NCTM Annual Meeting & Exposition (Session 1) San Diego 23 April 2010

1. problems from singapore classrooms Dr Yeap Ban Har National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg www.singaporemath.com

2. Primary Mathematics Standards Edition (Grade 6) problems to teach new concepts or skills

3. Primary Mathematics Standards Edition (Grade 6)

4. Primary Mathematics Standards Edition (Grade 6)

5. Primary Mathematics Standards Edition (Grade 6)

6. Primary Mathematics Standards Edition (Grade 6)

10. Area > 2r2

11. Area < 4r2

12. 2r2 < Area < 4r2

18. 2r2 < Area < 4r2

19. 2r2 < r2 < 4r2

20. problems for students to apply what they learn Primary Mathematics Standards Edition (Grade 6)

21. Primary Mathematics Standards Edition (Grade 6)

22. Primary Mathematics Standards Edition (Grade 6)

23. Primary Mathematics Standards Edition (Grade 6)

24. Primary Mathematics Standards Edition (Grade 6)

25. Primary Mathematics Standards Edition (Grade 6)

26. Primary Mathematics Standards Edition (Grade 6)

27. Primary Mathematics Standards Edition (Grade 6)

28. Primary Mathematics Standards Edition (Grade 6)

29. Primary Mathematics Standards Edition (Grade 6)

35. 1 h = 60 min 60 ÷ 4 = 15 15 x 3 = 45 ¾ x 60 = 45 She practiced for 45 minutes. Primary Mathematics Standards Edition

36. Mathematical Variation 16 Primary Mathematics Standards Edition

37. 16 Mathematical Variation 30 Primary Mathematics Standards Edition

38. Keys Grade School, Manila, The Philippines

39. Keys Grade School, Manila, The Philippines

40. problems to teach new concepts or skills Keys Grade School, Manila, The Philippines

41. Skemp Understanding in mathematics relational (conceptual) instrumental (procedural) conventional Teaching for conceptual understanding is given emphasis in Singapore Math. Primary Mathematics Standards Edition Grade 6

42. Primary Mathematics Standards Edition Grade 6

43. problems to teach new concepts or skills

44. How to make sure the butterfly cannot flyHow do you get a butterfly?First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.If the butterfly is not left to struggle to come out of the cocoon, it will never fly.We can learn an important lesson from the butterfly.If we do not have struggles and challenges in our work, we will never grow strong and capable. If life has no difficulties, we will become weak and helpless.Lim Siong GuanHead, Civil Service

45. Mathematical Variation

46. Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence .. Ministry of Education 2006 DaQiao Primary School

53. problems from singapore classrooms Dr Yeap Ban Har National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg Another session by Yeap Ban Har will be presented today at Manchester Hyatt Douglas Pavilion A 3:00 – 4:30 www.singaporemath.com