Scottish Survey of Literacy & Numeracy Support Material Second Level – Fractions

1. Scottish Survey of Literacy & Numeracy • Support Material • Second Level – Fractions • Produced by Education Scotland Transforming lives through learning

2. Simplify Visualise

3. 16 16 16 16 16 16 X3

4. Level 2 Fractions Did 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 is2/3 of £24000?’ and ‘What is1/8 of 400g?’. 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’ How can we improve P7 pupil’s confidence and skills in dealing with problems involving fractions?

5. Level 2 Fractions Key Points: Pupils are having difficulty with • Finding a fraction of an amount • Simplifying 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.

6. Finding a fraction of an amount

7. Strategies Strategy 1 Step 1: 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?

8. Strategies Step 2 We 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.

9. Strategies

10. Strategies Remove 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?

11. Finding a fraction of an amount

13. 50g 50g 50g 50g 50g 50g 50g 50g 200g 200g 100g 100g 100g 100g Strategy 400g Whole Amount 2 Halves 4 Quarters 8 Eighths

14. Strategies Counting and shading 1,2,3 and leaving the 4th un-shaded. Splitting into convenient groups of 4 Does it matter how they select these groups of 4?

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

16. Simplifying fractions Suppose we want to simplify the fraction Strategy 1 Draw two identical rectangles. Split one into 8 equal parts and the other into 4 equal parts. Shade the same area in each: What fraction of the first rectangle is shaded? What fraction of the second rectangle is shaded? How else could we tackle this?

17. Strategies Strategy 2

18. Strategies

19. Strategies Combine all of this understanding to show that:

20. More about equivalent fractions

21. Strategies Would 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 andis so that istherefore bigger.

22. Questions in Context 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: Paul got £5 for his birthday from his Gran. How much did he save? How can we move pupils away from writing answers with remainders?

23. Strategies 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: 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?

24. Strategies 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: How much does it cost in the sale? What different strategies could pupils use to solve this problem? How could they check their answer?

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