1. MATH WORKSHOP FOR P1 PARENTS FRIDAY, 10 APRIL 2015

2. http://www.moe.gov.sg/education/syllabuses/ sciences/files/maths-primary-2013.pdf Mathematics Framework

3. Chongfu’s Curriculum Focus: Heuristics and Thinking Skills Development of mathematical problem solving ability through the use of heuristics and thinking skills

4. CHONGFU SCHOOL MATHEMATICS SKILLS ACQUIRED AT THE END OF EACH LEVEL P1P2P3P4P5P6P5FP6F Heuristics/Thinking Skills Part-whole model√√√√√√√√ Comparison model√√√√√√√√ Multiplication and Division model √√√√√√√ Guess and Check√√√√√√√√ Listing√√√√√√√√ Looking for Pattern√√√√√√√√ Before and After model√√√√√√ Working backwards√√√√√ Make suppositions√√ Use equations√√ Simplify the problem√√√√√√

6. Heuristics for Problem Solving (P1 & P2) Model DrawingModel Drawing Guess and CheckGuess and Check Looking for PatternLooking for Pattern ListingListing

7. Model approach Systematic way of solving mathematical problems Systematic way of solving mathematical problems Types of model Types of model – Part-whole – Comparison

8. Examples 64 ? Part-whole Model Comparison Model 6 4 ? Anna Ben

9. WHY Model Drawing? Visual representation of details and actions which assists pupils with problem solving Helps pupils think logically using visuals to determine their computations Empowers pupils to think systematically and master more challenging problems 9

10. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether? Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data?

11. Peter  6 toy cars John  12 toy cars What is the total? ST A R Chongfu Star Approach to Problem-Solving

12. Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether? Step 2: T hink of a plan  What strategy should I use?  Have I solved similar problems before?

13. Peter  6 toy cars John  12 toy cars What is the total? ST A R I must find the total number of toy cars. I can use a part-whole model to represent the number of toy cars. Chongfu Star Approach to Problem-Solving

14. Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether? Step 3: A ct on the plan I will write out the steps of my solutions

15. Peter  6 toy cars John  12 toy cars What is the total? ST A R I must find the total number of toy cars. I can use a part-whole model to represent the number of toy cars. 612 PeterJohn ? 6 + 12 = 18 They have 18 toy cars altogether. Chongfu Star Approach to Problem-Solving

16. Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether? Step 4: R eflect Have I answered the question? Is my answer reasonable? Have I checked my answers? Is there a better alternative?

17. Peter  6 toy cars John  12 toy cars What is the total? ST A R I must find the total number of toy cars. I can use a part-whole model to represent the number of toy cars. 612 PeterJohn ? 6 + 12 = 18 They have 18 toy cars altogether. The answer must be greater than the number that each person has. (reasonableness) Check by working backwards: 18 – 6 = 12 (John) (√) 18 – 12 = 6 (Peter) (√) Chongfu Star Approach to Problem-Solving

18. Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? Kelvin has 25 storybooks. 10 of them are English storybooks. The rest of them are Chinese storybooks. How many Chinese storybooks are there?

19. ?10 EnglishChinese 25 25  10 = 15 There are 15 Chinese storybooks. ST A R Total No. of storybooks  25 English  10 How many Chinese storybooks? I must find the number of Chinese storybooks. I can use a part-whole model to represent the number of storybooks. The answer must be less than 25. (reasonableness) Check by working backwards: 10 + 15 = 25 (√) Chongfu Star Approach to Problem-Solving

20. Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? Ali has 5 ice-cream sticks. Jane has 18 ice-cream sticks. How many more ice-creams sticks does Jane have than Ali?

21. ST A R Ali  5 ice-cream sticks Jane  18 ice-cream sticks How many more? I must compare the number of ice-cream sticks Ali and Jane have. I can use a comparison model to find the difference. 18 – 5 = 13 Jane has 13 more ice-cream sticks than Ali. The answer must be smaller than 18. (reasonableness) Check by working backwards: 5 + 13 = 18 (√) Or 13 + 5 = 18 (√) Chongfu Star Approach to Problem-Solving 5 18 Ali Jane ?

22. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? Steven collected 376 Australia stamps. He collected 142 fewer Australia stamps than China stamps. How many China stamps did he collect?

23. 376 + 142 = 518 He collected 518 China stamps. ST A R Australia  376 China  Australia + 142 How many China stamps? I must find the number of China stamps. I can use a comparison model to find the number of China stamps. The answer must be more than 376. (reasonableness) Check by working backwards: 518 - 142 = 376 (√) Chongfu Star Approach to Problem-Solving 142 376 Australia 376 China ?

