, count the number of squares.There are 15 squares. Each square has an areaof 1 cm2. The area is 15 cm2.

Volume (always measured in units3, eg mm3, cm3, m3)

To find the volume, count the number of small cubes.

There are 8 small cubes on the top layer.There are 8 small cubes on the middle layer.There are 8 small cubes on the bottom layer.

Each small cube has a volume of 1 cm3.

The volume of the shape is 24 cm3.

Question

Each small cube has a volume of 1 cm3.What is the volume of this shape? ___________

AnswerThe top layer has 6 cubes.The bottom layer has 6 cubes.

The volume of this shape is 12 cm3.




5 cm

3 cm 3 cm

5 cm

4 cm

2 cm

3 cm

1 cm 1 cm

1 cm

Top layer

Bottom layer

Perimeter, area and volume

Exercises

1 Find the perimeter and area of each shape. The dots are 1 cm apart.

2 Find the volumes (each small cube has a volume of 1 cm3).

a b

c d




H

A

G

BC

D

E F

a ________

b ________

c ________

d ________

Frequency tables

When we complete a tally chart we count in fives.

Question

These are the numbers of sweets in 20 packets:

178 165 172 163 181164 158 161 164 183152 173 166 161 183172 166 164 183 174

Complete this table to show the information.

AnswerUse a pencil to cross out the original data as it is tallied.

Cross out 178 and record a tally in the tally column for 170-179. Cross out 165 and record a tally in thetally column for 160-169.

When you have completed the table, check that the frequency total is correct. In this question thereare 20 packets, so the total must be 20.


KS3 Mathematics Pack A: Level 4 Handling Data


Number of sweets in a packet

Tally Frequency

150-159

160-169

170-179

180-189

Total

Number of sweets in a packet Tally Frequency

150-159

160-169

170-179

180-189

Total

2

9

5

4

20

represents 5 represents 12

Frequency tables

Exercises

1 These are the ages of people in a cinema:

47 25 58 48 38 43 52 37 53 47

58 23 63 46 54 29 45 38 45 63

36 52 37 54 47 36 28 37 41 51

38 47 43 39 45 42 52 47 38 46

Complete the table below to show this information:

2 These are the shoe sizes of boys in a class:

3 4 6 4 3 5 4 6 5 7

4 6 5 6 5 5 4 3 7 4

Complete the table below to show this information:




Age Tally Frequency

20-29

30-39

40-49

50-59

Total

60-69

Shoe size Tally Frequency

3

4

5

6

Total

7

Median and mode

The median is the middle number when the numbers are placed in order.

The mode is the most common number.

Questions

1 Find the median and mode of these numbers:

2, 3, 5, 3, 2, 4, 2.

median _____________ mode _____________

2 Find the median of these numbers:

7, 3, 10, 2.

median _____________

3 The masses of boxers in a tournament are given in kilograms:

65, 63, 68, 64, 69, 68, 63, 64, 67, 69, 63, 61, 63, 67, 60.

Find the median and the mode.

median _____________ mode _____________

Answers1 First place the numbers in order of size.

2 Place the numbers in order.

3 Place the data in order: 60, 61, 63, 63, 63, 63, 64, 64, 65, 67, 67, 68, 68, 69, 69.

The median is 64. The mode is 63.




2 2 2 3 3 4 5

There are more 2s than any other number therefore the mode is 2.

3 is the middle number, therefore the median is 3.

2 3 7 10

The median is between 3 and 7.

3 + 7=

10

25

2=

The median is 5.

Median and mode

Exercises

In the following questions find: a the median b the mode.

1 The heights of players in a football team are:

1.82 m 1.93 m 1.79 m 1.83 m 1.93 m 1.79 m

1.93 m 1.94 m 1.88 m 1.84 m 1.85 m

a ____________ b ____________

2 The ages of students on a school bus are:

13 17 13 14 16 18 14 13 15 16

14 13 17 15 14 13 13

a ____________ b ____________

3 The number of goals scored by a football team in 15 matches were:

3 0 3 1 0 3 2 1 2 2

3 3 3 4 1

a ____________ b ____________

4 The shoe sizes of pupils in a class are:

2 3 6 4 3 6 5 5 6 4

6 4 5 3 5 2 5 7 3 2

4 3 7 6 3

a ____________ b ____________

5 The heights of pupils in a class were:

106 cm 120 cm 132 cm 120 cm

112 cm 108 cm 110 cm 116 cm

a ____________ b ____________




Frequency diagramsThis is a frequency diagram. It shows the heights of pupils in a class.

