1. Exploring Decimal Fractions Louise Addison Pip Arnold TEAM Solutions

2. Purpose of this session  Have a look at decimal fractions from a SNP viewpoint.  Share a possible framework for you to use with the teachers in your department on other topics / workshops. Twofold:

3. Structure of workshop…  PART ONE Why is this not easy? – A look at misconceptions. What are the key ideas?  PART TWO How can these key ideas be taught?  PART THREE Who is ready to learn this? When should it be taught? Where is it going?

4. WWWWH Template  Overview of topic from pedagogy point of view…

5. Why?  Why is this not easy?  What are the major misconceptions / issues that need to be addressed?

6. Decimal Diagnostic Test  Analyse the answers to the decimals diagnostic test…  What are some of the common issues / misconceptions that students have with decimal fractions?

7. Your student results  Total for your group the number of students who got each question incorrect. Make a column and record this on your table.  Find and list the five most common incorrect questions.  What were the five most common correct questions?

8. Deeper Analysis  Use the actual student responses to do a deeper analysis for questions: 3d, 6a, 9 and 15. List the particular responses that students give and tally up how many gave that response across your group.  For each question pick the most common incorrect response.  Discuss in your group what the misconception is that the students might have.

9. Question 3d  5.1 for 56.

10. Question 3d  5.1 for 56. 5.118/~60 9 correct Yr 9

11. Question 6a  Write down the bigger of the two numbers 0.65 and 0.7

12. Question 6a  Write down the bigger of the two numbers 0.65 and 0.7 0.6519/~60 8 correct Yr 9

13. Question 9  Add ten to 0.15

14. Question 9  Add ten to 0.15 0.2538/~60 5 correct Yr 9

15. Question 15  Multiply 4.17 by ten

16. Question 15  Multiply 4.17 by ten 40.177/~60 4.1704/~60 26 incorrect 19 no attempt 3 correct Yr 9

17. What?  What are the key ideas / concepts to be introduced? What do they need to know? What do they need to understand? What do they need to be able to do?  What number knowledge do they need?

18. Brainstorm – decimal fractions  What do they need to know?  What do they need to understand?  What do they need to be able to do?

19. A look back to 1948…  Key idea: Information – can be ‘told’ Concept – needs to be taught Look at this video and explore what is information and what are concepts… http://www.youtube.com/watch?v=4Iv8O TmBBaM

20. How?  How will this be taught? Materials Imaging Generalising Resources

21. Materials  Why not money?  Unifix cubes

22. Question One:  Use the unifix materials to solve this problem… 6  5 6 bars of chocolate shared amongst 5 people write your answer as:  wholes and  tenths

23. Further examples to explore… 6  4 9  2

24. Imaging  Solve the following problem by imaging - clearly explain how you could have used the materials… 4.2  3  Decode / Recode

25. Other problems  1.9 + 2.4  6.1 – 2.7  3  1.8

26. Generalising  Canon of Place Value 10 for 1, 1 for 10  Use of words to link meaning and symbols

27. Who?  Who is ready to learn this?  What diagnostic question could I ask to assess what they already know / understand?

28. Place Value knowledge  Look at numeracy framework – what stage are decimal fractions introduced?  What about 2 decimal places?

29. When?  When will this be introduced?  What prior knowledge is needed?

30. Progression…  In what order does this work suggest the following should be taught in?  Decimals  Fractions  Percentages

31. Where?  Where is this going?  What comes next?

32. What about 2 decimal places?  5  4  Record as:  whole +  tenths +  _______ What are these called and why?  Use of decimats

33. Where else do decimal fractions appear?  Discuss where in your current Junior programmes decimal fractions appear…  Rounding – Book 8  Measurement  Estimating – number, statistics  Probability

34. Further explorations  Purple Books … Book 4 p4, 5, 8-9, 13, 19, 21, 28-30 Book 5 p46-50 Book 6 p60-62 Book 7 p22-29, 36-37 Book 8 p19-22, 24-25, 31, 37-38

35. Further explorations Planning sheets www.nzmaths.co.nz AA -> AM

36. Further explorations Planning sheets www.nzmaths.co.nz AM -> AP

37. Further explorations  Link to Kath Hart tests / Kay Irwin research: Link to Kath Hart tests / Kay Irwin research: