1. Professional Development for Singapore Math (Upper Grades) Yeap Ban Har banhar@sg.marshallcavendish.com Pearl City, Hawaii Day 3 10 August 2011 Presentations are available at www.banhar.blogspot.com

2. Professional Development for Singapore Math (Upper Grades) Day 3 Session 1 Video Study Problem-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 2011 How 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 2 Problem 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 Sessions Bar 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 = 12 12 x 8 = 96 There are 76 people. 60

18. 12 58

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

20. 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.

21. 1st Day 2nd Day 4 3rd Day 4 4 4th Day 4 4 4 250 5th Day 4 4 4 4 6th Day 4 4 4 4 4 7th Day 4 4 4 4 4 4 8th Day 4 4 4 4 4 4 4

23. 5 1st Day 250 – 40 = 210 210 : 5 = ? 2nd Day 4 42 + 16 = ? 250 3rd Day 4 4 Rosa made 58 paper cranes on the last day. 4th Day 4 4 4 5th Day 4 4 4 4 Differentiation for struggling students

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

28. Sam 72 Terry Vanessa

29. Pablo Wynn ? Zena 100

30. 270 110

31. boys 34 girls 100

32. boys 68 girls

33. boys 88 – 68 = 20 girls

34. boys 88 – 68 = 20 girls

35. boys girls

36. boys girls

37. boys 2 girls units = 14 34 1 girls unit = 7 girls 3 girls units = 21 21 girls wear spectacles. 34 – 20

39. flour flour flour cookies cake 3.6 kg 3.6 kg x 2 = 7.2 kg She bought 7.2 kg of flour.

40. 16 Miss Siti flour flour flour cookies 3.6 kg ÷ 5 = 0.72 kg 8 x 0.72 kg = 5.76 kg She bought 5.76 kg of flour.

41. 14 Mrs Rani flour flour flour cookies 3.6 kg ÷ 3 = 1.2 kg 1.2 kg x 4 = 4.8 kg 4.8 kg ÷ 3 = 1.6 kg 1.6 kg x 4 = 6.4 kg She bought 6.4 kg of flour. cake

42. Answer: 60 basketball soccer Answer: 100 basketball soccer

43. Answer: 84 basketball soccer

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

46. Emphasis on Spiral Approach Grade 1 Multiplication using drawing Math in Focus Singapore Math by Marshall Cavendish

47. Emphasis on Spiral Approach Grade 2 Multiplication of 2, 5, 10 and 3, 4 Math in Focus Singapore Math by Marshall Cavendish

48. Pensar sin Limites MatematicaMetodoSingapur

49. Daqiao Primary School Singapore

50. Emphasis on Spiral Approach Grade 3 Multiplication of 6, 7, 8, 9 2-digit x 1 digit, 3-digit x 1-digit 6 6 6 6 EscuelaNo. 1577 TenienteDagobertoGodoy Chile Math in Focus Singapore Math by Marshall Cavendish

51. Emphasis on Spiral Approach Grade 3 Multiplication of 2-digit x 1 digit 3-digit x 1-digit National Institute of Education Singapore

52. 42 Emphasis on Spiral Approach 4 Grade 4 Multiplication of 4-digit x 1 digit, 2-digit x 2-digit 30

53. National Institute of Education Singapore