Blue
5
Grow
your
brain
The wee
Maths Book
of
Big
Brain
Growth
Volume and Nets
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.
Tips for Parents
#5
Talk about your child's brain power improving, through hard
work, and not being something that is fixed
1.
Ability in Maths is not fixed – It can change.
Reinforce regularly with your child, that no matter their present
level of ability in Maths, that hard work and resilience in the face of
a challenge can make them improve.
2.
Acknowledge that Maths can be challenging
Always encourage your child to be ambitious in Maths even when
they find it challenging. Maths should be challenging and will
require your child to put in enough effort to meet this challenge.
Page | 2
Volume (MNU 3-11a, MTH 3-11b)
M13s
1.
I can comfortably convert between litres,
millilitres and cubic centimetres
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
Page | 3
(g)
(h)
(i)
500 ml
750 ml
3500 cm3
(j)
(k)
(l)
5000 cm3
330 ml
160000 cm3
2.
3.
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
For each of your answers in Q2, give an example of a container
which would normally contain that volume.
Page | 4
4.
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?
5.
I have 1 litre of Sprite.
I give 300ml to William, 200ml to Paul and 250ml to Mia.
How much do I have left?
6.
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?
7.
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?
8.
𝟏
Sarah needs 𝟏 litres of vegetable stock for making lentil soup.
𝟒
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?
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9.
Drew is looking at the materials needed for the Fizzing and
Foaming experiment.
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
(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?
10.
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 | 6
M14f
1.
I can calculate the volume of a variety of 3D
shapes including prisms by applying a formula
A fish tank is 55 cm long, 40 cm wide and 25 cm high, as shown.
25 cm
40 cm
55cm
(a) What formula would you use to calculate the volume of the
tank?
(b) Calculate how much water you need to fill the tank to the
top.
(c) Another fish tank holds twice the amount of water.
How much water do you need to fill it to the top?
2.
A 5 litre jug of water is poured into this tank.
19cm
30cm
Will the tank overflow?
Page | 7
9cm
3.
4.
Find the volume of the prisms shown.
(a)
(b)
(c)
(d)
The diagram shows a triangular prism.
The dimensions are given on the diagram.
(a) Calculate the area of the cross section of the prism.
(b) Calculate the volume of the prism.
Page | 8
5.
The maths department were having cheese, what is the volume
of this wedge of Emmental?
60 cm²
7∙5 cm
6.
A rubbish skip is prism shaped
as shown below.
2m
The skip has a length of two
metres and a cross sectional
area of 3∙6 m².
Hops Skips for
Hire
3∙6 m²
Find the volume of the skip in
cubic metres.
7.
A farmer turns a tap in order to fill this drinking trough, which is
in the shape of a cuboid, with water.
75cm
30cm
120cm
What volume of water will the trough hold?
Page | 9
8.
This swimming pool is 25 metres long and the area of the cross
section is 62∙5 m².
Calculate the volume of the pool in cubic metres when it is full.
10 m
62∙5 m²
9.
A tin of soup has a volume
1256 ml.
Calculate the height of
the tin, to the nearest
millimetre, if the crosssectional area is 150 cm2.
Page | 10
ℎ cm
10.
The front of a hut has an area of 4∙6 m², it also has a volume of
11∙04 m³.
Calculate the depth of the hut in millimetres.
4∙6 m²
Depth mm
11.
A wedge of cheese has a volume of 259∙2 cm³.
If it has a cross sectional area of 72 cm², then how thick is the
cheese?
Give your answer in millimetres.
Thickness mm
Page | 11
12.
A baker has been asked to make alphabet shaped cakes.
The letter A cake mould
has a uniform cross
section of area 350 cm2.
The depth of the mould
is 8.5 cm.
The baker has 2.9 litres
of cake mix. Is this
enough to make the
cake?
You must justify your answer.
13.
