N4 Numeracy

Book 2

The wee

Maths Book

of Big Brain

Growth

Length, Volume and Percentages

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

D Length and Volume

D1 I am aware of the different metric units in which length is

measured and can decide which unit is most appropriate in

a given context.

Complete this exercise without the aid of a calculator

1. Change these measurements into millimetres

(a) 7cm (b) 12cm (c) 8·6cm

(d) 3cm 4mm (e) 59·1cm (f) 702cm

2. Change these measurements to centimetres

(a) 60mm (b) 400mm (c) 250mm

(d) 3mm (e) 4m (f) 0·5m

(g) 17m (h) 8m 90cm (i) 9m 8cm

(j) 3·6m (k) 0·02m (l) 1·75m

3. Convert these measurements into metres

(a) 300cm (b) 5000cm (c) 1400cm

(d) 590cm (e) 60cm (f) 71cm

4. Convert these measurements into kilometres

(a) 19300m (b) 8650m (c) 450m

(d) 900000cm (e) 20000cm (f) 1400cm

Page | 3

5. Change the units of the following measurements as indicated

(a) 2·4 cm into mm (b) 3·2 km into m

(c) 180 cm into m (d) 1060 mm into cm

(e) 760 m into km (f) 0·03 m into cm

(g) 5·6 cm into mm (h) 0·72 km into m

(i) 69·35 cm into m (j) 34256 mm into cm

(k) 501 m into km (l) 1·94 m into cm

6. Change the units of the following measurements as indicated

(a) 31·3 cm into mm (b) 0·201 km into m

(c) 0·00503 m into cm (d) 43 mm into cm

(e) 34 m into km (f) 846·81 cm into m

(g) 0·062 cm into mm (h) 1·5 km into m

(i) 0·02 cm into m (j) 342·67 mm into cm

(k) 0·089 m into km (l) 43 m into cm

7. Change the units of the following measurements as indicated

(a) 0·71 cm into mm (b) 7·8 km into m

(c) 89·4 m into cm (d) 6·67 mm into cm

(e) 231 m into km (f) 9·08 cm into m

(g) 0·802 cm into mm (h) 1·05 km into m

(i) 27 cm into m (j) 9·34 mm into cm

(k) 0·9091 m into km (l) 202 m into cm

Page | 4

8. Elle is building some raised beds for growing vegetables.

She needs pieces of wood that are 1∙45 metres long.

When Elle goes to purchase the wood, she finds all the measurements

are in millimetres.

What length of wood does Elle need to order?

9. The heights of all of the members of One Direction are listed below.

Name Height

Niall 171cm

Harry 1780mm

Louis 1∙74m

Liam 177cm

What is the mean (average) height of the band?

10. Calculate the perimeter of the rectangle below.

32cm

1∙05m

Page | 5

11. Shaun uses a trundle wheel to measure the perimeter of the school’s

fence; he finds that it is 879 metres long. How many complete laps of

the school will Shaun need to run to ensure he covers 5 kilometres?

12. The distance from the Earth to

the Moon is approximately

370000 kilometres.

The Samsung Wind turbine in Fife is

200 metres tall.

How many of these wind turbines

would fit end-to-end between the

Earth and the Moon.?

13. Baked beans come in cylindrical tins 11 centimetres high and with

diameter 7 centimetres. The tins are packed into boxes measuring

420 mm by 280 mm by 350 mm.

(a) One layer of cans is placed (upright) into the bottom of the box

above.

How many cans will fit into the bottom layer?

(b) How many tins can be packed into the box altogether?

420mm

280mm

350mm

7cm

11cm

(tin and box not to scale)

Page | 6

D2 I can solve problems which involve perimeter and can

include inconsistent units

14. The diagram shows the dimensions of a swing park.

(a) Find the perimeter of the swing park in metres.

(b) Is 22 metres of fencing enough to fence the swing park.

Justify your answer with a calculation.

15. Another swing park is

shown.

