This is the second and final day of the professional development for teachers in K-2. This event held in Pearl City Hawaii was made possible by Kamehameha Schools, Nanakuli Elementary School and State of Hawaii Department of Education.

1. Professional Development for Singapore Math (Lower Grades) Yeap Ban Har banhar@sg.marshallcavendish.com Pearl City, Hawaii 12 August 2011 Photo: Nanakuli ElementarySchool Presentations are available at www.banhar.blogspot.com

2. Professional Development for Singapore Math (Lower Grades) Day 2 Session 1 Video Study Focus on Thinking Patterning & Generalization Photo: Princess Elizabeth Primary School

3. Students have learnt to add three one-digit numbers prior to this lesson. These are grade one students towards the end of the school year.

4. The problem-solving lesson in the video follows the lesson we studied yesterday in the Open Lesson.

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9. Professional Development for Singapore Math (Lower Grades) Day 2 Session 2 Number Bonds Photo: Princess Elizabeth Primary School

10. Number bonds is taught before addition and subtraction. www.marshallcavendish.com/education/mci

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12. Number Bonds Number Bonds is emphasized prior to the learning of addition. Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5. Earlybird Kindergarten Mathematics (Standards Edition)

13. Photo: PCF TelokBlangah Kindergarten

14. One duck is big. Six ducklings are small. Photo: PCF Telok Blangah Kindergarten

15. Photo: PCF Telok Blangah Kindergarten

16. Photo: PCF Telok Blangah Kindergarten

17. Photo: PCF Telok Blangah Kindergarten

18. Photo: PCF TelokBlangah Kindergarten

19. Number Bonds continues to receive attention in Grade 1. My Pals Are Here! Mathematics 1

20. Addition Facts Addition Facts are given emphasis in the first six months of grade one. The children learn it in stages as the textbooks distinguished between Numbers to 10 and Numbers to 20. Count On and Count All are used in Numbers to 10. Earlybird Kindergarten Mathematics (Standards Edition)

21. Addition Facts &Number Sense While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20. Photo: Princess Elizabeth Primary School

22. 27 – 3 10 27 – 13 27 – 18 17 24 27 ÷ 3 3 Applications of Number Bonds

23. Professional Development for Singapore Math (Lower Grades) Day 2 Session 3 Emphasis on Visualization, Connections and Number Sense Photo: Princess Elizabeth Primary School

24. Communication Articulating one’s thoughts orally, at first, and in written forms using words, pictures, diagrams and symbols is important. Maris Stella High (Primary) School

25. Connections Looking for Patterns is introduced through exploration with Shapes. Subsequently, this is done using numbers – in a more abstract context. Photo: Princess Elizabeth Primary School MakeConnections to Generalize

26. Connections Photo: Princess Elizabeth Primary School

27. Visualization Visualization is, among other things, the ability to manipulate visual images without the benefit of concrete objects. In the Japanese lessons, we saw children engaged in three-dimensional visualization (bean-container task) and two-dimensional visualization (pattern-block task). Photo: A Japanese Public School

28. “an excellent vehicle for the development and improvement of a person’s intellectual competence” This is the rationale stated in Singapore Mathematics curriculum document.

29. Professional Development for Singapore Math (Lower Grades) Day 2 Session 3 Regrouping & Place Value Photo: Princess Elizabeth Primary School

32. Professional Development for Singapore Math (Lower Grades) Day 2 Session 3 Addition Theory of Variations Photo: Princess Elizabeth Primary School

33. 12 + 9 What are the different ways to add 12 and 9?

34. Students first add by counting all …

35. And then counting on and making ten.

37. For large number addition, students can add the tens and ones separately – regrouping may be necessary.

41. 100 Chart helps counting on for larger numbers.

44. Study the variations over several lessons.

51. “A curriculum as it develops should revisit these basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.” Jerome Bruner 1960 The Process of Education One feature of Singapore Math is the spiral approach.

52. Professional Development for Singapore Math (Lower Grades) Day 2 Session 3 Subtraction Spiral Approach Photo: Princess Elizabeth Primary School

53. Ready for Maths Series

54. Shaping Maths 1

55. Shaping Maths 1

56. “A curriculum as it develops should revisit these basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.” Jerome Bruner 1960 The Process of Education Students have many opportunities to learn subtraction but each time building upon the strategies learnt previously.

57. My Pals Are Here! Mathematics 2

58. Drill-and-practice and thinking are not exclusive.

59. Professional Development for Singapore Math (Lower Grades) Day 2 Session 4 Bar Model Method Photo: Princess Elizabeth Primary School

60. Modeling using real objects, pictures of real objects and more abstract model drawings.

61. Bar models are used to represent quantities – discrete and continuous ones.

66. 12 58

67. Observe how this problem is different from the last one even though numbers used are the same.

68. 12 58 – 12 = 46 46 ÷ 2 = 23 Natalie’s bag is 35 kg. Peter’s bag is 23 kg. Natalie 58 Peter Observe how this problem is different from the last one even though numbers used are the same.