This document provides an overview of the bar model method for teaching mathematics. It discusses using bar models to develop visualization, number sense, and problem-solving abilities. It provides examples of using part-whole and comparison bar models to represent word problems involving fractions, percentages, multi-step word problems, algebra, and real-world scenarios. It also discusses how bar models can be used to differentiate instruction for different levels of learners.

1. Welkom Master Class Singapore Math Dr.Yeap Ban Har Marshall Cavendish Institute 2011alt/ HCO R MAP111 Bar Model Method in Primary 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 the Bar Model Method?

4. 5 units = 60 1 units = 60 : 5 = 12 8 units = 8 x 12 = 80 + 16 = 96 There are 96 people at the party. Number of women Number of men Number of children

6. Bar Model Method In Early Grades

10. Jack Kyla 3 units = $300 1 units = $300 : 3 = $100 Kyla gets $100.

12. Larry Maria 4 units = $300 1 units = $300 : 4 = $75 3 units = 3 x $75 = $300 - $75 = $225 Maria gets $225.

14. What if the larger number is 58? 1st Number 2nd Number Then the smaller number is 58 – 12 = 46. 12 What if the sum of the numbers is 58? 58 – 12 = 46 46 : 2 = 23 Then the smaller number is 23 and the larger number is 23 + 12 = 35. 58 + 12 = 70 The larger number is 70.

15. What if the total number of boys and girls is 58?

16. 58 – 12 = 46 46 : 2 = 23 Peter Natalia 12 Peter’s bag weighs 23 kg. Natalia’s bag weighs 23 kg + 12 kg = 35 kg.

17. Basic Models include Part-Whole Model and Comparison Model

18. Mathematics to develop visualization through bar models, number sense through mental calculation, and ability to manage information through word problems.

19. 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

20. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = ? 1st Day There are 45 fours. 45 x 4 = 180 2nd Day 4 10 units = 250 – 180 = 70 01 units = 70 : 10 = 7 3rd Day 4 4 She made (7 + 9 x 4) = 43 paper cranes on the last day. 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

22. 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

25. Sam 72 Terry Vanessa

26. 36 years old Sam 72 Terry Vanessa 36

27. Vanessa 72 Terry

28. Sam Sam 72 Terry Vanessa

29. Pablo Wynn ? Zena 100

30. Advanced Techniques

31. 270 110

32. 2 units = 160 g 1 units = 160 g : 2 = 80 g The container weighs 110 g – 80 g = 30 g 270 Using algebra x+ 3y = 270 x + y = 110 So, 2y = 160 y = 160 : 2 = 80 x + y = 110 So, x = 30 The container weighs 30 g. 110

33. y y y x 270 y x 110

34. boys 34 girls

35. boys 68 girls

36. boys 88 – 68 = 20 girls

37. boys 88 – 68 = 20 girls

38. boys girls

39. boys girls

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

42. Differentiated Instruction for Struggling and Advanced Learners

43. cookies cake 3,6 kg

44. cookies

45. cookies cookies

46. Homework

47. basketball soccer Answer: 60 basketball soccer Answer: 100

48. basketball soccer Answer: 84

49. 38−15=740 15 740->210 210 140->210 :7=30 38 3040->30 × 30=900