Scottish Survey of Literacy &
Numeracy
Support Material
Third Level – Fractions
Classroom version
Produced by Education Scotland
Transforming
Transforming lives
lives through
through learning
learning
Third Level Fractions
Key Points:
Pupils have difficulty with:
• Finding equivalent fractions, decimal fractions and percentages
• Working with fractions, decimal fractions and percentages in context
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.
Introduction
Fractions
Equivalent Decimal
Equivalent Percentage
3
4
of S2 pupils experience problems
Problems with equivalent forms
Review & Reflect
• What concepts do learners find difficult?
• Support for understanding
• Look at your own practice
• Look at exemplars of effective practice
Consider
• Language being used
Decimal Fraction
Decimal
• Allows pupils to make connections
Learning & Teaching Process
Third Level Fractions
How can we improve pupils’ understanding of fractions and help them develop
strategies to solve problems involving fractions?
Primary / Secondary Liaison
Fractions / Decimal Fractions / %
Effective strategies required for:
Decimals
Fractions
Fractions
Percentages
Issues
Fractions
Fractions
Percentages
Decimal
Fractions
Decimal fractions
Effective Questioning
Fraction
Familiar Contexts
To support understanding
decimal notation
% representation
Significance of % sign
1% = 1 ÷ 100
Decimal fraction
Fraction
To turn 0.65 into a fraction, consider reinforcing place value by showing
0.65 visually as:
Pupils can then read this number as 65 hundredths.
And so can then write 0.65 as
65
100
To simplify this fraction, use strategies developed previously.
In this case, we can divide both the numerator and denominator by 5, so
5
65
0.65 =
100
13
=
20
5
Fraction
Decimal fractions
1
Change
into a decimal fraction.
5
What are the key things for pupils to consider when linking fractions
with decimal fractions?
Fraction
Decimal fractions
Encourage pupils to first think of tenths and hundredths when linking
fractions with decimal fractions.
x2
1
2

5
10
x2
x 20
20
1

100
5
x 20
Reading this as two tenths and twenty hundredths should enable pupils to
understand that this is written as 0.2 in decimal fraction form.
Fraction
Percentage
For percentages, think ‘out of 100’.
• 10 x 10 grid
• split into blocks of 6 and shade
1 out of every 6
?
• this works for the first 16 blocks
but it is not possible to create the
17th block ?
.
1
 0.1666
6
Percentage
Fraction
Change 64% to a fraction in its simplest form
Percent means out of 100, so 64% means 64 out of 100
64
?
64% 
100
Percentage
Fraction
64
100
Percentage
Fraction
32
50
Percentage
Fraction
16
25
Strategies
Consider playing games, such as matching pairs to develop pupils’
understanding of equivalent fractions
75%
3
12
1
4
0.6
3
4
3
5
Percentage
Fraction
200 blocks
12.5%
Ideal for investigat ion
Why/how we use questions in context
Effective Questioning
Familiar Contexts
Developing Higher Order Skills
Creating
Giving pupils the opportunity to create their own
matching card game.
Evaluating
Giving pupils the opportunity to justify their
answers to given problems.
Analysing
Giving pupils the opportunity to make the
connection between fractions, decimal fractions
and percentages.
Questions in Context
In all types of fraction problem, ensure that pupils are able to transfer the
skills they develop in answering simply worded questions, to problems
written in context.
For example, what steps would you encourage a pupil to go through to
answer questions such as:
‘Emma saves 10% of her pocket money each week.
What fraction of her pocket money does she save?’
Reflective Questions
• What range of strategies could be used to answer
this problem?
• Would using a specific numerical example help,
then generalising from there?
• How would you help visual learners deal with this?
Questions in Context
In all types of fraction problem, ensure that pupils are able to transfer the
skills they develop in answering simply worded questions, to problems
written in context.
For example, what steps would you encourage a pupil to go through to
answer questions such as:
‘In a Science test, Lewis got 70% of the test correct.
In the same test, Amy answered 3 of the questions correctly.
4
Amy’s actual mark in the test was 30.
What was Lewis’s actual mark?’
What’s the crucial thing that pupils have to find here?
What numerical strategies could be used?
1
Why might 52 2 be a common incorrect answer
given by pupils?
Would a visual representation help?
Reflective Questions
• What’s the crucial thing that pupils have to find here?
• What numerical strategies could be used?
1
52 2 be
• Why might
given by pupils?
a common incorrect answer
•Would a visual representation help?
www.educationscotland.gov.uk