Blue

4

The wee

Maths Book of Big Brain

Growth

Length (including circumference) and

Area Calculations

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

Tips for Parents #4

Talk about your child's brain power improving, through hard

work, and not being something that is fixed

1. Discuss brain growth with your child

Make your child aware hard work, and persistent effort, can

actually change their brain, making physical connection between

neutrons which in turn will make their brain grow fitter and

stronger.

2. Define smart as a process not an attribute

Say things like:

"It was smart to try those five questions, check the answer and to

learn from all your mistakes"

Page | 3

Length (MTH 3-17c)

M5s 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 questions 1 to 10 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 | 4

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 | 5

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 boy band are listed below.

Name Height

Niall 171cm

Harry 1780mm

Louis 1∙74m

Liam 177cm

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

10. Calculate the perimeter of the rectangle below.

32cm

1∙05m

Page | 6

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

fence; he finds that it is 926 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. John’s pedometer shows he has

walked 10258 steps.

Each step of John’s steps measures

90 centimetres.

How far has John walked?

Give your answer in kilometres to

1 decimal place.

Page | 7

M6s I can solve problems which involve perimeter and can

include inconsistent units

1. 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.

2. 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

200cm

450cm

5 m

Page | 8

3. The following two shapes have the same perimeter.

Use algebra to find the missing length of the triangle.

4. 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 | 9

5. The diagram, which is not drawn to scale, 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?

(c) Tammy’s bed is 2100 millimetres in length.

When the door is fully open, as shown in the diagram, there is a

gap between the door and the bed.

How big is this gap?

420cm

3·7m

Page | 10

M7t I can use a simple scale to make enlargements and

reductions.

1. Use a scale of 1cm to 5km to make an accurate scale drawing of the

sketch below.

2. Use a scale of 1cm to 2km to make an accurate scale drawing of the

sketch below.

Page | 11

3. Use a scale of 1cm to 10km to make an accurate scale drawing of the

sketch below.

4. Use a scale of 1cm to 10m to make an accurate scale drawing of the

sketch below.

All internal angles in the shape are right angles.

Page | 12

Circumference (MTH 4-16b)

M8s I am able to recognise and label a circle and understand

the relationship between radius and diameter.

1. Copy the diagram shown into your

jotter.

2. The Olympic symbol consists of five

identical circles.

Part of the symbol is shown in the diagram below.

• the length of the symbol is 45 centimetres

• the circles are equally spaced

• the gap between the adjacent circles is 1·5 centimetres.

Calculate the radius of a circle.

Page | 13

3. An ornamental fence is made from semi-circles.

Part of the ornamental fence, made from 12 touching semi-circles, is

shown below.

Calculate the radius of one semi-circle.

4. Measure the radius of each of these three circles in centimetres and

write the answers in your jotter.

(a) (b)

(c)

295.2 centimetres

Page | 14

M9f Working with others I can investigate Pi and with the

help of our research arrive at an approximate value to 2

decimal places.

Pi or 𝜋 is a mathematical constant whose value is the circumference divided

by the diameter in any circle.

𝜋 =𝐶

𝑑

Rearranging by dividing both sides by 𝑑 gives

𝜋 × 𝑑 = 𝐶

𝐶 = 𝜋 × 𝑑

𝜋 is one of the most important mathematical and physical constants, many

formulae from mathematics, science, and engineering involve 𝜋.

Task

Your teacher will give you some circles so that you can investigate the value

of Pi.

Page | 15

M10f I can use my approximation for Pi to calculate the

circumference given the diameter and vice versa.

1. Calculate the circumference of these circles.

Make sure you set down all the working.

Remember to provide units in your answers

(a) (b) (c)

(d) (e) (f)

2. The London Eye, is a giant Ferris

Wheel with a diameter of 120

metres.

How far does a passenger on the

London Eye travel in one

rotation?

6m 12mm

25cm

7mm 1·5m

4·2cm

Page | 16

3. An ant is walking around the rim of a

circular pot.

The pot has a radius of

6 centimetres.

(a) How far will the ant walk in one

lap of the pot?

The ant manages one lap every twenty seconds.

(b) How far will it walk in a minute?

Ben notices that the ant is still walking around the pot after an hour.

(c) Assuming the ant has kept to the same pace, how far would it

walk in an hour?

Give your answer in kilometres to one decimal place.

4. A bike has a wheel with a

diameter 65 centimetres.

How far would this wheel go in

250 revolutions (turns)?

Give your answer in kilometres

to two decimal place.

65 cm

Page | 17

5. Eva has a trundle wheel with a radius of

18 centimetres.

How many complete metres are

measured by 15 rotations of the wheel?

6. A farmer found a crop circle in his

field one day. He measured the

circle and found it had a radius of 20

metres.

Calculate the circumference of the

circle.

7. The average radius of the human iris

is 5·9 mm.

What is the average circumference

of the human iris to the nearest

centimetre?

8. On Pi Day, Eva baked a circular cake.

She wanted to put a ribbon around

the cake.

The cake was 30 centimetres in

diameter and Eva had 1 metre of

ribbon.

Is this enough to go around the cake?

Justify your answer

Page | 18

9. The ancient people of Scotland built stone circles.

The precise date and function of the circles can be unclear, but some

people think they may have been used in religious rituals.

Ben measures the inside diameter of one of these circles and found it

to be 13 metres. Ben found the outside diameter to be 15 metres.

Ben tells Cara that if you walk around the outside of the circle you’ll

walk over six metres further than if you walk around the inside.

Is Ben Correct?

Justify your answer

15m

13m

Page | 19

10. Calculate the diameter of circles with the following circumference.

Round your answers to 1 decimal place.

(a) 12 centimetres (b) 53 millimetres (c) 2·5 metres

11. A circle has a circumference of 22∙86 centimetres.

Calculate the size of the radius of this circle.

Round your answer to 2 decimal place.

12. A toy train travels 157

centimetres when it

completes one lap of the

track.

Find the diameter of the

track in metres.

13. A roulette wheel has an outside

circumference of 2·5 metres.

Find the length of the radius

from the centre of the roulette

wheel, to the outer edge.

Give your answer to the

nearest centimetre.

Page | 20

14. The circumference of the Earth is

40 000 kilometres.

Calculate the diameter of the

Earth.

Give your answer to the nearest

1000 kilometres.

15. Mills were once common in

Scotland and most communities

would have had a mill.

Mills were used to ground wheat

to make flour for bread.

The wheat was ground by large

rotating millstones.

The millstone shown in the picture has a circumference of 3·2 metres.

What would be the diameter of the millstone?

Round your answers to the nearest whole metre.

16. In Cara’s drum kit the

circumference of the snare drum is

half the circumference of the base

drum

The circumference of the bass

drum is 240 centimetres.

Find the diameter of the snare

drum.

Page | 21

17. Find the perimeter of the semi-circles shown below

(a) (b) (c)

18. Find the perimeter of the quarter circles shown below

(a) (b) (c)

19. The opening of the fireplace is shown in the diagram.

The fireplace has a shape which

comprises of a rectangle and a

semicircle.

A metal strip is to be placed around

the fireplace opening.

Calculate the length of metal strip.

38 mm 2·4 cm

5·1 m

38 cm

5 m

14 mm

45 cm

40 cm

Page | 22

20. Cara’s garden, shown in the sketch below, has two flower beds in the

shape of quarter circles and one in the shape of a semi-circle.

Cara plans to plant seeds along all of the edges of the flower beds

A packet of seeds can sow a line 2 metres long.

How many packets of seeds does Cara need?

Show all working

21. A joiner is making tables for a new

coffee shop.

The shape of the top of a table is a

semi-circle as shown.

The top of the table is made of wood and a metal edge is to be fixed

to its perimeter.

(a) Calculate the total length of the metal edge.

(b) The coffee shop needs 16 tables.

The joiner has 50 metres of the metal edge in the workshop.

Will this be enough for all sixteen tables?

Give a reason for your answer.

120 cm

Page | 23

Area (MNU 3-11a, MTH 3-11b, MTH 4-11b)

M11t I can use a formula to calculate the area of a rectangle.

I can use the formula 12

A bh to calculate the area of a

triangle.

1. Find the area of each shape using the appropriate formula and

showing all of your working.

Don’t forget to include units in your answer.

