transforming lives through learning scottish survey of literacy & numeracy support material...
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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:
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
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
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
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