The document discusses a seminar aimed at helping parents understand PSLE mathematics, focusing on teaching methodologies that enhance problem-solving skills and visualization. It highlights the challenges and parental concerns regarding the difficulty of PSLE mathematics papers, especially after the introduction of calculators. Various mathematical examples and teaching strategies are provided to support children's learning in a curriculum that emphasizes mental computation and visualization.

1. A Seminar for Parents Helping Students withPSLE MathematicsFebruary 2010www.askyeapbanhar.blogspot.comYeap Ban HarNational Institute of EducationNanyang Technological University Singaporebanhar.yeap@nie.edu.sg

2. What is PSLE Mathematics?

3. PSLE MathematicsPaper 1 (50 min)Paper 2 (1 hr 40 min)

4. PSLE Foundation MathematicsPaper 1 (1 hr)Paper 2 (1 hr 15 min)

5. Challenging MCQsfor problems that are difficult for students to communicate solution methods

7. Ann, Beng and Siti each had some money at first. Ann gave Beng $0.50. Beng then gave Siti $0.75. Siti spent $0.25 on a ruler. At the end, they had $3 each. What is the difference between the amount of money that Ann and Siti had at first?$1.00$0.50$0.75$1.25Ann $3$3.50Beng $3$3.75$3.25Siti $3$3.25$2.50

8. What kind of curriculum is it based on?

10. rationale of the curriculumThe rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence”.

12. Visualization – an intellectual competence - is one of the most important ability in solving problems

13. Basic Skillsemphasis on visualization in the learning process

16. 

17. 

18. 

19. Basic Skillsmental strategies strengthen visualization ability

20. Find the value of 12.2 ÷ 4 .It is not expected that P6 students need to perform written working to do it.P4 students may need to perform written working as their ability in mental strategies is not as developed as that of P6 students.Basic Skills Items

21. 3.05312.2012.2041220 hundredths120.200.20Number Bond Method0Long Division Method

22. A show started at 10.55 a.m. and ended at 1.30 p.m.How long was the show in hours and minutes?It is not expected that P6 students need to perform written working to do it.P3 students may need to draw a time line as their ability in using mental strategies is not as developed as that of P6 students.Basic Skills Items

23. 11001330

24. Prawns are sold at $1.35 per 100 g at a market. What is the price of 1.5 kg of prawns? Basic Skills Items $13.50 + $6.75 = $ …Answer: $_________

25. Find <y in the figure below.It is not expected that P6 students need to perform written working to do it.P5 students may need to perform written working 360o – 210oas the content is new to them.Basic Skills Items70 o70 oy70 o

26. Basic Skillscomputation and procedures is not everything

27. The height of the classroom door is about __. 1 m 2 m10 m20 mSome tasks simply do not require written working.Basic Skills Items

28. Cup cakes are sold at 40 cents each. What is the greatest number of cup cakes that can be bought with $95? $95 ÷ 40 cents = 237.5Answer: 237 cupcakesBasic Skill Item

29. Basic Application Item

30. Basic Skillsmental computation is an important part of the curriculum

31. Find the value of99 + 9756 ÷ 8Find the value of200 – 53 9 x 9Find the value of73 – 15 42 ÷ 7Find the value of169 + 348 x 7

32. Challenging Problemswhat makes them challenging

33. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97The first 97 whole numbers are added up.What is the ones digit in the total?Challenging Items: Novel

34. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97The first 97 whole numbers are added up.What is the ones digit in the total?Challenging Items: Novel

35. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97The first 97 whole numbers are added up.What is the ones digit in the total?Challenging Items: Novel

36. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97The first 97 whole numbers are added up.What is the ones digit in the total? The method is difficult to communicate in written form. Hence, the problem is presented in the MCQ format where credit is not given for written method.Challenging Items: Novel

37. Challenging Problem: Connection1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556

38. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.(a) Kay puts the frame on 9 squares as shown in the figure below.3451113192021What is the average of the 8 numbers that can be seen in the frame?

39. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.(a) Kay puts the frame on 9 squares as shown in the figure below.3+4+5+11+13+19+20 = 9696 ÷ 8 = 12345Alternate Method4 x 24 = 9696 ÷ 8 = 121113192021What is the average of the 8 numbers that can be seen in the frame?

