Howden School

Year 7 Mathematics

Homework Booklet

Half Term 2

Please complete your maths homework regularly – each

week is broken into three sections. Section A, which

checks your recall of key ideas and skills Section B is a

task based on recent work and a ‘challenge’ task (a

problem for you to try and solve). Hand your work in

regularly and your teacher will let you know how well

you are doing and what progress you are making – good

luck and have fun!

Name Tutor

group

Maths Teacher

Hand this booklet in

Dear Parent

2

As outlined on the front cover, mathematics homework in year

7 is organised in a three section format. The Section B tasks

are split into different levels and your child should attempt

work in line with their working level and target. Your child

should attempt Section A and the level ____ task of Section

B, each week unless otherwise directed by their teacher – this

may mean them completing questions at one, two or even three

levels. The challenge tasks are short problem solving activities

that any pupil can attempt. These questions are taken from

‘UKMT Mathematics Challenge’ papers – some pupils will take

part in the annual national UKMT Challenge during year 7.

Your child’s working level at the start of year 7 and their end

of year 7 target level is shown at the bottom of this page.

Any task that has a bold heading or is marked with an asterisk

(*) indicates that the task is linked to a key area of maths,

which needs to be understood in order to contribute towards

being confident working at that level. These areas will be

assessed in more detail in lessons and formal assessments.

We hope that your child enjoys attempting their maths

homework and achieves success in the process.

Howden Mathematics Department.

KS2 level End of Year 7

Target

3

HOMEWORK 8

SECTION A

1 A rectangle has a length of 7cm and an area of 21cm2. What is its perimeter?

2 Change 5430ml into litres.

3 What is 12.3 + 2.035? 4 What is 11.06 – 2.035?

5 A cuboid has a base of 5cm, length 10cm and height 6cm. What is its surface area?

6 List all the factors of 24.

7 What is the outcome if I subtract an even number from an even number?

8 What is 14 squared?

9 What is 652 x 13? 10 Divide the following numbers by 10. 6 4.5 0.25

4

SECTION B

Note that there are 2 sections to this homework you need to do the

correct level from BOTH sections.

Level 4

Produce a tally chart for the data below: Pink Yellow Blue Green Pink

Red Blue Green Red Blue

Pink Red Blue Orange Blue

Green Red Red Blue Green

Yellow Red Blue Green Yellow

Pink Blue Green Pink Purple

Colour Tally

5

Use the following frequency table to complete the bar

chart.

Type of transport Frequency

Bike 10

Bus 10

Car 50

Lorry 15

Van 5

6

Level 5

Produce a tally table by grouping the following data. They are

students’ heights in centimetres

153 164 157 137 149

152 152 141 142 158

149 152 152 166 153

159 156 149 148 168

161 162 164 152 167

Height (cm) 130 - 134 135 - 139

7

Draw a bar chart to show the following information:

Days off school frequency

0-4 18

5-9 6

10-14 3

15-19 2

20+ 1

8

Level 6

Time Taken to Travel to School

0

2

4

6

8

10

12

0-10 11-20 21-30 31-40 41-50

Time (minutes)

Fre

qu

en

cy

Produce a frequency table for the data shown in the bar chart

above.

9

Draw a Duel bar chart for the following information:

Test result (out of 60) Science Maths

0-10 8 1

11-20 17 8

21-30 40 50

31-40 25 25

41-50 10 15

51-60 0 1

10

Second Section Homework 8

Use the bar chart to answer the questions you are set. (all

levels)

How Students Travel to School

0

10

20

30

40

50

Walking School

Bus

Service

Bus

Car Bicycle

Method of Transport

Fre

qu

en

cy

Level 4

1. Which method of travelling

to school is the mode? ………………………………………

2. How many students travel

to school by car? ……………………………………..

11

Level 5

1. How many students does each

small section of the frequency

axis represent? ………………………………….

2. How many more students

walk to school than cycle? ………………………………….

Level 6

1. How many students are represented

by the bar chart? ………………………………….

2. True or False? More students travel to school by bus

than by all the other methods together.

………………………………….

