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A Seminar for Parents Helping Your Child Prepare for PSLE Mathematics

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A Seminar for Parents
Helping Your Child Prepare for
PSLE Mathematics

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A Seminar for Parents Helping Your Child Prepare for PSLE Mathematics

1. 1. A Seminar for Parents Helping Your Child Prepare for PSLE Mathematics Yeap Ban Har National Institute of Education Nanyang Technological University Singapore [email_address]
2. 3. <ul><li>Paper 1 (50 min) </li></ul><ul><li>Paper 2 (1 hr 40 min) </li></ul>Type Mark Value Number MCQ 1 mark 10 MCQ 2 marks 5 SAQ 1 mark 10 SAQ 2 marks 5 Type Mark Value Number SAQ 2 marks 5 LAQ 3 marks 4 marks 5 marks 13
3. 5. MATHEMATICAL PROBLEM SOLVING
4. 7. The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence ”.
5. 8. <ul><li>Find the value of 12.2 ÷ 4 . </li></ul><ul><li>It is not expected that P6 students need to perform written working to do it. </li></ul><ul><li>P4 students may need to perform written working as their ability in mental strategies is not as developed as that of P6 students. </li></ul>
6. 9. <ul><li>A show started at 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes? </li></ul><ul><li>It is not expected that P6 students need to perform written working to do it. </li></ul><ul><li>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. </li></ul>
7. 10. <ul><li>Find <y in the figure below. </li></ul><ul><li>It is not expected that P6 students need to perform written working to do it. </li></ul><ul><li>P5 students may need to perform written working 360 o – 210 o as the content is new to them. </li></ul>70 o 70 o 70 o y
8. 11. <ul><li>The height of the classroom door is about __. </li></ul><ul><li>1 m </li></ul><ul><li>2 m </li></ul><ul><li>10 m </li></ul><ul><li>20 m </li></ul><ul><li>Some tasks simply do not require written working. </li></ul>
9. 12. <ul><li>Cup cakes are sold at 40 cents each. </li></ul><ul><li>What is the greatest number of cup cakes that can be bought with \$95? </li></ul><ul><li> \$95 ÷ 40 cents = 237.5 </li></ul><ul><li>Answer: 237 cupcakes </li></ul>
10. 13. <ul><li>Non-Calculator Item </li></ul><ul><li>Calculator Item </li></ul><ul><li>From January to August last year, Mr Tang sold an average of 4.5 cars per month, He did not sell any car in the next 4 months. On average, how many cars did he sell per month last year? </li></ul><ul><li>  </li></ul><ul><li>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? </li></ul>
11. 14. <ul><li>Non-Calculator Item </li></ul><ul><li>Calculator Item </li></ul><ul><li>From January to August last year, Mr Tang sold an average of 4.5 cars per month, He did not sell any car in the next 4 months. On average, how many cars did he sell per month last year? </li></ul><ul><li>  4.5 x 8 = 36 </li></ul><ul><li>36 ÷ 12 = 3 </li></ul><ul><li>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? </li></ul><ul><li>\$155 x 3 = \$465 </li></ul><ul><li>\$767.40 - \$465 = \$302.4 </li></ul><ul><li>\$302.40 ÷ 60 cents/km </li></ul><ul><li>= 504 km </li></ul>
12. 15. <ul><li>1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 </li></ul><ul><li>The first 97 whole numbers are added up. </li></ul><ul><li>What is the ones digit in the total? </li></ul>
13. 16. <ul><li>1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 </li></ul><ul><li>The first 97 whole numbers are added up. </li></ul><ul><li>What is the ones digit in the total? </li></ul>
14. 17. <ul><li>1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 </li></ul><ul><li>The first 97 whole numbers are added up. </li></ul><ul><li>What is the ones digit in the total? </li></ul>
15. 18. <ul><li>1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97 </li></ul><ul><li>The first 97 whole numbers are added up. </li></ul><ul><li>What is the ones digit in the total? </li></ul><ul><li>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. </li></ul>
16. 19. 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
17. 20. 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. What is the average of the 8 numbers that can be seen in the frame? 3 4 5 11 13 19 20 21
18. 21. 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. What is the average of the 8 numbers that can be seen in the frame? 4 x 24 = 96 96 ÷ 8 = 12 3+4+5+11+13+19+20 = 96 96 ÷ 8 = 12 3 4 5 11 13 19 20 21
19. 22. (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 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 34
20. 23. Challenging Items: Visualization