40. (b) Lin puts the frame on some other 9 squares. The sum of the 8 numbers that can be seen in the frame is 272. What is the largest number that can be seen in the frame?123456789101112131415161718192021222324252627282930313233343536373839403441424344454647484950515253545556

41. New Emphasis on Looking for Pattern (Item from 2006) Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47th sticker?  ………? 1st 12th 47th

42. New Emphasis on Looking for Pattern (Item from 2006) Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47th sticker?  ………? 1 5 9

43. New Emphasis on Looking for Pattern (Item from 2006) Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47th sticker?  ………? 4 8 12

44. rationale of the curriculumThe rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence”.

45. 9 cm26 cm2With visualization, one does not need to know a formula to calculate the area of a trapezium.

46. Parents Up In Arms Over PSLE Mathematics Paper TODAY’S 10 OCT 2009SINGAPORE: The first thing her son did when he came out from the Primary School Leaving Examination (PSLE) maths paper on Thursday this week was to gesture as if he was "slitting his throat". "One look at his face and I thought 'oh no'. I could see that he felt he was condemned," said Mrs Karen Sng. "When he was telling me about how he couldn't answer some of the questions, he got very emotional and started crying. He said his hopes of getting (an) A* are dashed." Not for the first time, parents are up in arms over the PSLE Mathematics paper, which some have described as "unbelievably tough" this year. As recently as two years ago, the PSLE Mathematics paper had also caused a similar uproar. The reason for Thursday's tough paper, opined the seven parents whom MediaCorp spoke to, was because Primary 6 students were allowed to use calculators while solving Paper 2 for the first time. …Said Mrs Vivian Weng: "I think the setters feel it'll be faster for them to compute with a calculator. So the problems they set are much more complex; there are more values, more steps. But it's unfair because this is the first time they can do so and they do not know what to expect!" …"The introduction of the use of calculators does not have any bearing on the difficulty of paper. The use of calculators has been introduced into the primary maths curriculum so as to enhance the teaching and learning of maths by expanding the repertoire of learning activities, to achieve a better balance between the time and effort spent developing problem solving skills and computation skills. Calculators can also help to reduce computational errors." …Another common gripe: There was not enough time for them to complete the paper. A private tutor, who declined to be named, told MediaCorp she concurred with parents' opinions. "This year's paper demanded more from students. It required them to read and understand more complex questions, and go through more steps, so time constraints would have been a concern," the 28-year-old said.

48. chocolatessweets12Jim121212121218Ken3 parts  12 + 12 + 12 + 12 + 18 = 661 part  22Half of the sweets Jim bought = 22 + 12 = 34So Jim bought 68 sweets.`

50. 180o – 2 x 21o – 2 x 28o = …

51. The tickets for a show are priced at $10 and $5. The number of ten-dollar tickets available is 1.5 times the number of five-dollar tickets. 5 out of 6 ten-dollar tickets and all the five-dollar tickets were sold. The ticket sales amounted to $5 600. How much more would have been collected if all the tickets were sold?FMPS

52. The tickets for a show are priced at $10 and $5. The number of ten-dollar tickets available is 1.5 times the number of five-dollar tickets. 5 out of 6 ten-dollar tickets and all the five-dollar tickets were sold. The ticket sales amounted to $5 600. How much more would have been collected if all the tickets were sold?FMPS7 units  $5600$51 units  $800$10This amount would have been collected: $5600 + $800 = $6400

53. Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3 : 1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first?FMPS

54. Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3 : 1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first?FMPSChongfuAzmanBala

55. Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3 : 1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first?FMPS60Chongfu1006040Azman100Bala100

56. Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3 : 1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first?FMPS60Chongfu100780 – 380 = 3006040Azman100Bala100

57. Some stamps were placed in Album A and Album B. If 30 stamps were removed from Album A, the ratio of the number of stamps in Album A to the number of stamps in Album B would be 1 : 4. If 60 stamps were removed from Album B, the ratio would be 5 : 2. How many stamps were there in Album B?FMPS