Challenge

The faces of a cube are painted so that any two faces which

have an edge in common are painted different colours. What is

the smallest number of colours required?

A 2 B 3 C 4 D 5 E 6 From UKMT 2008

12

HOMEWORK 9

SECTION A

1 Find 35% of 40. 2 What is ¾ of 60?

3 What is;

4 What is 564 ÷ 3

5 Write 0.24 as a percentage and a fraction in its simplest form.

6 What is 33?

7 Find the median for the following data:

4, 7, 5, 11, 3, 8, 4, 12

8 Two angles in a triangle are 38° and 74°. What is the third angle?

9 What is -7 + -13 ? 10 Find the HCF of 20 and 35

13

SECTION B

Level 4, 5 and 6

Decide if the following statements, about a standard pack of

playing cards, are true or false. CIRCLE your answer.

1. There are 13 suits. True/False

2. There are 12 picture cards. True/False

3. There are 4 of each number card True/False

4. There are 54 cards in a pack. True/False

5. The suits are either black or red. True/False

6. Jokers are part of a standard deck of cards.

True/False

7. All the cards are different. True/False

8. Two of the suits are called ‘Clubs’ and ‘Diamonds’.

True/False

9. There are 8 Aces in a pack. True/False

10. Playing cards are often referred to in probability

questions. True/False

14

Level 4

Write a sentence using each of the following keywords:

Impossible

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

Certain

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

Even chance

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

Equally likely

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

Unlikely

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

15

Level 5

Answer the following questions based on the diagram above.

You must give answers as fractions, decimals or percentages to

achieve level 5.

What is the probability of choosing:

a) A heart? ………

b) A rectangle? ………

c) A shaded triangle? ………

d) An unshaded shape? ………

e) An unshaded rectangle? ………

16

Level 6

An octahedral (8 sided) die is numbered from 1 to 8.

What is the probability of rolling:

a) An even number? ………

b) A prime number? ………

c) A number less than 4? ………

d) A number smaller than 7? ………

e) A 10? ………

f) Not a square number? ………

Challenge

In 1833 a ship arrived in Calcutta with 120 tons remaining of

its cargo of ice. One third of the original cargo was lost

because it had melted on the voyage. How many tons of ice was

the ship carrying when it set sail?

A 40 B 80 C 120 D 150 E 180 From UKMT 2008

17

HOMEWORK 10

SECTION A

1 Find 65% of 70. 2 What is of 45?

3 What is;

4 What is 654÷ 6

5 Write 0.65 as a percentage and a fraction in its simplest form.

6 What is 53?

7 Find the mode for the following data:

4, 7, 5, 11, 3, 8, 4, 12

8 Two angles in a triangle are 104° and 25°. What is the third angle?

9 What is -7 x -6 ? 10 Find the HCF of 16 and 48

18

SECTION B

Level 4

Shade in the given fractions.

21

31

124

32

Which of these fractions are equivalent?

………………………………………………………………………………………………………………

19

Write down the fractions shown in each diagram:

………………………

………………………

………………………

………………………

………………………

………………………

20

Level 5

Complete the lists of equivalent fractions.

a) 20 = 10 = __ = 1 = 3 = __

40 10 24

b) 15 = __ = 6 = 3 = 30 = __

30 5 40

c) Write down 3 fractions which are equivalent to three

quarters.

…………………………………………………………………………………………………………………

d) Cancel down the following fractions to their simplest

form:

18

15 ………… 36

27 …………. 24

16 ………… 52

24 …………

21

Level 6

Find the Lowest Common Multiple (LCM) of the following pairs

of numbers:

a) 5 and 7

b) 12 and 15

c) 8 and 12

d) 6 and 9

e) 4 and 10

Answer the following questions. You must show your working

out.

f) ¼ + ¼ =

g) ⅜ + ⅛ =

h) ⅞ + ¾ =

i) ⅝ - ¼ =

j) ¾ - ⅛ =

k) ½ + ⅝ =

l) 3

2 + ¾ =

22

m)

4

3 +

10

3 =

n) 12

7 -

15

2 =

Challenge

A rectangle PQRS is cut into two pieces along PX, where PX =

XR and PS = SX as shown. The two are reassembled without

turning either piece over, by matching two edges of equal

length. Not counting the original rectangle, how many

different shapes are possible?