24. Make an educated guess Make an educated guess Check its accuracy and revise guess if Check its accuracy and revise guess if necessary necessary Guess and Check

25. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? 10 motorcycles and cars are parked at a carpark. There are a total of 34 wheels. How many motorcycles and cars are there? (motorcycle: 2 wheels and car: 4 wheels )

26. ST A R I should make a table and use guess and check Check the 2 given conditions: 1. 3 + 7 = 10 (vehicles) 2. 6 + 28 = 34 (wheels) Chongfu Star Approach to Problem-Solving Motorcycles and cars  10 Number of wheels  34 M  2 wheels C  4 wheels Find the number of motorcycles and cars. Find the 2 numbers that fit the 2 conditions: - Motorcycles + cars = 10 - Total number of wheels = 34 MCMotorcycle wheels Car wheels Total No. of wheels Check There are 3 motorcycles and 7 cars. 10 34 555x2 = 105x4 = 2010+20 = 30 x 373x2 = 67x4 = 286+28 = 34 

27. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? Mr Lim has a total of 15 birds and cats in his pet shop. All the birds and cats have a total of 48 legs. How many birds and cats are there in Mr Lim pet shop? (bird: 2 legs and cat: 4 legs )

28. ST A R I should make a table and use guess and check Check the 2 given conditions: 1. 6 + 9 = 15 (animals) 2. 12 + 36 = 48 (legs) Chongfu Star Approach to Problem-Solving Birds and cats  15 Number of legs  48 B  2 legs C  4 legs Find the number of birds and cats. Find the 2 numbers that fit the 2 conditions: - Birds + cats = 15 - Total number of legs = 48 BCBird legs Cat legs Total No. of legs Check There are 6 birds and 9 cats. 1548 10510x2 = 205x4 = 2020+20= 40 x 878x2 = 167x4 = 2816+28= 44 x 696x2 = 129x4 = 3612+36= 48 

29. Looking for Pattern Systematic way of solving mathematical problems Systematic way of solving mathematical problems Examine the available data for patterns or relationships. Examine the available data for patterns or relationships.

30. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Study the pattern of the figures. Find the number of tiles in figure 5. Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? Figure 1 Figure 2 Figure 3

31. ST A R Chongfu Star Approach to Problem-Solving Observe the pattern There are 16 tiles in the 5 th figure. Check pattern 4, 7, 10, 13, 16…… (+3 repeatedly) Use given data to check the relationship e.g. Figure 3: 4 + 3 + 3 = 10 e.g. Figure 4: 4 + 3 + 3 + 3 = 13 We need to find the number of tiles for the 5 th figure. Present the data in a table and try to identify a pattern/relationship. FigureTiles 14 27 310 FigNo. of tiles 14 27 310 4 13 5 16 Figure 1 Figure 2 Figure 3 + 3

32. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Study the pattern of the figures. Find the number of shaded triangles in Figure 10. Figure 1 Figure 2 Figure 3 Figure 10 ………….. ? Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data?

33. ST A R Chongfu Star Approach to Problem-Solving Observe the pattern Figure123 No. of Shaded triangle 135 FigureNumber of shaded triangles 11 22+1=3 33+2=5 44+3=7 1010+9=19 There are 19 shaded triangles in the 10 th figure. Check pattern 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (+2 repeatedly) Use data to check the relationship e.g. Figure 2: 2 +1 = 3 e.g. Figure 4: 4 + 3 =7 We need to find the number of shaded triangles for the 10 th figure. Present the data in a table and try to identify a pattern/relationship. FigureTriangle 11 23 35 + 2

34. Listing Systematic way of solving mathematical problems Systematic way of solving mathematical problems Organise, present or generate the available data in a systematic way Organise, present or generate the available data in a systematic way

35. Chongfu Star Approach to Problem-Solving Step 2: Think of a Plan Step 1: Study the Problem Step 3: Act on the Plan Step 4: Reflect Step 1: S tudy the problem  What am I given? (facts/ information/ data)  What am I asked to find?  How can I make sense of the information given to me?  What can I infer from the given data? Meiling has a blue blouse, a white blouse, a skirt and a pair of jeans. How many different ways can Meiling wear her outfit?

36. ST A R Check: -Are all combinations made up of 1 top and 1 bottom? -Are there any repeated combination? Chongfu Star Approach to Problem-Solving Blue blouse, white blouse, skirt and jeans. Outfit -> 1 top and 1 bottom Since there are many combinations of the different outfit, we need to make a list systematically. TopBottom Blue BlouseSkirt White BlouseSkirt Blue BlouseJeans White BlouseJeans There are 4 ways.

