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:

Introduction Fractions Equivalent DecimalEquivalent Percentage

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 Fraction Decimal Allows pupils to make connections Many S2 pupils experience problems

Learning & Teaching Process Level 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

Issues Decimals Fractions Decimal Fractions Fractions Percentages Fractions Effective strategies required for:

Decimal fractions Effective QuestioningFamiliar Contexts To support understanding decimal notation % representation Significance of % sign 1% = 1 ÷ 100 Fraction

To turn 0.65 into a fraction, consider reinforcing place value by showing 0.65 visually as: Pupils can then read this number as 65 hundredths. And so can then write 0.65 as Decimal fractions Fraction To simplify this fraction, use strategies developed previously. In this case, we can divide both the numerator and denominator by 5, so 0.65 = =

What are the key things for pupils to consider when linking fractions with decimal fractions? Change into a decimal fraction. Decimal fractions Fraction

Encourage pupils to first think of tenths and hundredths when linking fractions with decimal fractions. 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 fractions Fraction

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 17 th block ?.

Percentage Fraction Change 64% to a fraction in its simplest form Percent means out of 100, so 64% means 64 out of 100

Percentage Fraction

Strategies Consider playing games, such as matching pairs to develop pupils understanding of equivalent fractions

Percentage Fraction Ideal for investigation

Why/how we use questions in context Effective QuestioningFamiliar Contexts Developing Higher Order Skills Creating Giving pupils the opportunity to create their own matching card game. Evaluating Giving 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 Context In 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 Context In 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: Whats the crucial thing that pupils have to find here? In the same test, Amy answered of the questions correctly. Amys actual mark in the test was 30. What was Lewiss actual mark? Whats 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?

Reflective Questions Whats 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?