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

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

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3. First Level Fractions Did you know?… Recent survey results have shown that more than 51% of P4 pupils have difficulty when asked to carry out basic calculations involving fractions. What strategies can we teach children to address this?

4. Think about the language used when teaching fractions. • You may wish to make a list of key words or terms. • Are you confident that you know and understand the meanings of key terms such as ‘numerator’ and ‘denominator’? • What strategies can you use to support the children’s understanding and use of the vocabulary of fractions? Consider these reflective questions -then move to next section

5. First Level Fractions Key Points: Pupils have difficulty with • Finding a simple fraction of a whole • Finding a simple fraction of a quantity, using division

6. The numeracy survey tells us that many children have difficulties with finding fractions of a whole or of an amount (using division). Do you teach children about important relationships such as that between fractions and division? • What other important relationships should be highlighted? • Why do you believe children have these difficulties and how can you help them avoid or overcome them? • What other aspects of fraction work do children find difficult? Consider these reflective questions -then move to next section

7. Finding a simple fraction of a single item Or How can pupils be helped to tackle problems like this?

8. Strategies Shade 1 out of these 4 Shade 1 out of these 4 This could be done in a number of ways, such as:

9. Strategies They can then shade 1 out of each group of 3. For example or

10. Strategies How might you work with pupils to help them understand how to shade ½ of this regular pentagon, which has been split into unequal parts? How would this type of problem help you assess a pupil’s understanding of fractions? Demonstrating that two unequal parts can make a fraction in this way will: • Provide a good basis in developing understanding of adding fractions • Reinforce the importance of part : part – whole relationships.

11. How well do you believe children understand the relationship between ‘fraction of a whole’ and ‘fraction of an amount or quantity’?For example:Shade one quarter of a rectangleShade one quarter of 8 • How can you help children make this connection? How can you ensure that children can do so when the number of parts is not so friendly to work with? For example:Shade one quarter of a rectangle Consider these reflective questions -then move to next section

12. Finding a simple fraction of a single item

13. Strategies Consider though not only shading 1 out of every 4 circles, such as: Splitting into convenient groups of 4 Shading 1 then counting and leaving 2,3 and 4un-shaded. But also...

14. Strategies • Consider shading 1 out of the 4 rows: • In what other ways could you encourage pupils to look at this type of problem?

15. Finding a simple fraction of a single item

16. Finding a simple fraction of an amount

17. Consider this reflective question -then move to next section • Children tend to relate fractions in terms of ‘shading’ or identifying parts of something eg a cake or a pizza? How do you extend their thinking of fractions as numbers ie they lie on the number line?

18. Strategies Pupils must recognise that the problem requires them to divide 66 by 3. Strategy 1: Partitioning Partitioning 66 into numbers that are easily divisible by 3: 66 = 60 + 6 So 66 ÷ 3 = 60 ÷ 3 + 6÷ 3 = 20 + 2 = 22 If 60 is still seen as too large a number by pupils, they could consider splitting 66 into parts which fall within the ‘normal’ range of the 3 times table For example: 66 = 30 + 30 + 6 So 66 ÷ 3 = 30÷ 3 + 30÷ 3 + 6÷ 3 = 10 + 10 + 2 = 22

19. Strategies Strategy 2: Using a number line Many pupils are visual learners and may feel more comfortable with a visual approach to solving a problem. Using a number line can help with this. Consider, for example: or What questions might you pose to pupils to help them to find the numbers represented by and ?

20. Strategies Strategy 3 Consider another visual approach: Split a plate into 3 equal parts Consider doing this with concrete resources such as paper plates and counters

21. Strategies Split 66 equally among the 3 sections. Pupils can ‘chunk’ 66 to do this. For example: Start by putting 10 onto each section. This only gets us to 30, so repeat this: We’re now at 60, so we have 6 left to split among the sections, so 2 goes onto each section

22. Finding a simple fraction of an amount What are the transferrable skills from previous knowledge? How could pupils check their answer?

23. Consider these reflective questions -then move to next section

24. Key skills Linking number facts Pupils should be able to make the link between finding a fraction of an amount and dividing. This in turn requires them to understand the link between division and multiplication. Work with pupils to develop their understanding of number facts…………

25. Key skills

26. Key skills

27. Consider this final reflective question • How do you use word problems and contextualised examples to develop children’s ability to apply their fraction skills?

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