Scottish Survey of Literacy &
Numeracy
Support Material
Second Level – Fractions
Produced by Education Scotland
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Level 2 Fractions
Did you know?…
Recent surveys have shown that around 47% of P7 pupils have difficulty carrying
out calculations involving fractions.
Pupils could not correctly answer questions such as
‘Find 4/5 of 5400’, ‘Calculate 2/3 of 372’, ‘How much is 2/3 of £24000?’ and
‘What is 1/8 of 400g?’.
Did you also know….
P7 pupils have shown themselves to be even less confident in simplifying
fractions, with between 70% and 78% of pupils have difficulty with questions
such as ‘Write 25/60 as a fraction in its simplest form’ or ‘ Write 4 out of 28
as a fraction in its simplest form’
How can we improve P7 pupil’s confidence and skills in dealing with
problems involving fractions?
Level 2 Fractions
Key Points:
Pupils are having difficulty with
• Finding a fraction of an amount
• Simplifying fractions
We need to consider the reasons why these areas cause problems and look at
some ways that these skills could be developed and improved upon.
Finding a fraction of an amount
Strategies
Strategy 1
Step 1:
How would you teach
pupils to divide 400 by 5?
If they know 40÷5 = 8 then
they should realise that
400÷5 = 80
What about doing 400÷10?
What would you then have
to do to get to the answer
to 400÷5?
Strategies
Step 2
We could now use a visual strategy developed in earlier years – sharing a
pizza.
Split the pizza into 5 equal parts:
Now share 5400 equally between the 5 slices – 1080 on each slice.
Strategies
Strategies
Remove one fifth to leave four fifths:
Add 1080 + 1080 + 1080 + 1080 to find the answer.
• Is one of the two strategies easier?
• Might one strategy be better in one situation and the other for a
different problem?
• Could it be that pupils’ recall of multiplication and division facts is
actually the real problem for them? Should these basic number
skills be worked on more?
• Could simplifying the problem help?
Finding a fraction of an amount
Strategy
400g
Whole Amount
200g
100g
100g
50g
50g
50g
50g
100g
100g
50g
50g
50g
50g
200g
2 Halves
4 Quarters
8 Eighths
Strategies
Splitting into convenient groups of 4
Counting and shading 1,2,3 and
leaving the 4th un-shaded.
Does it matter how they select these groups of 4?
Strategies
Consider though not only shading 3 out of every 4 circles, but also
consider shading 3 out of 4 rows
Simplifying fractions
Suppose we want to simplify the fraction
2
8
Strategy 1
Draw two identical rectangles.
Split one into 8 equal parts and the other into 4 equal parts.
Shade the same area in each:
2 1

8 4
How else could we tackle this?
What fraction of the first
rectangle is shaded?
What fraction of the second
rectangle is shaded?
Strategies
Strategy 2
6 2

9 3
Strategies
Strategies
Combine all of this understanding to show that:
More about equivalent fractions
Strategies
Would laying the two rectangles over one another help?
What’s the key thing to consider about how the rectangles are split?
Pupils can then shade 1 and 1 to get:
4
3
and see that 1 is 4
3
12
and 1 is 3 so that 1 is therefore bigger.
4
12
3
Questions in Context
In all types of fraction problems, ensure that pupils are able to transfer the
skills they develop in answering simply worded questions, to problems
written in context.
What steps would you encourage a pupil to go through to answer questions
such as:
Paul got £5 for his birthday from his Gran.
How much did he save?
How can we move pupils away from writing answers with remainders?
Strategies
In all types of fraction problems, ensure that pupils are able to transfer the
skills they develop in answering simply worded questions, to problems
written in context.
What steps would you encourage a pupil to go through to answer questions
such as:
Carol has a 3 metre length of ribbon.
3
She cuts off of it.
4
What length does she cut off?
What is the first thing you’d want pupils to do when answering this question?
What other learning are you relying on?
Might you need to recap on some previous learning?
Strategies
In all types of fraction problems, ensure that pupils are able to transfer the
skills they develop in answering simply worded questions, to problems
written in context.
What steps would you encourage a pupil to go through to answer questions
such as:
How much does it cost in the sale?
What different strategies could pupils use to solve this problem?
How could they check their answer?
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