Scottish Survey of Literacy &
Numeracy
Support Material
Third Level Fractions, decimal fractions and
percentages
Produced by Education Scotland
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Introduction
Fractions, decimal fractions & percentages
Knowing which one to use ?
Demonstrating a deep understanding
25% of £48
1
of £48
4
8.6 x 1.5
8.6  half of 8.6
48 ÷ 4
8.6  4.3
£12
12.9
Nearly 80% of S2 pupils are unable calculate
9.5 x 0.5
If asked in a different way
What is half of 9.5
Would 4 out of 5 pupils still get it wrong?
Reflective Questions
• How are problems in context presented?
• How can we help pupils translate the text
into understandable numeracy
operations?
• Can they make the connections between
fractions, decimal fractions and
percentages?
1
Taking into account that 0.5 =
2
Reflect on other examples where pupils need to decide on
the most appropriate form to use.
12.5% of £160
1
of £160
8
160 ÷ 8
£20
Strategy
Changing 0.5
1
to 2
might help answer 9.5 x 0.5
This changes the questions to 9.5 x
1
2
Do pupils recognise that 9.5 is the same as 9.50?
Pupils then need to realise that this is the same as asking
1
‘How much is 2 of 9.5’
So, all that is required is dividing 9.50 by 2
Points to reflect on
Does this simplify the problem for pupils?
Is there a visual representation that might help?
How would you suggest pupils tackle questions such as 4.8
x 0.25 ?
Could a similar approach be used for percentage problems,
such as
‘Find 75% of 10.8’?
Equivalent fractions, decimal fractions and
percentages
Katie is changing some money from pounds into dollars
The exchange rate is £1 = $1.58
How much will Katie get in dollars if she exchanges £4.50?
Did you know…
Recent surveys have shown that more than 80% of pupils cannot find
the correct answer to problems like the above.
Why might this be difficult for pupils?
Strategy
Strategy
Pupils may realise they need to multiply £4.50 by 1.58
Is trying to do this the best strategy?
Without a calculator, long multiplication can prove tricky calculation for
pupils.
Using direct proportion might help.
A key step might be for pupils to think of £4.50 as 4
This need not involve multiplying by 4
1
2
1
pounds
2
though.
Pupils can apply direct proportion to solve the problem, as well as some basic
number strategies:
Strategies
Double it
1
2
1
2
0.79
Double it
So £4.50 is worth $6.32 + $0.79
= $7.11
Direct proportion can also be a really useful approach for percentage
calculations.
it
Step by step approach
Pupils should be encouraged to look for the simplest calculations.
Finding 10% and 1% is generally something which pupils find straightforward.
10%
1%
.
This combination allow us to calculate any percentage.
÷2
5%
10%
÷ 10
1%
In a local election, 17% of voters voted for the Green Party.
28000 people voted in the election.
How many voted for the Green Party?
½ it
So 4760 people voted for the Green Party.
Double it
Investigate
3
75% 
4
10%
1
50% 
2
1%
5%
How can you apply your knowledge of the above to calculate the
following percentages?
43%
74%
62%
81%
56%
Misconceptions of
the link between
fractions & ratio
2:5
2
5
3: 2
3
2
This needs to be investigated.
or
2
3
Link between ratio & fractions
1
Shade 4 of
the circles
Shaded : Not shaded
1:
3
4=1+3
Link between ratio & fractions
The ratio is
Carol : James
3 : 2
Think of this as 3 for Carol and 2 for James, and shade the rectangle
accordingly until it is completely coloured in.
Let’s make Carol’s share red and James’s share yellow:
So, Carol has 9 squared coloured and James has 6.
So, Carol gets 9 crayons and James gets 6 crayons.
Link between ratio & fractions
What numerical strategies developed for working with fractions could
we use to solve this ratio problem?
The ratio is 3:2, meaning Carol gets 3 shares and James gets 2 shares, giving 5 in total.
This means that Carol gets 3 of the crayons and James gets 2 of them.
5
5
Use skills developed in finding a fraction of an amount to find that 1
5
of the 15 crayons is 3 crayons
Carol gets
3
, so she gets 3 lots of 3, which is 9
5
James gets
2
, so he gets 2 lots of 3, which is 6.
5
How could pupils check their answer?
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