This document summarizes a presentation on Singapore Math. It discusses how Singapore Math focuses on thinking, visualization using bar models, patterns and generalization, problem solving, and applying knowledge through problem solving. It provides examples of how concepts like fractions division and place value are taught using hands-on approaches like paper folding rather than solely drill-and-practice.

1. Welkom Master Class Singapore Math Dr.Yeap Ban Har Marshall Cavendish Institute 2011alt/ HCO R MAP101 Fundamentals in Singapore Mathematics

2. Masterclass Singapore Rekenen Rotterdam  Utrecht DrYeap Ban Har banhar@sg.marshallcavendish.com Marshall Cavendish Institute Singapore Presentation slides are available at www.banhar.blogspot.com

3. what is singapore mathematics

4. Singapore Mathematics: Focus on Thinking an excellent vehicle for the development & improvement of a person’s intellectual competencies Ministry of Education Singapore 2006

6. 110 g 180 g 110 g Bella puts 180 g brown sugar on the dish. 290 g

7. on an identical dish 110 g 2 units = 180 g 1 unit = 90 g 110 g 180 g 3 units = 270 g Bella puts 270 g brown sugar on the dish. 290 g

8. Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.

9. Singapore Math Visualization

11. C H E R Y L

12. C H E R Y L 1

13. C H E R Y L 2

14. C H E R Y L 3

15. C H E R Y L 4

16. C H E R Y L 5

17. C H E R Y L 6

18. C H E R Y L 7

19. C H E R Y L 8

20. C H E R Y L 9

21. C H E R Y L

22. C H E R Y L

23. C H E R Y L

24. C H E R Y L

25. C H E R Y L

26. C H E R Y L Which letter is 99?

28. Method 1 The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located. Method 4 The position for 99 can be found by writing out all the numbers but this is not efficient method. Method 3 Numbers ending with 9 are at E. So, 99 is at E too. Method 2 The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.

29. D A V I D

31. Method 1 The letters under A and I are even. So 99 cannot be there. Method 2 The positions of numbers ending with 9 form a diagonal pattern. Method 3 The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out. Method 4 The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out. Method 5 Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.

32. Method 2 The positions of numbers ending with 9 form a diagonal pattern. The methods were the ones that participants in Chile came up with.

33. Another Method In a course done in December 2010 with a group of Chilean teachers, there was a method that involves division. For Cheryl, it was 99 : 10. For David, it was 99 : 8. Are you able to figure out that method?

34. Singapore Math Patterns & Generalization

35. Singapore Mathematics: Focus on Problem Solving

41. CPA Approach based on Jerome Bruner was used to learn division of fractions – using paper folding and subsequent drawing.

43. Singapore Math Learn New Concept Through Problem Solving

47. Singapore Math Drill-and-Practice Through Problem Solving

55. Singapore Math Applying Knowledge in Problem Solving

57. Learning Theories

63. How many 4s are there in 12? 12 ÷ 4 = 3