Physiotherapists often use exercise pools with movable bases to
help rehabilitate injured patients. A physiotherapist wants to
work with 4 patients simultaneously.
Guidelines advise that for a
group of 2 to 5 people the
floor area of the pool should
be between 80000 cm2 and
200000 cm2.
The maximum depth of this
pool is 2 metres. The floor
is raised by 60 cm.
If the volume of water in the pool is 12600 litres, will the floor
area meet the guidelines? You must justify your answer.
Page | 12
14.
An exotic fish is placed in an aquarium which is a rectangular
prism with a base of area 1500cm2.
1500cm2
cm
If the water level rises by 0.2cm, what is the volume of the fish?
15.
A contestant on BBC MasterChef makes 500 ml of jelly mix in
preparation to pour into a mould.
The mould is a prism as shown below.
64 cm2
7cm
Will she have enough mix to fill the entire mould?
Page | 13
M15t
1.
Having investigated different routes to a solution, I
can find volume of compound 3D objects, applying
my knowledge to solve practical problems.
The diagram shows two compound shapes made from cuboids.
The dimensions are given on the diagrams.
Find the volume of each shape.
(a)
2.
(b)
The volume of the prism, shown below, can be calculated using
the prism formula or from the fact that it is made up from
compound cuboids.
Find the volume using the two methods and check that in both
cases the answers are equal.
Page | 14
3.
Again, the volume of the prism, shown below, can be calculated
using the prism formula or from the fact that it is made up from
compound cuboids.
Find the volume using the two methods and check that in both
cases the answers are equal.
4.
Calculate the volume of the composite shape shown below,
which is made up from two cuboids.
Is the shape a prism?
Page | 15
Nets and Surface Area (MNU 4-11a, MTH 4-11b)
M16f
Working with others I have accurately made the
net of a cube, cuboid and triangular prism and I
can calculate surface area of a cube, cuboid and
triangular prism.
1.
Pick the correct net for the shape
2.
Pick the correct net for the shape
3.
Pick the correct net for the shape
Page | 16
4.
Pick the correct net for the shape
5.
Pick the correct net for the shape
6.
Pick the correct net for the shape
7.
Pick the correct net for the shape
Page | 17
8.
A cuboid and its net are shown below.
2 cm
6 cm
3 cm
3 cm
2 cm
3 cm
Calculate the surface area of the cuboid.
9.
A triangular prism and its net are shown below.
Calculate the surface are of the triangular prism.
6 cm
10 cm
8 cm
10 cm
5 cm
6 cm
Page | 18
5 cm
10.
On squared paper draw three different nets of a cube.
11.
Which of the following nets below represent a net of a cube
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Page | 19
M17f
1.
I have investigated problems involving container
packaging.
Ben works for an electrical manufacturer packing items in boxes.
He is packing a product, in their box, into larger boxes for
delivery.
5 cm
80 cm
40 cm
100 cm
180 cm
30 cm
What is the maximum number of product boxes that can be
fitted into the large box?
Justify your answer
Page | 20
2.
Cereal boxes are transported in larger boxes to ship around the
country.
A cereal manufacturer has two options as show below.
13
c
50
c
35
c
245
250
c
c
420
260
c
c
Option A
260
400
c
Option B
If they want to transport the most cereal boxes at once should
they choose option A or B?
Justify your answer.
Page | 21
c
3.
Packaging is cut out of cardboard in the form of a net, and then
folded to create a box.
A net for a box is shown below.
40 cm
30 cm
50 cm
These boxes are then filled with pens and put into a larger box
shown below for transporting.
90 cm
160 cm
250 cm
What is the maximum number of small boxes that can be fitted
into the large box?
Justify your answer.
Page | 22
4.
A library gets a new bookcase delivered.
22 cm
195 cm
16 cm
If all the books are the size shown, how many books can they fit
into the bookcase?
3 cm
Justify your answer.
20 cm
14 cm
Page | 23
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.
Page | 24