Transforming lives through learning

Scottish Survey of Literacy & Numeracy

Support Material

Second Level – Fractions

Produced by Education Scotland

Transforming lives through learning

Simplify

Visualise

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Level 2 FractionsDid 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?’.

How can we improve P7 pupil’s confidence and skills in dealing with problems involving fractions?

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’

Key Points:

Pupils are having difficulty with• Finding a fraction of an amount• Simplifying fractions

Level 2 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

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?

Strategy 1 Step 1:

StrategiesStep 2We 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

StrategiesRemove 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 200g

100g

100g 100g

100g

50g

50g50g

50g 50g 50g

50g50g

2 Halves 4 Quarters 8 Eighths

Strategies

Does it matter how they select these groups of 4?

Splitting into convenient groups of 4 Counting and shading 1,2,3 and

leaving the 4th un-shaded.

Strategies

Consider though not only shading 3 out of every 4 circles, but also consider shading 3 out of 4 rows

Simplifying fractionsSuppose we want to simplify the fraction

Strategy 1Draw two identical rectangles.Split one into 8 equal parts and the other into 4 equal parts.Shade the same area in each:

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What fraction of the first rectangle is shaded?

What fraction of the second rectangle is shaded?

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How else could we tackle this?

StrategiesStrategy 2

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Strategies

StrategiesCombine all of this understanding to show that:

More about equivalent fractions

StrategiesWould 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 and to get:

and see that is and is so that is therefore bigger.

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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:

Questions in Context

How can we move pupils away from writing answers with remainders?

How much did he save?

Paul got £5 for his birthday from his Gran.

StrategiesIn 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.

She cuts off of it.

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?

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StrategiesIn 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 could they check their answer?

What different strategies could pupils use to solve this problem?

How much does it cost in the sale?

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