37. Mary puts a teddy bear, a toy car and a doll in a row on a shelf. How many ways can she arrange the toys on the shelf? Make a Systematic List Chongfu Star Approach to Problem-Solving

38. ST A R -Teddy bear, toy car and doll -Arranged in a row Since there are many combinations, we need to make a list systematically. There are 6 ways to arrange the toys. Chongfu Star Approach to Problem-Solving Starting with bear Starting with car Starting with doll Check: -Are all combinations made up of three toys? Are there any repeated combination? B, C, D B, D, C C, B, D C, D, B D, C, B D, B, C

39. Identify the Heuristics to solve the problems Let’s Practise 39 Heuristics Model drawing Guess and check Looking for pattern Listing

40. The figures below are made of sticks of equal length. Find the number of sticks required to form Figure 10. ………………….. Figure 10 ? Heuristics Model drawing Guess and check Looking for pattern Listing Figure 1 Figure 2Figure 3

41. Figure123 No. of sticks 357 ST A R Chongfu Star Approach to Problem-Solving Observe the pattern FigureNo. of sticks 13 23+2 = 5 33+2+2 = 7 43+2+2+2 = 9 103+(9x2) = 21 There are 21 sticks in the 10 th figure. We need to find the number of sticks for figure 10. Present the data in a table and try to identify a pattern/relationship. FigureSticks 13 25 37 Check the pattern 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 (+2 repeatedly) Use given data to check the relationship Figure 1  3 sticks Figure 2  3+2 = 5 sticks Figure 3  3+2+2 =7 sticks Figure 10  3+(9x2) = 21 sticks + 2

42. Jenny had 315 stickers. Her sister gave her 45 stickers. How many stickers did she have altogether? Heuristics Model drawing Guess and check Looking for pattern Listing

43. ST A R Jenny  315 stickers Sister gave  45 stickers How many stickers altogether? I must find the total number of stickers. I can use a part-whole model to represent the number of stickers. 45315 Sister Jenny ? 315 + 45 = 360 She had 360 stickers altogether. The answer must be greater than 315 (reasonableness) Check by working backwards: 360 – 315 = 45 (√) Or 360 – 45 = 315 (√) Chongfu Star Approach to Problem-Solving

44. There are a total of 16 bicycles and tricycles in a park. There are 36 wheels altogether. How many bicycles and tricycles are there? Heuristics Model drawing Guess and check Looking for pattern Listing

45. ST A R There are 12 bicycles and 4 tricycles. Chongfu Star Approach to Problem-Solving Bicycles and tricycles  16 Number of wheels  36 Find number of bicycles and tricycles Find number of bicycles and tricycles I should make a table and use guess and check B T No. of bicycle wheels No. of tricycle wheels Total no. of wheels Check 10 6 10x2=206x3=1838 × 115 11x2=225x3=1537 × 124 12x2=244x3=1236√ Check 2 conditions are met: 1.12 + 4 = 16 (√) 2.24 + 12 = 36 (√)

46. Lyn’s height is 120cm. Jenny is 10cm taller than Lyn. Carol is 15 cm taller than Jenny. How much taller is Carol than Lyn ? Heuristics Model drawing Guess and check Looking for pattern Listing

47. S T A R Lyn  120 cm Jenny  Lyn + 10 cm Carol  Jenny + 15 cm How much taller is Carol than Lyn? I must find how much taller is Carol than Lyn I can use a comparison model to represent all their height. Carol must be taller than Lyn (reasonableness) 120 cm + 10 cm + 15 cm = 145 cm (Carol ) 145 cm – 120 cm = 25 cm Chongfu Star Approach to Problem-Solving 10 cm + 15 cm = 25 cm Carol is 25 cm taller than Lyn. 120 cm 10 Carol Jenny Lyn 15 10

48. Heuristics Model drawing Guess and check Looking for pattern Listing How many 2-digit numbers can you form using the following 4 digits? You can only use a digit once in each number. 2 45 3

49. ST A R - 2-digit numbers - Use all 4 digits - Use a digit once in each number Since there are many combinations, we need to make a list systematically. I can form 12 2-digit numbers. Chongfu Star Approach to Problem-Solving 2345 23324252 24344353 25354554 Check: - Are all numbers made up of different digits? E.g. 33 (×) - Are there any repeated numbers?

50. Q and A

51. THE END