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A Seminar for Parents Helping Your Child Prepare for  PSLE Mathematics Yeap Ban Har National Institute of Education Nanyan...
 
<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 mark...
 
MATHEMATICAL PROBLEM SOLVING
 
The rationale of teaching mathematics is that it is “a  good vehicle  for the development and improvement of a person’s  i...
<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...
<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><l...
<ul><li>Find <y in the figure below. </li></ul><ul><li>It is not expected that P6 students need to perform written working...
<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 <...
<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 bough...
<ul><li>Non-Calculator Item </li></ul><ul><li>Calculator Item </li></ul><ul><li>From January to August last year, Mr Tang ...
<ul><li>Non-Calculator Item </li></ul><ul><li>Calculator Item </li></ul><ul><li>From January to August last year, Mr Tang ...
<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>...
<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><...
<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>1 + 2 +  3  +  4  +  5  + … +  95  +  96  +  97 </li></ul><ul><li>The first 97 whole numbers are added up. </li></...
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...
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 w...
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 w...
(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 th...
Challenging Items: Visualization
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 ...
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...
<ul><li>Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the...
<ul><li>Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the...
<ul><li>Rena used stickers of four different shapes to make a pattern. The first 12 stickers are shown below. What was the...
The rationale of teaching mathematics is that it is “a  good vehicle  for the development and improvement of a person’s  i...
It is so basic, students doing Foundation Mathematics are expected to have the ability …
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 ...
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 ...
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 ...
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 ...
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 ...
<ul><li>David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout the...
<ul><li>David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout the...
<ul><li>Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and...
11 kg 29 kg
11 kg 29 kg
11 kg 18 kg 11 kg
18 kg 9 kg
9 kg 27 kg
<ul><li>Every minute Machine A prints 12 pages more than Machine B. Machine A and Machine B together print a total of 528 ...
<ul><li>Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amo...
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.
With visualization, one does not need to know a formula to calculate the area of a trapezium. 9 cm 2 6 cm 2
<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, t...
<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, t...
<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, t...
<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, t...
<ul><li>88 children took part in a swimming competition.  1/3 of the boys and 3/7  of the girls wore swimming goggles. Alt...
 
34 88 54
34 54 – 34 = 20 34 – 20 = 14 3 x 7 = 21 girls wear goggles
<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 numbe...
<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 numbe...
<ul><li>Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala los...
<ul><li>Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala los...
<ul><li>Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala los...
<ul><li>Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala los...
<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...
<ul><li>An Example from Textbook </li></ul>
    
     
                     
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A Seminar for Parents Helping Your Child Prepare for PSLE Mathematics

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A Seminar for Parents
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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.            

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