Will 42 metres of

fencing be enough to

fence this swing park?

Justify your answer

with a calculation.

9 m

525cm

3 m

250cm

12 m

150cm

450cm

5 m

Page | 7

16. The following two shapes have the same perimeter.

Find the missing length of the triangle.

17. Lucy wants to decorate her kite with new ribbon around the

perimeter.

She bought a one metre roll of ribbon.

Will this be enough ribbon to decorate around her kite?

5cm

110mm

x

150mm

30cm

70mm 10mm

20mm 5cm

4cm

Page | 8

18. The diagram shows the room dimensions of Tammy’s bedroom.

Tammy wants to put new skirting boards round her bedroom.

(a) The door entrance is 60cm wide and will not require any skirting.

Calculate the amount of skirting board required.

(b) Skirting board costs £2·50 per metre.

Tammy has £45 will this be enough to buy the new skirting

boards?

520cm

4·7m

Page | 9

D3 I can comfortably convert between litres, millilitres and

cubic centimetres

19. Write the volume of each of the following items in litres.

(a) (b) (c)

2000 cm3 1400 cm3 350 cm3

(d) (e) (f)

5 ml 568 cm3 150 ml

(g) (h) (i)

Page | 10

500 ml 750 ml 3500 cm3

(j) (k) (l)

160000 cm3 5000 cm3 330 ml

20. Write the volume of each of the following items in millilitres.

(a) 160 litres (b) 50 litres (c) 2 litres

(d) 0·333 litres (e) 4 litres (f) 0·5 litres

(g) 0·568 litres (h) 0·75 litres (i) 0·05 litres

21. For each of your answers in Q2, give an example of a container which

would normally contain that volume.

Page | 11

22. I have 1 litre of water in a jug to be used in an experiment.

On the way to my table I spill some.

I have 780ml left. How much have I lost?

23. I have 1 litre of Sprite.

I give 300ml to William, 200ml to Paul and 250ml to Mia.

How much do I have left?

24. Mr Hart has to have a fluid intake of at least 2 litres.

He has drunk two 275ml of tea, one 300ml of coffee, 200ml of orange

juice and 180ml of water.

How much more fluid does Mr Hart require?

25. Clare is having a party and has bought three 2 litre bottles of fizzy

pop.

She has 30 party cups and decides to share the fizzy pop evenly.

How many millilitres will go in a cup?

26. Sarah needs 𝟏𝟏

𝟒 litres of vegetable stock for making lentil soup.

She decides to use OXO vegetable stock cubes and on the box it says:

“For a tasty stock dissolve one cube in 190 ml of boiling water.”

How many stock cubes will Sarah need for making her stock?

Page | 12

For this experiment you will need:

15 cm3 (1 tablespoon) of baking soda (sodium bicarbonate)

15 cm3 (1 tablespoon) of laundry detergent about 180 millilitres (3/4 cup) of water about 60 millilitres (1/4 cup) of vinegar several drops of food colouring (optional) a 400-milliliter (12-ounce) drinking glass a waterproof (plastic or metal) tray a teaspoon

27. Drew is looking at the materials needed for the Fizzing and Foaming

experiment.

(a) How many millilitres does a tablespoon hold?

(b) How many tablespoons of water are required?

(c) Drew has a 1 litre bottle of vinegar, how many Fizzing and

Foaming experiments can he complete with this bottle?

28. For the Mentos Geyser Experiment it is

advised to have one Mentos sweet per

250 ml of Diet Coke.

(a) Kate has a 1.75 litre bottle of Diet

Coke, how many Mentos sweets does

she need?

(b) Craig has a 3 litre bottle of Diet

Coke, how many Mentos sweets does

he need?

Page | 13

E Percentages

E1 I can convert comfortably between (common) fractions,

decimals fractions and percentages in order to compare

quantities given in different formats.

