Transforming lives through learning

Scottish Survey of Literacy & Numeracy

Support Material

Third Level - Fractions

Produced by Education Scotland

Transforming lives through learning

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.

Level 3 Fractions

Key Points:

Introduction

Fractions

Equivalent Decimal Equivalent Percentage

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 FractionDecimal

• Allows pupils to make connections

Many S2 pupils experience problems

Learning & Teaching ProcessLevel 3 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 / %

Joint approach

Effective strategies required for:

Decimal fractions

Effective Questioning Familiar Contexts

To support understandingdecimal notation % representation

Significance of % sign1% = 1 ÷ 100

Fraction

To turn 0.65 into a fraction, consider reinforcing place value by showing 0.65 visually as:

100

65Pupils can then read this number as 65 hundredths.

And so can then write 0.65 as

Decimal fractions Fraction

20

13

100

65

To simplify this fraction, use strategies developed previously.In this case, we can divide both the numerator and denominator by 5, so

0.65 = =

5

5

What are the key things for pupils to consider when linking fractions with decimal fractions?

5

1Change into a decimal fraction.

Decimal fractionsFraction

Encourage pupils to first think of tenths and hundredths when linking fractions with decimal fractions.

105

1

1005

1

2 20

2x 20x

2x 20x

Reading this as two tenths and twenty hundredths should enable pupils to understand that this is written as 0.2 in decimal fraction form.

Decimal fractionsFraction

For percentages, think ‘out of 100’.

Fraction Percentage

?

• 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 ?

1666.06

1

.

Percentage Fraction

Change 64% to a fraction in its simplest form

Percent means out of 100, so 64% means 64 out of 100

?100

64%64

100

64

Percentage Fraction

50

32

Percentage Fraction

25

16

Percentage Fraction

Strategies

Consider playing games, such as matching pairs to develop pupils’ understanding of equivalent fractions

4

1

5

3

4

3

12

3%75

6.0

Percentage Fraction

%5.12 blocks 200

Ideal for investigation

Why/how we use questions in contextEffective Questioning Familiar Contexts

Developing Higher Order Skills Creating

Giving pupils the opportunity to create their own matching card game.

EvaluatingGiving 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 ContextIn 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?’

• 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?

Reflective Questions

Questions in ContextIn 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:

What’s the crucial thing that pupils have to find here?In the same test, Amy answered of the questions correctly.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?Why might 52 be a common incorrect answer given by pupils?Would a visual representation help?

4

3

2

1

Reflective Questions

• What’s the crucial thing that pupils have to find here?

• What numerical strategies could be used?

• Why might 52 be a common incorrect answer given by pupils?

•Would a visual representation help?

2

1

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