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A Seminar for Parents Helping Your Child Prepare for  PSLE Mathematics Yeap Ban Har National Institute of Education Nanyang Technological University  Singapore [email_address]
 
[object Object],[object Object],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
 
MATHEMATICAL PROBLEM SOLVING
 
The rationale of teaching mathematics is that it is “a  good vehicle  for the development and improvement of a person’s  intellectual competence ”.
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[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],70  o 70  o 70  o y
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[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object]
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[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
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
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
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
(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
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 is 24 cm
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.
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object]
The rationale of teaching mathematics is that it is “a  good vehicle  for the development and improvement of a person’s  intellectual competence ”.
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 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?
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?
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?
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?
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.
[object Object]
[object Object],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.
[object Object],[object Object],[object Object]
11 kg 29 kg
11 kg 29 kg
11 kg 18 kg 11 kg
18 kg 9 kg
9 kg 27 kg
[object Object],[object Object],12 176 B prints 82 pages per minutes
[object Object]
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
[object Object]
[object Object],B A 156 72
[object Object],B A 156 72
[object Object],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.
[object Object]
 
34 88 54
34 54 – 34 = 20 34 – 20 = 14 3 x 7 = 21 girls wear goggles
[object Object]
[object Object],$10 $5 7 units    $5600 1 units    $800 This amount would have been collected: $5600 + $800 = $6400
[object Object]
[object Object],Chongfu Azman Bala
[object Object],60 Chongfu Azman Bala 60 100 100 100 40
[object Object],60 Chongfu Azman Bala 60 100 100 100 40 780 – 380 = 300
[object Object]
[object Object]
    
     
                     

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A Seminar for Parents Helping Your Child Prepare for PSLE Mathematics

  • 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.
  • 4.  
  • 6.  
  • 7. The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence ”.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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.
  • 26.
  • 27.
  • 28.
  • 29. The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence ”.
  • 30. It is so basic, students doing Foundation Mathematics are expected to have the ability …
  • 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?
  • 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?
  • 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?
  • 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?
  • 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.
  • 36.
  • 37.
  • 38.
  • 39. 11 kg 29 kg
  • 40. 11 kg 29 kg
  • 41. 11 kg 18 kg 11 kg
  • 42. 18 kg 9 kg
  • 43. 9 kg 27 kg
  • 44.
  • 45.
  • 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.
  • 47. With visualization, one does not need to know a formula to calculate the area of a trapezium. 9 cm 2 6 cm 2
  • 48.
  • 49.
  • 50.
  • 51.
  • 52.
  • 53.  
  • 55. 34 54 – 34 = 20 34 – 20 = 14 3 x 7 = 21 girls wear goggles
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62.
  • 63.
  • 65.    
  • 66.            