Transforming lives through learning Scottish Survey of Literacy & Numeracy Support Material Third Level - Fractions, decimal fractions and percentages Produced by Education Scotland Transforming lives through learning

Introduction Fractions, decimal fractions & percentages Knowing which one to use ?

Demonstrating a deep understanding ÷ 4

Nearly 80% of S2 pupils are unable calculate 9.5 x 0.5 If asked in a different way What is half of 9.5 Would 4 out of 5 pupils still get it wrong?

Reflective Questions How are problems in context presented? How can we help pupils translate the text into understandable numeracy operations? Can they make the connections between fractions, decimal fractions and percentages?

Reflect on other examples where pupils need to decide on the most appropriate form to use. ÷ 8 Taking into account that 0.5 =

Strategy Changing 0.5 to might help answer 9.5 x 0.5 This changes the questions to 9.5 x Do pupils recognise that 9.5 is the same as 9.50? Pupils then need to realise that this is the same as asking ‘How much is of 9.5’ So, all that is required is dividing 9.50 by 2

Does this simplify the problem for pupils? Is there a visual representation that might help? How would you suggest pupils tackle questions such as 4.8 x 0.25 ? Could a similar approach be used for percentage problems, such as ‘Find 75% of 10.8’? Points to reflect on

Equivalent fractions, decimal fractions and percentages Did you know… Recent surveys have shown that more than 80% of pupils cannot find the correct answer to problems like the above. Why might this be difficult for pupils? Katie is changing some money from pounds into dollars The exchange rate is £1 = $1.58 How much will Katie get in dollars if she exchanges £4.50?

Strategy Pupils may realise they need to multiply £4.50 by 1.58 Is trying to do this the best strategy? Without a calculator, long multiplication can prove tricky calculation for pupils. Using direct proportion might help. A key step might be for pupils to think of £4.50 as 4 pounds This need not involve multiplying by 4 though. Pupils can apply direct proportion to solve the problem, as well as some basic number strategies:

Strategies Double it So £4.50 is worth $ $0.79 = $7.11 Direct proportion can also be a really useful approach for percentage calculations it

Step by step approach Pupils should be encouraged to look for the simplest calculations. Finding 10% and 1% is generally something which pupils find straightforward.. This combination allow us to calculate any percentage. ÷ 2 ÷ 10

½ it Double it In a local election, 17% of voters voted for the Green Party people voted in the election. How many voted for the Green Party? So 4760 people voted for the Green Party.

Investigate How can you apply your knowledge of the above to calculate the following percentages?

Misconceptions of the link between fractions & ratio This needs to be investigated. or

Link between ratio & fractions Shaded : Not shaded 1: 3 Shade of the circles 4 = 1 + 3

The ratio is Carol : James 3 : 2 Think of this as 3 for Carol and 2 for James, and shade the rectangle accordingly until it is completely coloured in. Let’s make Carol’s share red and James’s share yellow: So, Carol has 9 squared coloured and James has 6. So, Carol gets 9 crayons and James gets 6 crayons. Link between ratio & fractions

What numerical strategies developed for working with fractions could we use to solve this ratio problem? The ratio is 3:2, meaning Carol gets 3 shares and James gets 2 shares, giving 5 in total. This means that Carol gets of the crayons and James gets of them. Use skills developed in finding a fraction of an amount to find that of the 15 crayons is 3 crayons Carol gets, so she gets 3 lots of 3, which is 9James gets, so he gets 2 lots of 3, which is 6. How could pupils check their answer? Link between ratio & fractions