N4 Numeracy

Book 1

The wee

Maths Book

of Big Brain

Growth

Number Problems, Negative Numbers

and Fractions.

Grow your brain

Guaranteed to make

your brain grow, just

add some effort and

hard work

Don’t be afraid if

you don’t know how

to do it, yet!

It’s not how fast you

finish, but that you

finish.

It’s always better to

try something than

to try nothing.

Don’t be worried

about getting it

wrong, getting it

wrong is just part of

the process known

better as learning.

Page | 2

A Number problems involving Whole Numbers and

Decimals

A1 I can complete additions and subtractions

without a calculator.

1. In 2008, Waste Management was responsible for 23 million tonnes of

greenhouse gases. This compares to 219 million tonnes of greenhouse

gases from Energy Supply and 132 million tonnes of greenhouse gases

from Transport.

(a) How many million tonnes of greenhouse gases is this altogether?

(b) Energy Supply produces more greenhouse gases than Transport.

How many million tonnes more?

2. The Environmental Services

Association reports that in 2008 its

members were responsible for

producing 8 800 000 tonnes of

greenhouse gases.

However they saved 5 300 000 tonnes of greenhouse gases through

their material and energy recovery activities the difference being

released into the atmosphere.

How many tonnes of greenhouse gases did the Environmental Services

Association members release into the atmosphere?

Page | 3

3. An empty box has a weight of 225 g.

When a TV is placed in the box it has a total weight of 1625 g.

What is the weight of the TV?

4. An empty glass bottle has a weight of 589 g.

When some juice in filled into the bottle the

total weight is 922 g.

What is the weight of the juice?

5. You collect data on the passengers arriving at Glasgow Airport.

You want to know what type of accommodation travellers use.

The results of your survey are shown in the table below:

Type of

accommodation

Business Tourist Total

Hotel 123 (a) 283

Bed & breakfast 46 184 230

Self-catering (b) 135 171

Friends 25 82 (c)

total 230 (d) 791

Find the values of (a), (b), (c) and (d).

Page | 4

6. Last year a school collected data about the attractions at the school

fair.

The results of the survey are shown in the table below:

Type of

attraction

Children Adults Total

Food stall 241 (a) 853

Photo shoot 46 184 230

Bring and buy (b) 162 674

Music stand 250 182 (c)

Total 1049 (d) 2189

Find the values of (a), (b), (c) and (d).

Page | 5

A2 I can use addition, subtraction, multiplication

and/or division in a problem (calculator

allowed).

You can use a calculator for these questions.

7. The government spent £357 million on animal health in 2009.

If this level of spending is maintained for 15 years how much would

the total spend be?

8. The government audit office claims to have made savings and other

efficiency gains worth £890 million in 2009.

On average how much is this per month?

9. The government raised £837 million in

Landfill Tax receipts.

How much does this work out per

person if the population of the UK is 62

million.

10. Recycling glass saves 315kg of carbon dioxide being released into the

atmosphere per tonne of glass recycled.

If 27 000 tonnes of glass are recycled in Scotland each year, how

much carbon dioxide does this save being released into the

atmosphere?

11. A bike factory makes an average of 232 bikes every day.

How many bikes would be made in 14 days?

Page | 6

12. Ben bought a car for £9600.

When he sold it 3 years later, he made a loss of £5196.

(a) How much did he sell it for?

(b) How much did he lose per year on average?

13. Mark has 23 boxes of recycling

to take to his local recycling

centre by car.

Mark’s car can hold 4 boxes at

one time.

How many trips will Mark need

to make to the recycling

centre to dispose of all his

recycling?

14. Sandy’s car can travel 26 kilometres on 1 litre of fuel.

He has 30 litres of fuel and is planning a journey of 800 kilometres.

Will Sandy have enough fuel for the journey?

15. Cara ran 13 miles and raised £312.

How much was she sponsored per mile?