(a) (b)

(c) (d)

12 cm

5 cm

2 m

2 m 2 m

2 m 15 cm

200 mm

20 cm

150 mm

Page | 24

(e) (f)

(g) (h)

(i) (j)

18 m

30 m

6 cm

8 m

9 m

12 cm

3 cm

4 cm

5 cm

16 cm

15 cm

Page | 25

2. The side view of a wooden door wedge shows the height is 4cm and

the length is 16∙5cm.

Calculate the area of the shaded part of the wedge.

3. The white sail of the yacht “Ocean Voyager” is in the shape of a right

angled triangle with dimensions shown.

Calculate its area in m².

4cm

16∙5cm

4∙6m

5∙5m

Page | 26

4. Alan gets a driveway company to give him a quote for the cost of

mono-blocking his 4∙5m by 6m rectangular driveway.

The price quoted is £85 per square metre including all materials and

labour.

If Alan chooses this company, what would be the cost of mono-

blocking his driveway?

5. Susan wants to turf her rectangular back garden.

She orders the turf from her local garden centre who charge £2∙70 per

square metre and a delivery charge of £15.

How much would it cost Susan for the turf (including delivery)?

9m

5∙5m

Page | 27

M12f I can find the area of composite shapes made up from

rectangles and triangles.

1. Using a ruler, make a neat sketch of the shape shown below.

All internal angles are right angles.

(a) What is the value of 𝑥?

(b) Calculate the areas of rectangles A and B, showing all working.

(c) Calculate the total area for the composite shape, showing all

working.

2. The composite shape shown is

made up from two rectangles.

Calculate its area, showing all working.

6 cm

20 cm

4 cm

14 cm

A B

𝑥 cm

12 m

24 m

8 m

8 m

Page | 28

3. Calculate the area of these composite shapes.

(a) (b)

(c)

(d)

27 cm

13 cm

14 cm

80 cm

25 cm

70 cm

50 cm

24 cm

24 cm

2·4 m

3·8 m

25 m

Page | 29

4. The end face of a house has to

be roughcast.

Mr Smith has been quoted

£6.30 per square metre to

complete the job.

He has a budget of £450 – can

he afford the work to be done?

Justify your answer.

5. A factory punches out equilateral triangle shapes from sheet metal for

use in the car industry.

How much metal is left over at the end of the process?

8m

7m

3m

30cm

24cm 26cm

Page | 30

6. Jane is an artist. She is

designing a square window

pane made from coloured and

clear glass.

The window pane is 60 cm

wide.

Each coloured rectangle is

20 cm long and 10 cm wide.

The four corners are

congruent isosceles

triangles.

Jane thinks that she will use 1400 cm2 of clear glass in the design. Is

Jane correct?

You must justify your answer.

7. The front, back and

2 sides of this shed

need to be painted.

1 tin of paint can

treat 25 m2 of

wood.

Is one tin enough to paint this shed?

You must justify your answer.

Page | 31

8. A Jawa sandcrawler has

sucked up R2D2.

The Jawas constructed

their sandcrawler using a

combination of rectangular

and triangular sheets of

metal, as shown in the

diagram below.

Can you work out the area available to Luke Skywalker to fire his

blaster at? (Ignore the tracks)

22m 10m 4m 3m

7m

13m

Page | 32

A well nurtured and emotionally healthy pupil will know that

they can improve their brain power through regularly applying

themselves to his/her studies in class and by completing all of

the tasks in this booklet.

He/she will feel more included, respected and will develop greater levels of

responsibility if you regularly discuss with them their progress, both progress

in class and progress through this booklet.

You will encourage him/her to be a passive learner and intellectually lazy if

you show them how to attempt every question. Encourage them to think for

themselves. Your child will achieve more if they actively experiment with

the questions in this booklet, safe in the knowledge that they can learn from

any mistakes made.

Tips for Parents

1. Talk to your child on a regular basis about the work they are

attempting in Mathematics.

2. Give praise for appropriate effort and resilience, and avoid praise

which uses the words clever or smart.

3. Talk about your child's brain power improving through hard work

and not being something that is fixed.

4. Mistakes are part of the learning process. Your child should be able

to experiment with Maths safe in the knowledge that they can learn

from their mistakes.

5. Talk about your child’s progress in a way which emphasises their

own ability to influence a positive and successful future. This will

encourage them to become more resilient and equipped to meet

the challenges of the course.