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"
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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
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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
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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
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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.
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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
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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.
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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
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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
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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.