Page | 7

N20t I can add, subtract, multiply or divide any whole

number or decimal I meet in the context of a

problem with a calculator.

16. John went to the shop with £8∙96.

He bought a packet of crisps for £0∙56, a chocolate bar for £0∙78 and

a bottle of juice for £1∙05.

How much will John now have left?

17. A baby was born with a weight of 3∙75kg, after a month the baby’s

weight had increased by 0∙88kg.

What is the new weight of the baby?

18. A plank of wood weighs 1∙3kg.

A builder needs 58 of these planks of wood to build a small bridge.

What will the weight of the bridge be?

19. The height of a tower block is

51∙36m.

If there are 15 floors in the tower

block, what is the height of one of

the floors?

Page | 8

20. A group of 5 friends had lunch together at a local cafe.

James spent £5∙33, Elle spent £6∙85, Graham spent £4∙66, Jemma

spent £7∙62 and Jackie spent £5∙39.

(a) How much did they spend altogether?

(b) Elle complained about the lengthy wait for her food and the

manager took the price of her food off the bill.

All friends, including Elle decide to split the remainder of the

bill.

How much will they each have to pay?

21. Jane is an artist.

In January she bought 6 tubes of

different shades of red paint.

The costs were

£7∙59 £6∙40 £8∙05

£7∙40 £5∙66 £3∙20

In February she bought 5 tubes of different shade of blue paint.

The costs were

£6∙21 £9∙80 £7∙60 £3∙95 £4∙36

Jane thinks that the average cost per tube of red paint is more than

blue paint. Is Jane correct?

You must justify your answer.

Page | 9

A4 I can solve problems using Direct Proportion

22. Five bars of soap cost £7.50. What will be the cost of:

(a) 1 bar of soap (b) 7 bars of soap (c) 20 bars of soap?

23. Four textbooks cost £34.00.

What will be the cost of:

(a) 1 textbook (b) 15 text books (c) 30 text books?

24. A car uses 4 litres of petrol to travel 52km.

(a) How far will it travel on 8 litres of petrol?

(b) How far will it travel on 20 litres of petrol?

(c) How much petrol will it need for a journey of 442 km?

25. Eight loaves weigh 7 kilogrammes.

(a) What would two dozen loaves weigh?

(b) How many loaves would you have if their combined weight was

35kg?

Page | 10

26. A club secretary can address 5 envelopes in 2 minutes.

How many minutes will it take him to address envelopes for all 360

club members?

27. Six friends decided to go

ice skating.

The total cost of admission

was £25.50. At the last

minute 2 more people

decided to join in.

How much would it now

cost for admission?

28. To make a smoothie for herself and her two friends, Millie used 6

strawberries, 3 bananas, 45ml of honey and 300ml of milk.

Calculate how much honey would be needed to make smoothies for

five people.

29. A joiner, a plumber and an electrician were employed to carry out

emergency repairs on a house.

The joiner worked for 2 days, the plumber for 1 day and the

electrician for 3 days.

The house owner gave them £630 to cover their labour costs.

Assuming they all received the same daily pay, calculate how much

the joiner was due for his work.

Page | 11

B Negative Numbers

B1 I have revised how to extend the number line below zero

and know the meaning of the term Integer.

1. Use a ruler to neatly copy and complete these number lines filling in

all the gaps.

(a)

(b)

(c)

(d)

2. Copy the list of numbers below and circle all the integers.

3 −4 2∙7 3

4 0 −1∙2 8 −53

Page | 12

3. Copy the list of numbers below and circle the numbers which are not

integers.

62 21

2 −19 7 5∙1 0 −1∙2

3

4

4. Which of the numbers in each pair is the largest?

(a) 3, −1 (b) −3, 1 (c) −5, 0

(d) −95, 5 (e) −10, 2 (f) −17, 1

5. (a) What number is 5 greater than −3?

(b) What number is 7 less than 4?

