This seminar for parents is organised by Blue Orange.

1. How to Ace the PSLE Mathematics Yeap Ban Har National Institute of Education Nanyang Technological University

2. PSLE Mathematics

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

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

5. PSLE Mathematics is Based on a Problem-Solving Curriculum

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

8. “… over-emphasising procedural skills without understanding the underlying mathematical principles should be avoided.” Ministry of Education 2006

9. Find the value of (a) 11.98 – 2.6 (b) 43 ÷ 10 Example 0

10. Find the value of 12.2 ÷ 4 . Basic Skills Items Example 1

11. 3.05 3 12.20 12.20 4 12 20 hundredths 12 0.20 0.20 Number Bond Method 0 Long Division Method

12. Find <y in the figure below. 360o – 210o = 150o 70 o 70 o y 70 o Example 2

13. The height of the classroom door is about __. (1) 1 m (2) 2 m (3) 10 m (4) 20 m Example 3

14. “Mathematical problem solving is central to mathematics learning.” Ministry of Education 2006

15. Ali paid for a 85-cent pen with a $5 note. How much change should he get? Answer: $__________ Example 4

16. A show started at 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes? Example 5

17. During a sale, mugs are sold in sets of 3 for $1.45. How much must Bala pay for buying 15 mugs during the sale? $1.45 x 5 = $14.50 ÷ 2 = $7.25 Example 6

18. Sam had 295 eggs. He packed all the eggs into boxes of 9 with some left over. How many eggs are left over? 295 ÷ 9 = 32 remainder 7 7 eggs are left over Example 7

19. 295 270 25

20. 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 = 237.5 Answer: 237 cupcakes Basic Skill Item Example 8

21. Mr Tan rented a car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days? $767.40 – 3 x $155 = $302.40 $302.40 ÷ 60 cents per km = 504 km Example 9

22. Mr Tan rented a car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days? 767.40 – 3 x 155 = 302.40 302.40 ÷ 0.60 = 504 He travelled 504 km. Example 9

23. “Mathematical problem solving is central to mathematics learning.” Ministry of Education 2006

24. ““… including non-routine, open-ended and real-world problems.” Ministry of Education 2006

25. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 The first 97 whole numbers are added up. What is the ones digit in the total? Challenging Items: Novel

26. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 The first 97 whole numbers are added up. What is the ones digit in the total? Challenging Items: Novel

27. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 The first 97 whole numbers are added up. What is the ones digit in the total? Challenging Items: Novel

28. 1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 The 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

29.  -  = n where n is a whole number The difference between a 2-digit whole number and a 1-digit whole number is n. Find all the possible subtraction sentences when n = 4. Describe in words how the number of possible subtraction sentences depends on the value of n. Challenging Items: Novel Example 10

30. 10 - 6 = 4 11 - 7 = 4 12 - 8 = 4 13 - 9 = 4 10 – 7 = 3 11 – 8 = 3 12 – 9 = 3 Challenging Items: Novel Example 10

31. Challenging Problem: Connection 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Example 11

32. 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 21 What is the average of the 8 numbers that can be seen in the frame?

33. 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 = 96 96 ÷ 8 = 12 3 4 5 Alternate Method 4 x 24 = 96 96 ÷ 8 = 12 11 13 19 20 21 What is the average of the 8 numbers that can be seen in the frame?

34. (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? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 34 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

35. Example 13

37. Example 14

41. “Skill proficiencies include the ability to use technology confidently, where appropriate, for exploration and problem solving.” Ministry of Education 2006

42. 32 x 46 = 23 x 64 23 is obtained when the digits in 32 are reversed. 64 is obtained when the digits in 46 are reversed. Find three other pairs of 2-digit numbers where AB x CD = BA x DC. Example 15

43. Example 16

44. Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left. How many cookies did Mrs Hoon sell? almond cookies 5/8 3/8 210 chocolate cookies 1/5 3/8 – 1/5 = 7/40  210 1/40  30 Example 17 32/40  960 She sold 960 cookies.

45. Five Core Competencies Number Sense Patterns Visualization Communication Metacognition

46. Try to do as you read the problems. Do not wait till the end of the question to try to do something. Try to draw when you do not get what the question is getting at. Diagrams such as models are very useful. Do more mental computation when practising Paper 1. Some Strategies

47. After Shop A Shop B Example 18

48. 156 kg Before Shop A Shop B 156 kg – 72 kg = 84 kg 72kg 3 units = 84 kg 1 unit = 84 kg ÷ 3 = 28 kg 72 kg – 28 kg = 44 kg Shop B sold 44 kg of rice. Shop A sold 44 kg of rice.

49. The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end? (TeckWhye Primary School, Grade 6) Album A Album B Album C Example 19

50. The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end? (TeckWhye Primary School, Grade 6) 7 units  ? 7 units  36 x 7 = 210 + 42 = 252 There were 252 more stamps in Album C than Album A in the end. Album A Album B Album C 468 13 units  444 + 24 = 468 1 unit  468 ÷ 13 = 36 390 78

51. Example 11

52. Parents Up In Arms Over PSLE Mathematics Paper TODAY’S 10 OCT 2009 SINGAPORE: 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.

54. chocolates sweets 12 Jim 12 12 12 12 12 18 18 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.