A 1 B 2 C 3 D 4 E 5

From UKMT 2008

S X R

P Q

23

HOMEWORK 11

SECTION A

1 Find 32% of 120. 2 What is of 64?

3 What is;

4 What is 256 ÷ 8

5 Write 0.52 as a percentage and a fraction in its simplest form.

6 What is the cube root of 1000 ?

7 Find the range for the following data:

4, 7, 5, 11, 3, 8, 4, 12

8 Draw a quadrilateral with EXACTLY two right angles. Mark the right angles on the diagram.

9 What is -7 - -6 ? 10 Find the LCM of 15 and 20

24

SECTION B

Level 4

a) ½ of 20 = g) 4

1 of 20 =

b) ¼ of 12 = h) 5

1 of 30 =

c) ½ of 32 = i) 3

2 of 100 =

d) ½ of 60 = j) 10

1 of 50 =

e) ¾ of 40 = k) 10

3 of 40 =

f) 31

of 18 = l) 4

3 of 44 =

m) Half of an amount is 12. What is the amount?

……………………………………………………………………………………………………………….

n) One quarter of an amount is 13. What is the original

amount?

……………………………………………………………………………………………………………

25

Level 5

a) 81

of 48 = g) 7

6 x 42 =

b) ¾ of 28 = h) 9

10 x 81 =

c) 9

2 x 27 = i) 6

13 x 30 =

d) 8

7 x 16 = j) 13

6 x 52 =

e) 3

2 x 24= k) 11

4 x 77 =

f) 7

5 x 35= l) 15

7 x 45 =

m) Three quarters of an amount is 36. What is the original

amount?

………………………………………………………………………………………………………………….

…………………………………………………………………………………………………………………

n) Two fifths of an amount is 22. What is the original

amount?

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

26

Level 6

a) 5 x 52

= h) 11 x 8

3 =

b) 12 x ¾ = i) 8 x 7

5 =

c) 18 x 3½ = j) 32 ÷ 9

4 =

d) 10 x 4 52

= k) 56 ÷ 8

7 =

e) 24 ÷ 3

2 = l) 12 x 14

3 =

f) 20 ÷ 5

4 = m) 22 ÷ 11

5 =

g) 48 ÷ 5

22 = n) 52 x 2

13

9 =

o) Two fifths of an amount is 14. What is three fifths of

the amount?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

p) Three eighths of an amount is 21. What is one and one

eighth of the same amount?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

27

Challenge

A solid wooden cube is painted blue on the outside. The cube is

then cut into eight smaller cubes of equal size. What fraction

of the total surface area of these new cubes is blue?

A 1

8 B

1

3 C

3

8 D

1

2 E

3

4

From UKMT 2008

28

HOMEWORK 12

SECTION A

1 Find 74% of 300. 2 What is of 33?

3 What is;

4 What is 1375 ÷ 5

5 Write 85% as a decimal and a fraction in its simplest form.

6 What is the cube root of 8?

7 Find the mean for the following data, you may use a calculator.

4, 7, 5, 11, 3, 8, 4, 12

8 Is this a straight line? Give a reason for your answer.

9 What is13 + - 8 10 Find the LCM of 12 and 21

35° 48°

29

SECTION B

Section B of homework 12 is the second Key Skills homework

and will be set in a separate mini booklet by your teacher.

30

HOMEWORK 13

SECTION A

1 Find 28% of 50. 2 What is of 36?

3 What is;

4 What is 2763÷ 9

5 Write 12.5% as a decimal and a fraction in its simplest form.

6 What is the cube root of 125?

7 Find the mean for the following data, you may use a calculator.

21, 23, 15, 26, 7

8 Is this a straight line? Give a reason for your answer.

9 What is13 - - 8 10 Find the LCM of 12 and 16

35° 55°

31

SECTION B

Level 4

The diagrams below are all RIGHT ANGLES. Calculate the

missing angles, a, b, c, d, e and f.

a

50

°

b

35

°

c

27

°

43

°

d

d 40

°

a = …………… b = ………….

c = …………….. d = ………………

e e

e = ……………

f

2f

f = ……………

32

Find the missing angles on the straight lines below.