6. Put these numbers in order, smallest first

2, 1, −5, 4, 0, −3

Page | 13

B2 I can use negative numbers in the context of temperature

7. Write down the temperature shown on each thermometer.

The temperatures are all in degrees Celsius.

(a) (b) (c) (d) (e)

8. It was -6 °C in the morning. By lunchtime the temperature had risen

to 8 °C.

(a) Which of these calculations do you think apply?

(i) −6 + 8 (ii) −6 − 8

(iii) 8 + (−6) (iv) 8 − (−6)

(b) How many degrees had the temperature risen?

Page | 14

9. The temperature in Glasgow on Monday was 5°C, but by Friday it had

fallen to −3°C.

(a) Which of these calculations do you think apply?

(i) 5 + (−3) (ii) 5 − (−3)

(iii) −3 + 5 (iv) −3 − 5

(b) How many degrees had the temperature fallen?

10. The temperature in East Kilbride

was −15°C.

The weather report said that the

temperature would rise by 7

degrees.

(a) Which of these calculations do you think apply?

(i) −15 + 7 (ii) −15 − 7

(iii) 7 + (−15) (iv) 7 − (−15)

(b) What would be the new temperature after this rise?

11. A liquid is stored at −14°C.

If the temperature of the liquid is reduced by 9 degrees it would

reach its freezing point.

(a) Which of these calculations do you think apply?

(i) −14 + 9 (ii) −14 − 9

(iii) 9 + (−14) (iv) 9 − (−14)

(b) What is the freezing point of this liquid?

Page | 15

12. The temperature was −7°C at midnight.

By the next day, the temperature had risen by 11°C.

(a) Some of these calculations show how to figure out the

temperature the next day.

Which of these calculations apply.

(i) 7 − 11 (ii) 11 + (−7)

(iii) (−11) − (−7) (iv) (−7) + 11

(b) What was the temperature the next day?

13. Write down the temperature which is

(a) 12℃ higher than –8℃ (b) 4℃ lower than –2℃

14. It was extremely cold at

midnight. During the morning,

the temperature rose by 5°C. By

midday, it had reached -11°C.

What was the temperature at

midnight?

Page | 16

15. The temperature at midnight was −11°C. By midday, the temperature

was 5°C.

What was the temperature change?

16. At midday, the temperature was 5°C. The temperature then fell by

11°C.

What was the final temperature?

17. The table below shows the temperature at five airports one morning.

(a) What would be the temperature rise or drop flying from

(i) Berlin to Glasgow (ii) Madrid to Berlin

(iii) Tromso to London (iv) Glasgow to Tromso

(v) Berlin to Tromso (vi) Berlin to London

(vii) Tromso to Madrid (viii) Glasgow to London

(b) Write down a calculation, which could apply, for each of the

answers in part (a).

City Berlin Glasgow London Madrid Tromso

Temp −5℃ −1℃ 8℃ 18℃ −8℃

Page | 17

18. The map of Europe below appeared in a French Newspaper.

It displays the average daytime temperature in some countries.

(a) Which country was colder Germany or UK?

(b) Which country was warmer Holland or Switzerland?

(c) Write down the temperature which is 5℃ hotter than Ireland.

(d) Write down the temperature which is 17℃ colder than Spain.

(e) Next day, the average temperature in France increased by 7℃.

Write down a calculation which illustrates this increase.

Page | 18

B3 I can apply the four operations to negative numbers.

19. Write down the question then evaluate,

(a) 4 + (−11) (b) 2 – 12 (c) (−6) + 16

(d) −6 + (−9) (e) 7 − 15 (f) (−6) – 7

(g) (−63) ÷ 9 (h) 84 ÷ (−4) (i) 56 ÷ (−7)

(j) (−27) ÷ 3 (k) (−5) × (−4) (l) (−9) × (−8)

20. Write down the question then evaluate,

(a) 6 × (−6) b) 7 × (−8) c) (−8) × 4

(d) 15 × (−4) (e) (−7) × 3 (f) (−40) ÷ 8

(g) (−50) + (−70) (h) (−42) + 42 (i) (−11) − 4

(j) 18 + (−22) (k) 13 + (−14) (l) 36 − (−14)

