Dear Parent
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.
2

SECTION A
1 A rectangle has a length of 7cm and an area of 21cm 2 . 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
3

SECTION B
Note that there are 2 sections to this homework you need to do the correct level from BOTH sections.
Produce a tally chart for the data below:
Pink
Red
Pink
Green
Yellow
Pink
Yellow
Blue
Red
Red
Red
Blue
Blue
Green
Blue
Red
Blue
Green
Green
Red
Orange
Blue
Green
Pink
Colour Tally
Pink
Blue
Blue
Green
Yellow
Purple
4

5

Produce a tally table by grouping the following data. They are students’ heights in centimetres
153
152
149
159
164
152
152
156
157
141
152
149
137
142
166
148
149
158
153
168
161 162
164 152 167
130 - 134
135 - 139
6

7

Time Taken to Travel to School
12
10
8
6
4
2
0
0-10 11-20 21-30 31-40 41-50
Time (minutes)
Produce a frequency table for the data shown in the bar chart above.
8

Draw a Duel bar chart for the following information:
Test result (out of 60) Science
0-10 8
Maths
1
11-20
21-30
31-40
41-50
51-60
17
40
25
10
0
8
50
25
15
1
9

Second Section Homework 8
Use the bar chart to answer the questions you are set. (all levels)
50
40
30
20
10
0
Walking School
Bus
Service
Bus
Car
Method of Transport
Level 4
1. Which method of travelling to school is the mode?
2. How many students travel to school by car?
Bicycle
………………………………………
……………………………………..
10

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.
………………………………….
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
11

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 3 3 ?
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
12

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.
2. There are 12 picture cards.
3. There are 4 of each number card
True/False
True/False
True/False
4. There are 54 cards in a pack.
5. The suits are either black or red.
True/False
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’.
9. There are 8 Aces in a pack.
True/False
True/False
10. Playing cards are often referred to in probability questions. True/False
13

Level 4
Write a sentence using each of the following keywords:
Impossible
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Certain
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Even chance
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Equally likely
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Unlikely
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
14

Level 5
Answer the following questions based on the diagram above.
You must give answers as fractions, decimals or percentages to achieve level 5.
15

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
16

SECTION A
1 Find 65% of 70.
2
What is of 45?
3 What is; 4 Wha t is 654÷ 6
5 Write 0.65 as a percentage and a fraction in its simplest form.
6 What is 5 3 ?
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
17

SECTION B
Level 4
Shade in the given fractions.
2
1 1
3
4
12 3
2
Which of these fractions are equivalent?
………………………………………………………………………………………………………………
18

Write down the fractions shown in each diagram:
………………………
………………………
………………………
………………………
………………………
………………………
19

Level 5
Complete the lists of equivalent fractions. a) 20 = 10 = __ = 1 = 3 = __
40 10 24 b) 15 = __ = 6 = 3 = 30 = __
40 5 c) Write down 3 fractions which are equivalent to three quarters.
30
………………………………………………………………………………………………………………… d) Cancel down the following fractions to their simplest
form:
15 …………
18
27
36
…………. 16
24
………… 24
52
…………
20

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)
2
3
+
¾ =
21

m) 3
4
+ 3
10
= n)
7
12
-
2
15
=
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
S X R
P
Q
From UKMT 2008
22

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
23

Level 4 a)
½ of 20 = g) 1
4
of 20 = b)
¼ of 12 = h) 1
5
of 30 = c)
½ of 32 = i) 2
3
of 100 = d)
½ of 60 = j) 1
10
of 50 = e)
¾ of 40 = k) 3
10
of 40 =
1 f)
3 of 18 = l) 3 of 44 =
4 m) Half of an amount is 12. What is the amount?
………………………………………………………………………………………………………………. n) One quarter of an amount is 13. What is the original amount?
……………………………………………………………………………………………………………
24

Level 5 a)
1
8 of 48 = g) 6
7
x 42 = b)
¾
of 28 = h) 10 x 81 =
9 c) 2
9
x 27 = i) 13 x 30 =
6 d)
7
8
x 16 = j) 6
13
x 52 = e) 2
3
x 24= k) 4
11
x 77 = f) 5 x 35= l) 7 x 45 =
7 15 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?
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
25

Level 6 a) 5 x
2
5
= h) 11 x 3 =
8 b) 12 x
¾
= i) 8 x c) 18 x 3
= j) 32 ÷
7
5
9
4
=
= d) 10 x 4
2
5
= k) 56 ÷ 7
8
= e) 24 ÷ 2
3
= f) 20 ÷ 4
5
= l) 12 x 1 3
4
= m) 22 ÷ 5
11
= g) 48 ÷
2
2 = n) 52 x 2 9 =
5 13 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?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
26

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
Ошибка!
B
Ошибка!
C
Ошибка!
D
Ошибка!Ошибка!
E
Ошибка!
From UKMT 2008
27

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.
35°
48°
9 What is13 + - 8 10 Find the LCM of 12 and 21
28

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.
29

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.
35°
55°
9 What is13 - - 8 10 Find the LCM of 12 and 16
30

Level 4
The diagrams below are all RIGHT ANGLES. Calculate the missing angles, a, b, c, d, e and f. a
50
° a = …………… c
43
°
27
° c = …………….. b
35
° b = …………. d
40
° d d = ……………… e e e = …………… f = ……………
2f f
31

Find the missing angles on the straight lines below.
130° g
………………………………
……………………………… g = ………………………
30° h
………………………………
……………………………… h = ………………………
32

Level 5
Find the missing angles in the diagrams below.
1.
55° c b b = ………………… c = …………………
2. d
68°
37° d = ………………
3.
4. f
116° f
54 ° e
120 °
98 ° f = ………………… e = ………………..
33

5. g
38°
……………………………………………
…………………………………………… g = ……………………………. h
48°
2i 3i i
……………………………………………
…………………………………………… h = …………………………….
……………………………………………
…………………………………………… i = …………………………….
34

Level 6
Complete the sentences below using the diagram and keywords given. a b c d e f g h
Corresponding
Vertically Opposite
Allied
Alternate
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……………………………
…………………………………………………………………………………………………………………
35

Calculate the missing angles. Give a reason for your answer.
1. c a b
56°
2. 115° e d a = ………………
Reason ………………………………….. b = …………………
Reason ………………………………….. c = ………………….
Reason …………………………………… d = …………………..
Reason …………………………………… e = ……………………………………………….
Reason……………………………………..
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
36

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 4 3 ?
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
37

Level 4 to 5
1.) Draw a rectangle with a perimeter of 24cm 2
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
2.) A square has side length 10cm. What is it’s area?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
3.) Calculate 27 multiplied by 43.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
38

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=
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
39

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
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
40

Level 5 to 6
1.) What is the 12 th square number?
………………………………………………………………………………………………………………
2.) A triangle has an area of 18cm 2 . 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
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
41

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.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
42