1. Listening to you, working for you www.bexley.gov.uk Teaching Fractions, Decimals and Percentages at Levels 5/6 Elaine Lambert Secondary Mathematics Consultant Bexley LA

2. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Objectives Improve participants knowledge of resources and pedagogies that will enhance student understanding of FDP at levels 5 and 6 Participants will build a better understanding of the role of FDP in making progress through the mathematics curriculum Participants will identify individual next steps to improve learning of FDP in their classrooms

3. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk The Big Picture In small groups: Highlight all the criteria on the APP grids that are related to FDP Come up with two or three sentences that describe the big picture of FDP in levels 5 and 6

4. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk The Big Picture Fluency in calculation Equivalence Understanding proportionality Measurement MPA

5. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk The Big Picture “ Proportionality underlies key aspects of number, algebra, shape, space, measures and handling data” “ In many problems, making the appropriate choice between fractions, decimals, percentages or ratio will be crucial. Students can only make such a choice if they have a sound understanding of equivalence” SNS, Teaching Mental Maths from Level 5 “ Research shows that making links between interconnected ideas helps pupils to make sense of the subject, avoid misconceptions, and retain what they learn” SNS, Interacting with mathematics

6. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk The Big Picture “Teachers usually introduce rules to help pupils remember particular results or steps in methods. However, few are always true and many are never convincingly developed with pupils so that they understand the particular context within which a rule might be used” Eg To multiply by 10 you add a nought “Where it is considered that rules might be useful, they should be unambiguous and developed with the pupils. The unthinking use of rules should be discouraged” Understanding the score 2008 Ofsted

7. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk The Big Picture “Pupils’ learning is based too much on their acquisition of methods, rules and facts as part of the strong focus on tests and exams, and too little on their understanding of the underpinning concepts, on connections with earlier learning and other topics in mathematics, and on helping them to make sense of mathematics so that they can use it independently” Understanding the score, 2008, Ofsted

8. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Decimals Fluency in calculation –Rounding –Use known facts to derive unknown facts –Addition, subtraction, multiplication and division –Multiply and divide by 0.1, 0.01, 10, 100 etc –Ordering –Recurring decimals –Problem solving Equivalence –With fractions and percentages Measurement –Reading scales –Converting between units of length

9. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Web Diagrams

10. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Place value http://nationalstrategies.standards.dcsf.gov.u k/node/96385?uc=force_uj http://nationalstrategies.standards.dcsf.gov.u k/node/96385?uc=force_uj

11. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Place value chart

12. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Calculate this 0.024 x 0.04 How would you teach it?

13. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk 0.024 x 0.04 24 x 4 = 96 24 x 0.4 = 9.6 24 x 0.04 = 0.96 2.4 x 0.04 = 0.096 0.24 x 0.04 = 0.0096 0.024 x 0.04 = 0.00096

14. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk 0.024  0.04

15. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk 0.024  0.04 0.024 = 0.024 x 100 0.04 0.04 x 100 = 2.4 4 24  4 = 6 2.4  4 = 0.6

16. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk 0.024  0.04 24  4 1000 100 = 24 x 100 1000 4 = 24 = 24 = 3 4 x 10 40 5

17. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk

18. Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Problem Solving 349  18 = 19.38888…. 18  349 = 0.0515759…

19. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Two way tables

20. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Fractions (and percentages) Fluency in calculation –Addition, subtraction, multiplication and division –Ordering Equivalence –With decimals, percentages and ratio Understanding proportionality –Calculate fractions of quantities

21. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Equivalence with ratio The scale on a map Parts of a whole

22. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk http://www.fi.uu.nl/wisweb/applets/mainf rame_en.html Fraction Bar and Percent Bar

23. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Web Diagrams

24. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Web Diagrams

25. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Web Diagrams

26. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Web diagrams

27. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Number lines

28. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Aligning Diagrams Aaron earns £42 a week. He spends 23% of his earnings on CDs. How much money does he spend on CDs each week?

29. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Two way tables Aaron earns £42 a week. He spends 23% of his earnings on CDs. How much money does he spend on CDs each week?

30. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Mathematics ITP http://nationalstrategies.standards.dcsf.gov.u k/search/secondary/results/nav:50236 http://nationalstrategies.standards.dcsf.gov.u k/search/secondary/results/nav:50236 Fractions Decimal Number Line Moving Digits Number Dials Ratio and Proportion

31. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Gap Task – next session 10 th Feb Identify one or two personal targets to improve learning of FDP at levels 5/6 in your classrooms. Identify one or two different resources/techniques that you will trial that might help you meet those targets Report back next time

32. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Next session – 10 th Feb here in the Moorland Suite Feedback from Gap Tasks The use of Rich Tasks for learning and assessing FDP Next steps