21. 24. Challenging Items: Visualization 40 x 30 x 60 = 72 000 72 000 ÷ 5 x 2 = 14 400 x 2 = 28 800 28 800 ÷ 1200 = 24 The height is 24 cm
22. 25. Challenging Items: Visualization 40 x 30 x 60 ÷ 5 x 2 ÷ (40 x 30) = 24 The height is 24 cm. 40 x 30 x 60 ÷ 5 x 3 ÷ (40 x 45) = 24 The height is Tank B is 24 cm. It is the same for Tank A.
23. 26. <ul><li>Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47 th sticker? </li></ul><ul><li>            ……… ? </li></ul><ul><li>1 st 12 th 47 th </li></ul>
24. 27. <ul><li>Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47 th sticker? </li></ul><ul><li>            ……… ? </li></ul><ul><li>1 st 12 th 47 th </li></ul>
25. 28. <ul><li>Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the shape of the 47 th sticker? </li></ul><ul><li>            ……… ? </li></ul><ul><li>1 st 12 th 47 th </li></ul>
26. 29. The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence ”.
27. 30. It is so basic, students doing Foundation Mathematics are expected to have the ability …
28. 31. Emphasis on Visualization is not new. 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?
29. 32. Emphasis on Visualization is not new. 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?
30. 33. Emphasis on Visualization is not new. 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?
31. 34. Emphasis on Visualization is not new. 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?
32. 35. Emphasis on Visualization is not new. 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 = 55 cm 55 cm was left.
33. 36. <ul><li>David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 minutes earlier than Michael. However, Michael reached Town B 50 minutes earlier than David. When Michael reached Town B, David had travelled 4/5 of the journey and was 75 km away from Town B. </li></ul>
34. 37. <ul><li>David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 minutes earlier than Michael. However, Michael reached Town B 50 minutes earlier than David. When Michael reached Town B, David had travelled 4/5 of the journey and was 75 km away from Town B. </li></ul>Michael David 75 km 4/5 4 x 75 km = 300 km (a) Town A to Town B is 375 km. (b) 50 min  75 km 10 min  15 km 1 h  6 x 15 km = 90 km (c) 50 min  1/5 of the journey 250 min  whole journey Michael took 80 min less. He took 170 min.
35. 38. <ul><li>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. </li></ul><ul><li>What is the mass of Rahim’s clothes? </li></ul><ul><li>What is the mass of the suitcase? </li></ul>
36. 39. 11 kg 29 kg
37. 40. 11 kg 29 kg
38. 41. 11 kg 18 kg 11 kg
39. 42. 18 kg 9 kg
40. 43. 9 kg 27 kg
41. 44. <ul><li>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? </li></ul><ul><li>Every minute, A and B print 528 ÷ 3 = 176 pages. </li></ul>12 176 B prints 82 pages per minutes
42. 45. <ul><li>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? </li></ul>
43. 46. 20 20 20 20 20 20 20 20 20 20 \$6 \$6 – 10 x 20 cents = \$4 \$4 ÷ 5 = 80 cents She saved 80 cents on Monday.
44. 47. With visualization, one does not need to know a formula to calculate the area of a trapezium. 9 cm 2 6 cm 2
45. 48. <ul><li>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? </li></ul>
46. 49. <ul><li>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? </li></ul>B A 156 72
47. 50. <ul><li>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? </li></ul>B A 156 72
48. 51. <ul><li>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? </li></ul>B A 3 units  156 – 72 = 84 = 60 + 24 1 unit  28 Shop A sells (156 – 4 x 28) kg = 44 kg. Alternatively Shop B sells (72 – 28) kg = 44 kg. So does Shop A.
49. 52. <ul><li>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? </li></ul>
50. 54. 34 88 54
51. 55. 34 54 – 34 = 20 34 – 20 = 14 3 x 7 = 21 girls wear goggles
52. 56. <ul><li>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? </li></ul>
53. 57. <ul><li>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? </li></ul>\$10 \$5 7 units  \$5600 1 units  \$800 This amount would have been collected: \$5600 + \$800 = \$6400
54. 58. <ul><li>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? </li></ul>
55. 59. <ul><li>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? </li></ul>Chongfu Azman Bala
56. 60. <ul><li>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? </li></ul>60 Chongfu Azman Bala 60 100 100 100 40
57. 61. <ul><li>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? </li></ul>60 Chongfu Azman Bala 60 100 100 100 40 780 – 380 = 300
58. 62. <ul><li>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? </li></ul>
59. 63. <ul><li>An Example from Textbook </li></ul>
60. 64.   
61. 65.    
62. 66.            