130° g

………………………………

………………………………

g = ………………………

30° h

………………………………

………………………………

h = ………………………

33

Level 5

Find the missing angles in the diagrams below.

b 55°

c

d 37°

68°

b = …………………

c = …………………

d = ………………

1.

2.

f

f 116°

120°

98°

54°

e

f = ………………… e = ………………..

3.

4.

34

i 3i 2i

……………………………………………

……………………………………………

i = …………………………….

5.

38°

g

48°

h

……………………………………………

……………………………………………

h = …………………………….

……………………………………………

……………………………………………

g = …………………………….

35

Level 6

Complete the sentences below using the diagram and keywords

given.

Angles a and d are equal because they are ……………………………………

angles.

Angles a and e are equal because they are ……………………………………

angles.

Angles c and f are equal because they are ……………………………………

angles.

Angles f and g are equal because they are ……………………………………

angles.

Angles b and f are equal because they are ……………………………………

angles.

Complete the sentence below;

Angles ……… and ……… are allied angles because……………………………

…………………………………………………………………………………………………………………

Corresponding

Vertically Opposite

Allied

Alternate

a b

c d

e f

g h

36

Calculate the missing angles. Give a reason for your answer.

a = ……………… e = ……………………………………………….

Reason ………………………………….. Reason……………………………………..

b = …………………

Reason …………………………………..

c = ………………….

Reason ……………………………………

d = …………………..

Reason ……………………………………

Challenge An active sphagnum bog deposits a depth of about 1 metre of

peat per 1000 years. Roughly how many millimetres is that per

day?

A 0.0003 B 0.003 C 0.03 D 0.3 E 3 From UKMT 2008

1. 2.

56° a

b c

d

e

115°

37

HOMEWORK 14

SECTION A

1 Find 43% of 480. 2 What is of 56?

3 What is;

4 What is 2763÷ 3

5 Write 140% as a decimal and a fraction in its simplest form.

6 What is 43?

7 Find the median for the following data.

21, 23, 15, 26, 7, 11

8 Draw a diagram to show alternate angles

9 What is 3 x - 8 10 Find the HCF of 3, 4 and 5

38

SECTION B

Level 4 to 5

1.) Draw a rectangle with a perimeter of 24cm2

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

2.) A square has side length 10cm. What is it’s area?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

3.) Calculate 27 multiplied by 43.

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

39

4.) Continue the sequence by writing the next 3 terms.

3, 7, 11, 14, 17……

………………………………………………………………………………………………………………

What is the nth term?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

5.) Write the following numbers in order.

7, -3, 0.74, 0.08, -10

………………………………………………………………………………………………………………

6.) Write 34786 to;

The nearest 10

………………………………………………………………………………………………………………

The nearest 100

………………………………………………………………………………………………………………

The nearest 1000

………………………………………………………………………………………………………………

7.) 27.5 – 34.6=

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

40

8.) Simplify 4s + 4p + 3p – 2s

………………………………………………………………………………………………………………

9.) If A = bh

Find A when b = 3 and h= 5

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

10.) Find the mean, median and mode of the following data,

6, 3, 5, 8, 3, 9, 1

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

41

Level 5 to 6

1.) What is the 12th square number?

………………………………………………………………………………………………………………

2.) A triangle has an area of 18cm2. It has a perpendicular

height of 6cm. How long is its base?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

3.) A cube has side length 3m. What is its surface area?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

4.) Multiply 3.27 by 2.4

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

42

5.) What is 348 x 0.1?

………………………………………………………………………………………………………………

6.) What is the inverse of doubling then adding one?

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

7.) What is always true of corresponding angles?

………………………………………………………………………………………………………………

8.) Write down the first 3 cubic numbers.

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

9.) 3 + 5 x 9 ÷ (4 -1) =

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

10.) Write down three fractions that are smaller than ¼.

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………

………………………………………………………………………………………………………………