STU Seminar on The Model Method in Mathematical Problem Solving at NTUC Centre, Singapore 10 April 2010

1. word problems model method of solving mathematical Yeap Ban Har National Institute of Education Nanyang Technological University Singapore [email_address] Slides are available for download from www.mathz4kidz.com SEMINAR

2. intellectual competence introduction singapore curriculum

3. curriculum framework

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

5. Move 3 sticks to get two squares.

6. Move 3 sticks to get two squares.

7. Wellington Primary School, Singapore

8. Wellington Primary School, Singapore

9. Wellington Primary School, Singapore

10. Wellington Primary School, Singapore

11. Wellington Primary School, Singapore

12. Wellington Primary School, Singapore

13. visualization “… development and improvement of a person’s intellectual competencies...” Singapore Ministry of Education 2006

14. 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

15. Primary Mathematics Standards Edition

16. coaching techniques model method pre-algebra

17. Siti Rahim 29 kg 11 kg 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?

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? Siti Rahim 29 kg 11 kg 11 kg 18 kg 2 units = 18 kg 1 unit = 9 kg Rahim’s clothes is 9 kg. The suitcase is 2 kg. We can also find the mass of Siti’s clothes (27 kg) if required.

19. Siti Rahim x y x y y y x + y = 11 x + 3y = 29 2y = 29 – 11 = 18 y = 18 ÷ 2 = 9 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?

20. and primary one model method in kindergarten

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

24. mental computations model method alternate methods

25. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has. Cheryl David 20 $148

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

27. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has. Cheryl David 20 $148

28. Cheryl David 20 $148 + $20 = $168 20 $168 ÷ 2 = $84 David has $84. Cheryl has $64. Cheryl has $20 less than David. Cheryl and David have $148 altogether, Find the amount of money Cheryl has.

29. see abstract ideas model method helps average learners

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

31. 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 basketball 12 Soccer  12 x 3 = 36 How about basketball?

32. 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

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 3 units = 12 1 unit = 4 8 units = 32 There were 32 students in soccer at first

34. problem solving model method new situations

35. 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 girls 34 34

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 girls 34 34 88 – 34 – 34 = 20 34 2 units = 34 – 20 = 14 1 unit = 7 7 x 3 = 21 21 girls wore goggles

37. leaving examination model method primary school

38. Machine A Machine B 12 Every minute Machine A prints 12 pages more than Machine B. Machine A and Machine B together print a total of 528 pages in 3 minutes. At this rate, how many pages does Machine B print in 1 minute? 176

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 choco;ates 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 Jim Ken sweets 18 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.` 12 12 12 12 12 12

40. Monday Tuesday Wednesday Thursday Friday 20 20 20 20 20 20 20 20 20 20 Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday?

41. At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell? A B 156 kg 72 kg

42. At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell? A B 28 156 kg 72 kg 3 units = 156 kg – 72 kg = 84 kg 1 unit = 28 kg Each shop sold 64 kg of rice.

43. preliminary examination model method primary school

44. Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. Mrs Liu spent 1/5 of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary.

45. Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. Mrs Liu spent 1/5 of her monthly salary on a handbag, 1/4 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. 3 units = $1890

46. Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. Mrs Liu spent 1/5 of her monthly salary on a handbag, 3/8 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. 5 units = $1890

47. Mrs Liu spent some of her monthly salary on a handbag, some of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. Mrs Liu spent 1/5 of her monthly salary on a handbag, 4/7 of the remainder on a vacuum cleaner and saved the rest of her monthly salary. She saved $1890. Find her monthly salary. 12 units = $1890

48. There were 192 apples and pears in a box. John removed 2/5 of the apples from the box and he added 24 pears into the box. As a result, there was an equal number of apples and pears left in the box. How many more apples than pears were there in the box at first? apples pears 24 192

49. There were 192 apples and pears in a box. John removed 2/5 of the apples from the box and he added 24 pears into the box. As a result, there was an equal number of apples and pears left in the box. How many more apples than pears were there in the box at first? apples pears 24 192 + 24 8 units = 216 8 units = 160 + 56 1 unit = 27

50. apples pears 2 27 27 27 27 24 192 27 ? Apples = 27 x 5 = 135 Pears = 27 x 3 – 24 = 81 – 24 = 57 There were 135 – 55 – 2 = 78 more apples than pears at first.

51. A librarian counted the number of adults in the library and found that 2/5 of the number of women was equal to 2 times the number of men. When another 12 men entered the library and 45 women left the library, the ratio of the number of women to the number of men became 5 : 2. men women 12 45 30 5 units = 30 + 45 = 75 1 unit = 15 Men = 2 x 15 = 30 Women = 10 x 15 = 150

52. leaving examination other heuristics primary school