21. (a) 9 − (−9) (b) 560 + (−840) (c) 3 · 4 − ( −2 · 6)

(d) (−3) × (−6) (e) (−4) × (−12) (f) (−10)×(−6)

(g) (−3) − ( −7) (h) (−9) + (−12) (i) −15 − (−15)

(j) (−48) ÷ (−8) (k) (−27) ÷ (−3) (l) (−81) ÷ (−9)

22. (a) (−25𝑥) − (−5𝑥) (b) 9𝑔 − (−15𝑔) (c) 5𝑥 + (−6𝑥)

(d) (−63𝑞) ÷ (−7) (e) (−36𝑝) ÷ (−12) (f) 6𝑟 × (−7) ÷ 3

(g) −8 × (−3𝑥) ÷ (−4) (h) −4 × 𝑝 ÷ (−2) (i) −15 × 𝑟 ÷ (−3)

Page | 19

23. Simplify by gathering like terms

(a) 4𝑥 + (−11𝑥) (b) 2𝑦 − 12𝑦 (c) (−6𝑧) + 16𝑧

(d) −6𝑥 + (−9𝑥) (e) 7𝑦 − 15𝑦 (f) (−6𝑧) − 7𝑧

(g) 4𝑥 + 3𝑦 − 6𝑥 + 𝑦 (h) −3𝑝 + 𝑞 − 6𝑝 − 2𝑞 (i) 2𝑎 + 3 − 7𝑎

24. (j) 8𝑥 + 3 − 6𝑥 − 8 (k) −2𝑎 − 3 − 3𝑎 + 10 (l) −8𝑝 + 15 − 12𝑝

(m) 6𝑝 + 8 − 5𝑝 − 12 (n) 4𝑥 − 3𝑦 − 7𝑥 + 5𝑦 (o) −9𝑎 + 𝑏 + (−𝑎)

25. (p) −4 + 3𝑎 − 7𝑎 − 5 (q) −4𝑝 + 2𝑞 − (−3𝑝) (r) 9 + 4𝑥 − 11

(s) −19𝑎 + 6𝑏 + (−2𝑎) (t) −5𝑥 + 7𝑦 − 5𝑥 − 9𝑦 (u) 5𝑝 + 𝑞 + (−4𝑝)

26. Start by carrying out the multiplications, then gather up like terms

(a) −3×𝑥 + (−3)×𝑦 + 2𝑥 − 𝑦 (b) 4×𝑥 + 4×𝑦 − 2𝑥

(c) 3×2𝑥 + 3×(−2𝑦) − 3𝑥 + 6𝑦 (d) 5𝑎 − 3×𝑎 + 3×𝑏

(i) 8𝑥 − 2𝑦 + 5×(−𝑥) + 2×6𝑦 (j) 3 + (−2)×5𝑝 + (−7)×2

27. (a) −5×3𝑥 + (−5)×4𝑦 + 15𝑥 + 7𝑦 (b) 7×𝑥 − 5×𝑦 + 9𝑦

(c) −2𝑝 + 4𝑞 + (−4)×3𝑝 + (−4)×𝑦 (d) 9 + (−2)×𝑎 + (−2)×4

(e) 7𝑥 − 4𝑦 + 3×(−2𝑥) + 3×4𝑦 (f) 5 + (−3)×2𝑝 + (−3)×1

28. Write down the additive inverse (the number you add to the term

given to obtain zero) of,

(a) −2𝑥 (b) 5𝑦 (c) −10𝑧

(d) (−5)×(−2𝑥) (e) 7×−3𝑦 (f) 6×3𝑧

(g) −8𝑥 ÷ 4 (h) 20𝑦 ÷ (−4) (i) −21𝑧 ÷ −3

Page | 20

C Fractions

C1 I understand “the fraction of a whole” and

“equivalent fractions”.

