This document summarizes the key points from a 3-day professional development session on teaching Singapore Math for upper grades. On day 3, sessions included a video study on a problem-solving approach using addition, problem solving and drill practice techniques, and using bar modeling to represent quantities. The document also provides examples of homework solutions and further examples of how the Singapore Math approach emphasizes teaching multiplication in a spiral curriculum across grades 1 through 4.

1. Professional Development for Singapore Math (Upper Grades)Yeap Ban Harbanhar@sg.marshallcavendish.comPearl City, HawaiiDay 310 August 2011Presentations are available at www.banhar.blogspot.com

2. Professional Development for Singapore Math (Upper Grades)Day 3 Session 1Video StudyProblem-Solving Approach

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. Problem10 August 2011How many fifths are there?2×35 =(2×3) fifths = 6 fifths 4×35 =(4×3) fifths =12 fifths 4×35 = 4×35 = 125 The problem-solving approach can be used to teach new concepts or skills.

5. Professional Development for Singapore Math (Upper Grades)Day 3 Session 2Problem Solving& Drill-and-Practice

6. Problem solving is the focus of Singapore Math.

7. Problem solving can include drill-and-practice.

8. Problem solving can include drill-and-practice.

10. Professional Development for Singapore Math (Upper Grades)Day 3 Final SessionsBar Model Method

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

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

13. 60 ÷ 5 = 1212 x 8 = 96There are 76 people.60

18. 1258

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

20. 1258 – 12 = 4646 ÷ 2 = 23Natalie’s bag is 35 kg.Peter’s bag is 23 kg.Natalie58PeterObserve how this problem is different from the last one even though numbers used are the same.

21. 1st Day2nd Day43rd Day444th Day4442505th Day44446th Day444447th Day4444448th Day4444444

23. 51st Day250 – 40 = 210210 : 5 = ?2nd Day442 + 16 = ?2503rd Day44Rosa made 58 paper cranes on the last day.4th Day4445th Day4444Differentiation for struggling students

27. Professional Development for Singapore Math (Upper Grades)Solutions to Homework

28. Sam72TerryVanessa

29. PabloWynn?Zena100

30. 270110

31. boys34girls100

32. boys68girls

33. boys88 – 68 = 20girls

34. boys88 – 68 = 20girls

35. boysgirls

36. boysgirls

37. boys2 girls units = 14341 girls unit = 7girls3 girls units = 2121 girls wear spectacles.34 – 20

39. flourflourflourcookiescake3.6 kg3.6 kg x 2 = 7.2 kgShe bought 7.2 kg of flour.

40. 16 Miss Sitiflourflourflourcookies3.6 kg ÷ 5 = 0.72 kg8 x 0.72 kg = 5.76 kg She bought 5.76 kg of flour.

41. 14 Mrs Raniflourflourflourcookies3.6 kg ÷ 3 = 1.2 kg1.2 kg x 4 = 4.8 kg4.8 kg ÷ 3 = 1.6 kg 1.6 kg x 4 = 6.4 kgShe bought 6.4 kg of flour.cake

42. Answer: 60basketballsoccerAnswer: 100basketballsoccer

43. Answer: 84basketballsoccer

45. Professional Development for Singapore Math (Upper Grades)Further ExampleMultiplication of Whole Numbers

46. Emphasis on Spiral ApproachGrade 1 Multiplication using drawing Math in FocusSingapore Math by Marshall Cavendish

47. Emphasis on Spiral ApproachGrade 2 Multiplication of 2, 5, 10 and 3, 4 Math in FocusSingapore Math by Marshall Cavendish

48. Pensar sin LimitesMatematicaMetodoSingapur

49. Daqiao Primary SchoolSingapore

50. Emphasis on Spiral ApproachGrade 3 Multiplication of 6, 7, 8, 9 2-digit x 1 digit, 3-digit x 1-digit6666 EscuelaNo. 1577 TenienteDagobertoGodoy Chile Math in FocusSingapore Math by Marshall Cavendish

51. Emphasis on Spiral ApproachGrade 3 Multiplication of 2-digit x 1 digit3-digit x 1-digit National Institute of EducationSingapore

52. 42Emphasis on Spiral Approach4 Grade 4 Multiplication of 4-digit x 1 digit, 2-digit x 2-digit30

53. National Institute of EducationSingapore