Questions

1 How many pupils were between 130 and 135 centimetres? _____________



4 How many pupils were under 130 centimetres? _____________

5 How many pupils were in the class? _____________

Answers1 4 2 1

3 2 + 4 + 6 = 12 4 1 + 2 = 3

5 1 + 2 + 4 + 6 + 3 + 1 = 17




120 125 130 135 140 145 150

1

0

2

3

4

5

6

Height in centimetres

Freq

uenc

y

Frequency diagrams

Exercises

1 This frequency diagram shows the heights of people in a room:

a How many people were between 120 cm and 130 cm tall? _____________

b How many people were between 150 cm and 160 cm tall? _____________

c How many people were between 170 cm and 180 cm tall? _____________

Fill in the missing numbers:

d Four people were between _____ cm and _____ cm tall.

e Six people were between _____ cm and _____ cm tall.

f How many people were in the room? _____________

2 This frequency diagram shows the masses of people on a bus:

a How many people were between 60 kg and 70 kg? _____________

b How many people were over 90 kg? _____________

c How many people were on the bus? _____________




120 130 140 150

1

0

2

3

4

5

6

Height in centimetres

Freq

uenc

y

160 170 180

40 50 60 70

1

0

2

3

4

5

Mass in kilograms

Freq

uenc

y

80 90 100 110

Line graphs

This is a line graph. It shows the temperature in a room between 1 am and 6 am.

Questions

Use the line graph to answer the following questions:

1 What was the temperature at: a 2 am _______ b 6 am _______

2 At what time was the temperature: a 16°C _______ b 14°C _______

AnswersDraw dotted lines on the graph as shown to find the answers.

1 a 22°Cb 18°C

2 a 3 am and 5 amb 4 am




1 am 3 am 5 am4 am2 am 6 am

26°C

24°C

22°C

14°C

16°C

18°C

20°C

12°C

Time

Tem

per

atur

e

1 am 3 am 5 am4 am2 am 6 am

26°C

24°C

22°C

14°C

16°C

18°C

20°C

12°C

Tem

per

atur

e

Time

Line graphs

Exercises

1 This graph shows the number of hours of sunshine each month for a town inScotland:

a How many hours of sunshine did the town have in March? _______

b How many hours of sunshine did the town have in August? _______

c Which month had the least sunshine? _______________

d Which months had more than 100 hours of sunshine? _______________________

e Which months had less than 50 hours of sunshine? __________________________

2 Michelle’s maths marks over a period of six weeks were as follows:

Draw a line graph to show this information.




J F M

50

0

100

150

200

Month

Hou

rs o

f sun

shin

e

A M J J A S O N D

Week 1 2 3 4 5 6

8 6 7 5 3 2Mark

Probability

Exercises

1 A six-sided die is thrown. Decide, for each of the following events, if the event hasan even chance of happening, a less than even chance or a more than even chance.

even less more

a The die landing on a 6

b The die landing on an even number

c The die landing on a 1, 2, 3, 4, or 5

d The die landing on a 5

e The die landing on a 3 or less

f The die landing on a 3 or more

g The die landing on less than 5

h The die landing on more than 3

i The die landing on 5 or 6

j The die landing on 1, 2, or 3

2 State whether the chance of each of the following events happening is certain,likely, even, unlikely or impossible.

a Your television breaking down tonight ____________________

b Your pen running out of ink during this lesson ____________________

c An alien walking into your maths lesson today ____________________

d A coin landing on heads ____________________

e Your teacher falling over ____________________

f Your watch stopping today ____________________

g The school bell ringing at the end of the day ____________________

h A die landing on a 6 or less ____________________

3 In a game, a die is thrown. If a 6 is thrown, Lucy wins. If any other number is thrown,Matt wins. Does Lucy have a fair chance of winning? Explain your answer.

__________________________________________________________________________




Trapped

A game for two players. This sheet contains 25 games.

Start in any box. Think carefully. This is a game of skill.

Rules

1 The first player joins any two dots with a straight line(use a ruler) and puts an arrow to show the direction

2 The second player continues

3 The last person who can draw a line to an empty dotwithout crossing a line wins.

4 In the example it is impossible to move after move 4.


KS3 Mathematics Pack A: Level 4 Game


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KS3 Maths Level by Level Pack A: Level 4

Documents

Transcript of KS3 Maths Level by Level Pack A: Level 4