This presentation on bar modeling was for Grades Four and Five teachers from elementary and middle schools in Rye City School District in New York

1. bar model method of solving mathematical word problems SEMINAR at RYE CITY SCHOOL DISTRICT Yeap Ban Har National Institute of Education Nanyang Technological University Singapore yeapbanhar@gmail.com Slides are available for download from www.banhar.blogspot.com or www.mmepdpm.pbworks.com

2. introduction singapore curriculum intellectual competence

3. curriculum framework

4. mathematics Wellington Primary School, Singapore education “ an excellent vehicle for the development and improvement of a person’s intellectual competence ” intellectual competence Ministry of Education Singapore 2006

5. Move 3 sticks to get two squares.

6. Wellington Primary School, Singapore

7. Wellington Primary School, Singapore

8. Wellington Primary School, Singapore

9. Wellington Primary School, Singapore

10. Wellington Primary School, Singapore

11. Move 3 sticks to get two squares.

12. Move 3 sticks to get two squares.

13. Wellington Primary School, Singapore

14. “…development and improvement of a person’s intellectual competencies...” Singapore Ministry of Education 2006 Visualization Patterning Number Sense

15. PSLE Item John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left? 19 cm x 5 = 95 cm 150 cm – 95 cm = 105 cm 105 cm of the copper wire was left.

16. Primary Mathematics Standards Edition

17. model method pre-algebra coaching techniques

18. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. What is the mass of Rahim’s clothes? What is the mass of the suitcase? 29 kg Siti Rahim 11 kg

19. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. What is the mass of Rahim’s clothes? What is the mass of the suitcase? 29 kg 11 kg 18 kg Siti 2 units = 18 kg 1 unit = 9 kg Rahim Rahim’s clothes is 9 kg. The suitcase is 2 kg. 11 kg We can also find the mass of Siti’s clothes (27 kg) if required.

20. Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. What is the mass of Rahim’s clothes? What is the mass of the suitcase? x + y = 11 x + 3y = 29 x y y y Siti 2y = 29 – 11 = 18 x y Rahim y = 18 ÷ 2 = 9

21. model method in kindergarten and primary one

22. Ali has 3 sweets. Billy has 5 sweets. How many sweets do they have altogether?

25. model method alternate methods mental computations

26. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has. Let the amount of money that Cheryl has be $y. Cheryl y + (y + 20) = 148 $148 2y + 20 = 148 20 David

27. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has. Cheryl $148 - $20 = $128 20 David $128 ÷ 2 = $64 Cheryl has $64. How about David? $84 2y + 20 = 148 2y = 148 – 20 = 128 y = 128 ÷ 2 = 64 Cheryl has $64.

28. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has. Let the amount of money that David has be $y. Cheryl $148 20 David

29. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has. $148 + $20 = $168 20 Cheryl $168 ÷ 2 = $84 David has $84. Cheryl has $64. 20 David Let the amount of money that David has be $y. y + (y – 20) = 148 2y = 148 + 20 = 168 2y – 20 = 148 y = 168 ÷ 2 = 84 Cheryl has $64.

30. model method helps average learners see abstract ideas

31. Josh spent 2/5 of his savings to buy a gift and 1/6 of the remainder to buy a snack. Josh then has $7.50 left. Find the amount Josh spent on the gift. 5 units = $7.50 1 unit = $1.50 4 units = $1.50 x 4 = $6 Josh spent $6 on the gift. How about the snack? $1.50 How much is his savings? $7.50

32. There were three times as many students in soccer as there were in basketball. After 12 students moved from soccer to basketball, there number of students in both sports became equal. Find the number of students in soccer at first. Soccer  12 x 3 = 36 soccer There were 36 students in soccer . How about basketball? 12 basketball

33. There were four times as many students in soccer as there were in basketball. After 12 students moved from soccer to basketball, there number of students in both sports became equal. Find the number of students in soccer at first. soccer basketball

34. There were four times as many students in soccer as there were in basketball. After 12 students moved from soccer to basketball, there number of students in both sports became equal. Find the number of students in soccer at first. 1 unit = 4 soccer 8 units = 32 There were 32 students in soccer at first basketball 3 units = 12

35. model method new situations problem solving

36. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day? boys 34 34 girls

37. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day? 88 – 34 – 34 = 20 boys 34 34 34 girls 2 units = 34 – 20 = 14 1 unit = 7 7 x 3 = 21 21 girls wore goggles

38. model method primary school leaving examination

39. Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy? PSLE 2009 chocolates sweets 12 Jim 18 12 12 12 12 12 Ken 3 parts  12 + 12 + 12 + 12 + 18 = 66 1 part  22 Half of the sweets Ken bought = 22 + 12 = 34 So Ken bought 68 sweets.`