1. For each of the following, say what fraction of the whole has been

shaded:-

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Page | 21

2. For each of the following, say what fraction of the whole has been

shaded:-

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Page | 22

3. Eva told Ben that 5

8 was a bigger fraction than

3

4 .

Ben didn’t agree and backed his argument up with the following

diagrams.

(a) Do you agree with Ben or Eva?

Justify your answer using a reference to Ben’s diagrams.

(b) Use two similar diagrams to show that 6

8=

3

4 .

4. In each of the questions below, justify your answer by referring to a

diagram.

(a) Which is the greater fraction, 2

3 or

7

12 ?

(b) Which is the greater fraction, 1

3 or

4

9 ?

(c) Which is the greater fraction, 1

4 or

2

5 ?

(d) Which is the greater fraction, 1

4 or

2

8 ?

Page | 23

5. (a) Draw the following number line

Minimum of 0, maximum of 1, Grid step 1

16, Numbered step

1

4.

(b) On your number line, indicate with an arrow the following

(i) 1

8 (ii)

5

8 (iii)

1

16

(iv) 5

16 (v)

3

8 (vi)

15

16

(c) Which is the greater fraction 5

8 or

7

16.

(d) Which is the lower fraction 3

4 or

5

16.

(e) Which is the greater fraction 7

8 or

1

2.

6. (a) Draw the following number line

Minimum of 0, maximum of 1, Grid step 1

20, Numbered step

1

5.

(b) On your number line, indicate with an arrow the following

(i) 1

10 (ii)

3

10 (iii)

9

10

(iv) 3

20 (v)

17

20 (vi)

12

20

(c) Which is the greater fraction 2

5 or

9

10.

(d) Which is the lower fraction 4

5 or

17

20.

(e) Which is the greater fraction 7

10 or

3

5.

Page | 24

C2 I can find a number of equivalent fractions to any given

fraction and can simplify fractions to their simplest form.

7. Write four more fractions equivalent to the fraction given.

(a) 1

4 (b)

1

5 (c)

4

5

8. Write four more fractions equivalent to the fraction given.

(a) 2

7 (b)

5

6 (c)

3

4

9. Give each fraction in its simplest form

(a) 4

6 (b)

9

12 (c)

35

42 (d)

21

49 (e)

10

12

10. Give each fraction in its simplest form

(a) 10

30 (b)

6

9 (c)

15

25 (d)

42

48 (e)

25

55

11. Give each fraction in its simplest form

(a) 8

10 (b)

21

28 (c)

12

21 (d)

9

24 (e)

7

42

12. Give each fraction in its simplest form

(a) 10

100 (b)

50

100 (c)

25

100 (d)

75

100 (e)

60

100

Page | 25

13. (a) Write an equivalent fraction, with twelve in the denominator, to

each of these

(i) 5

6 (ii)

3

4 (iii)

2

3 (iv)

1

2

(b) Now write the fractions in order from smallest to largest.

14. (a) Write an equivalent fraction, with sixteen in the denominator, to

each of these

(i) 1

2 (ii)

3

4 (iii)

1

4 (iv)

3

8

(b) Now write the fractions in order from smallest to largest.

15. (a) Write an equivalent fraction, with twenty four in the

denominator, to each of these

(i) 5

6 (ii)

3

4 (iii)

2

3 (iv)

5

12

(b) Now write the fractions in order from smallest to largest.

16. John found five old drills in his granda’s toolbox.

The drills had their size, in inches, scribed on the side.

The sizes are shown below.

1

2 inch

5

8 inch

9

16 inch

3

4 inch

1

4 inch

Put the drills in order of size, starting with the smallest.

Page | 26

C3 I can calculate the fraction (unitary and non-unitary) of a

quantity involving at most 4 digits without a calculator.