1. Write each of the following as a fraction and as a decimal fraction

(a) 13% (b) 24% (c) 99%

(d) 56% (e) 25% (f) 83%

(g) 10% (h) 180% (i) 75%

(j) 116% (k) 5% (l) 103%

(m) 7.2% (n) 35% (o) 1%

2. Change each fraction into a percentage (calculator),

(a) 18

100 (b)

4

5 (c)

7

10

(d) 17

25 (e)

19

20 (f)

1

4

(g) 49

50 (h)

5

8 (i)

27

40

(j) 6

75 (k)

12

8 (l)

50

40

3. Write down the percentage which is equivalent to each of the

following fractions (without a calculator)

(a) 1

2 (b)

3

4 (c)

1

10

(d) 2

3 (e)

1

5 (f)

3

10

Page | 14

4. Work out the percentage which is equivalent to each of the following

fractions.

Give your answer to 2 significant figures and how your working

clearly.

(a) 9

11 (b)

7

13 (c)

11

15

(d) 1

3 (e)

13

30 (f)

87

90

(g) 5

8 (h)

37

40 (i)

1

66

5. Write down the fraction which is equivalent to each of the following

percentages (without a calculator).

(a) 25% (b) 1% (c) 20%

(d) 12½% (e) 10% (f) 30%

(g) 90% (h) 5% (i) 15%

6. Write each of the following percentages as a fraction in its simplest

form. Show your working clearly.

(a) 30% (b) 4% (c) 85%

(d) 7·5% (e) 9·4% (f) 0·3%

(g) 65·5% (h) 8·02% (i) 0·12%

(j) 5·55% (k) 0·05% (l) 0·64%

Page | 15

E2 I can find a percentage of a quantity involving at most 4

digits (Non Calculator and Calculator).

Without a calculator

7. At a comedy show 9% of the audience buy a programme.

If 1500 attend the show, how many buy a programme?

8. A travel firm offers a discount of 40% off the full price of package

holiday.

The full price of the package holiday is £760.

How much is the discount?

9. A salesperson is paid commission of 15% of her weekly sales.

How much will her commission be in a week when her sales total

£800?

10. A bottle of iodine solution contains 7% iodine by volume.

What volume of iodine is there in a 500ml bottle?

11. A metal alloy contains 60% pure gold.

How much gold is there in 270g of the alloy?

12. A hotel in Glasgow offers 30% off the full price of a weekend break.

How much is this saving if the full price of a weekend break is £700.

Page | 16

E3 I can calculate percentage increase and decrease.

13. A new luxury villa in Florida is valued at $375000. It is expected to

rise in value by 15% during its first year.

What will the value of the villa be at the end of the first year?

14. Mrs Dodds buys a new for £25000.

It depreciates in value by 12% during its first year.

How much will Mrs Dodds car be worth at the end of the first year?

15. Jorge buys a new house for £80 000. The value of the house

depreciates by 8% in the first year.

How much would his house be worth at the end of the first year?

16. Company shares worth £1,200 depreciate in value over a month by

12%.

How much were the shares worth at the end of the month?

17. The Pollards bought a bungalow for £110,000.

It appreciated in value by 8% in first year.

How much was the bungalow worth at the end of the first year?

Page | 17

E4 I can express one quantity as a percentage of another and

work out a percentage increase or decrease using the

original value and final value.

18. Alan scored 28 out of 40 in a Maths test.

What was his percentage score?

19. The Head of First Year knows there are 300 pupils in the year group.

160 of them are girls.

What percentage are boys?

20. Jamie bought a new car for

£18000 in 2009 and sold it for

£8000 three years later.

Calculate the depreciation, and express it as a percentage of the cost

when new?

Give your answer to 1 decimal place.

21. In the 2011-2012 season Lionel Messi scored 73 of the 190 goals scored

by Barcelona.

What percentage of Barcelona’s total goals Lionel Messi score?

Give your answer to 1 decimal place.

22. Last year Sally was paid £20 per hour.

This year she gets £22.50 per hour.

Calculate her percentage increase in pay.