Download Structure of HSNP Numeracy - Four levels of proficiency

Ratio and Proportion 1
Simple ratios
Overview
Objectives

Understand, recognise and use simple ratios in a context

Scale up or down using simple ratios in context

Make two quantities using a given simple ratio
For this unit you will need:
red and yellow paint, large spoon, two paint palettes, two brushes,
interconnecting cubes
Watch out for pupils who:

think that if 1/3 of cubes are red for example, that the ratio is 1 : 3
rather than 1 : 2;

think that if you add the same number to each quantity the ratio
will remain the same, rather than multiplying or dividing each
quantity by the same number.
HSNP © Hamilton 2013
Simmering Term 1
Ratio and Proportion 1
Session 1
Objectives: Understand, recognise and use simple ratios in a context
Teacher input with whole class
 Pour two spoons of red paint and one spoon of yellow paint onto one
palette and one spoon of red and two spoons of yellow onto the other.
Ask pupils what colour of paint will be made when the paints are
mixed on each palette, how the two colours will differ and why. Draw
out that the two shades of orange will be different as you have used
different ratios of red to yellow paint. Mix each and use them to paint
two blobs on a large sheet of paper, writing red : orange under each,
and the ratios 2 : 1 and 1 : 2. Say that each palette contained three
spoonfuls of paint. Ask how many spoonfuls would be needed of each
colour to make a total of 6 spoonfuls of the darker orange and of the
paler orange. Record the ratios 4 : 2 and 2 : 4 under the initial ratios.
What if we needed to double this amount of paint?
Paired pupil work
 Ask pupils to work in pairs to find equivalent ratios for purple paint,
made in the ratio of 3 blue spoonfuls for every 1 spoon of red paint.
They copy and complete the following table. Encourage them to add
their own rows.
Total number of spoons Spoons of blue point
Spoons of red point
4
3
1
8
12
20
Teacher input with whole class
 Discuss the relationship between the numbers in the second and third
columns, i.e. that the numbers in the second column are 3 times the
number in the third column. If purple paint is made with four spoons of
paint, what fraction of the spoonfuls is red? Blue? And if 8 spoons are
used using the same ratio?
HSNP © Hamilton 2013
Simmering Term 1
Ratio and Proportion 1
Session 2
Objectives: Understand, recognise and use simple ratios in a context;
Scale up or down using simple ratios in context
Teacher input with whole class
 Display the following list of ingredients for a berry smoothie:
50g blueberries
100g of raspberries
150g of strawberries
one banana
150ml apple juice
 What is the ratio of raspberries to blueberries? What is the ratio of
strawberries to blueberries? Strawberries to raspberries? Say that this
recipe serves 2 people and ask pupils what they would need to do to
make smoothies for 4 people. They write the new recipe on their
whiteboards. What is the ratio of raspberries to blueberries now?
Discuss the other ratios and agree that they are the same, and so the
smoothie will taste the same.
Paired pupil work
 Ask pupils to work together to adapt the recipe for 6 people, then 3
people, then 5 people.
Teacher input with whole class
 Say that cook is making up diluted squash for the pupils’ café. The
squash should be mixed 1 part squash to 4 parts water. Ask pupils how
much water needs to be added if she uses 100ml of squash. 300ml?
150ml?
 Ask how much squash she must have used if she added 800ml of
water, 1600ml or 2 litres of water.
HSNP © Hamilton 2013
Simmering Term 1
Ratio and Proportion 1
Session 3
Objective: Make two quantities using a given simple ratio
Teacher input with whole class
 Show pupils a stick of 4 red cubes and 2 blue cubes. What is the ratio
of red to blue cubes? Discuss how we can write the ratio as 4 : 2 but
can simplify it to 2 : 1. Remind pupils that this means that there are
twice as many red cubes as blue ones, or that there are 2 red cubes for
every one blue cube.

Repeat with 6 blue cubes and 2 blue cubes and then with 6 blue cubes
and 4 red cubes.
Paired pupil work
 Pupils work in pairs or group of four to make as many different sticks
of cubes as they can in 2 minutes such that the ratio of one colour to
the other is 3 to 1.
Teacher input with whole class
 What fraction is red? And blue? (Ensure pupils see that ¼ is in one
colour and ¾ in the other, not 1/3 and 2/3.)
Paired pupil work
 Pupils write as many pairs of numbers as they can with a ratio of 2 to 1
in one minute, then 4 to 1, then 3 to 2.
Simmering Term 1
HSNP © Hamilton 2013
Ratio 1