17. Carry out the following calculations

(a) 1

6 of 1404 (b)

1

4 of 248 (c)

1

5 of 430

18. Carry out the following calculations

(a) 2

3 of 1956 (b)

3

7 of 476 (c)

5

8 of 3528

19. A research project looking at the different uses of computers

found that on average 2

5 of the time is spent communicating

with others.

John notes that he has spent 640 hours on his computer since

he first bought it.

How much of this time would you expect him to have been

communicating with others?

20. A sample of air was taken in a food factory. The sample of air

was found to be 2

5 nitrogen by volume.

The volume of air in the factory is 150 cubic metres.

How many cubic metres of nitrogen are in the factory?

21. In a school of 1800 pupils, two thirds have a healthy lunch.

How many pupils have a healthy lunch?

Page | 27

22. A cinema has 730 seats.

On Monday night, the cinema was 3

5 full.

How many people were in the cinema on Monday night?

23. Paul is a diver. In his diver's cylinder, 3

4 of the breathing gas

mix is nitrogen.

The tank contains 1600 litres of the breathing gas mix.

How many litres of Nitrogen are in the cylinder?

24. Calderglen High School runs an annual charity event.

During the first year they raised £900 and donated 1

2 to a homeless

charity.

During the second year they raised £690 and donated 2

3 to the same

charity.

In which year did they donate the biggest amount to the charity?

Justify your answer with calculations

25. Sam is baking in Home Economics.

The first recipe has 1250g of ingredients of which 1

5 are flour.

The second recipe has 320g of ingredients of which 3

4 are flour.

Which recipe requires the most flour?

Justify your answer with calculations

Page | 28

26. Look at the two statements below.

Sample A contained 600 millilitres

of which 1

4 was fruit juice.

Sample B contained 265 millilitres

of which 3

5 were fruit juice.

Which sample contained the most fruit juice?

Justify your answer with calculations

27. Ben said “Over 2

5 of my salary is deducted in tax and National

Insurance”

Ben earns £750 a month and pays £290 in tax and National Insurance.

Is Ben’s claim true?

Justify your answer with calculations

28. A company claims “Over 7

8 of customers a satisfied with our products”.

In a survey 1070 customers out of 1216 said they were satisfied with

the company’s products.

Is the company’s claim true?

Justify your answer with calculations

Page | 29

C4 I can convert between fractions and decimals with a

calculator and round to a given number of decimal places.

29. Write each fraction as a decimal fraction to two decimal places.

(a) 1

6 (b)

1

7 (c)

1

15

(a) 3

11 (b)

2

3 (c)

7

13

30. Write each fraction as a decimal fraction to three decimal places.

(a) 1

9 (b)

2

9 (c)

3

9

(a) 4

9 (b)

5

9 (c)

6

9

31. Write the following decimals as fractions in their simplest form.

(a) 0.4 (b) 0.9 (c) 0.14

(a) 0.26 (b) 0.375 (c) 0.548

32. The following are results from a school for the number of pupils who

passed their exams:

Mathematics – out of 80 pupils, 65 of them passed.

Art and Design – out of 60 pupils, 40 of them passed.

If you were the deputy head teacher, which subject would you focus

on more to improve the number of pupils passing?

Justify your answer by calculation.

Page | 30

33. Three classes in a school were given the same test. The pass rate for

each class is shown below.

Class A: 26 out of 30 pupils passed.

Class B: 21 out of 25 pupils passed.

Class C: 19 out of 22 pupils passed.

Which class had the best pass rate?

Justify your answer by calculation.

34. Sally scored the following marks in three of her subject tests.

Maths: 25 out of 40.

English: 32 out of 50.

Science: 38 out of 60.

In which subject did she do best in?

Justify your answer by calculation.

35. Three netball teams play in the same league.

Calderglen Cats have won 5 out of 8 games.

Glasgow Giants have won 8 out of 12 games.

Edinburgh Eagles have won 9 out of 15 games.

Which team has the best winning record?

Justify your answer by calculation.