Parents Seminar on PSLE Mathematics

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Parents Seminar on PSLE Mathematics

  1. 1. Problem Solving inPSLE Mathematics Yeap Ban Har Marshall Cavendish Institute Singapore banhar.yeap@pathlight.org.sg Slides are available atwww.banhar.blogspot.com
  2. 2. Type Mark Number Type Mark Number Value Value MCQ 1 mark 10 (10%) SAQ 2 marks 5 (10%) MCQ 2 marks 5 (10%) 3 marks SAQ 1 mark 10 (10%) LAQ 4 marks 13 (50%) 5 marks SAQ 2 marks 5 (10%)Paper 1 (50 min) Paper 2 (1 hr 40 min)
  3. 3. Type Mark Number Type Mark Number Value Value MCQ 1 mark 10 (10%) SAQ 2 marks 10 (20%) MCQ 2 marks 10 (20%) 3 marks SAQ 2 marks 10 (20%) LAQ 4 marks 8 (30%) 5 marksPaper 1 (1 hr) Paper 2 (1 hr 15 min)
  4. 4. The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a person’s intellectual competence”.
  5. 5. Ministry of Education 2006
  6. 6. Find the value of 12.2 ÷ 4 . Answer : 3.05 [B1] Example 1
  7. 7. 3 .05 12.20 4 12.20 12 12 20 hundredths 0.20Number Bond Method 0.20 0 Long Division Method
  8. 8. A show started at 10.55 a.m. and endedat 1.30 p.m. How long was the show inhours and minutes? 2 h 30 min 11 a.m. 1.30 p.m. Answer : 2 h 35 min [B1] Example 2
  9. 9.  Find <y in the figure below. 70 o 70 o y 70 o 360o – 210o = 150o Example 3
  10. 10. The height of the classroom door is about __.(1) 1m(2) 2m(3) 10 m(4) 20 m Example 4
  11. 11. Ministry of Education 2006
  12. 12. Cup cakes are sold at 40 cents each.What is the greatest number of cup cakes thatcan be bought with $95? $95 ÷ 40 cents = 237.5 Answer: 237 cupcakes Example 5
  13. 13. From January to August last year, MrTang sold an average of 4.5 cars permonth, He did not sell any car in thenext 4 months. On average, how manycars did he sell per month last year?4.5 x 8 = 36 ÷ 12 = 3 Answer: 3 cars / month Example 6
  14. 14. Mr Tan rented a car for 3 days. He wascharged $155 per day and 60 cents forevery km that he travelled. He paid$767.40. What was the total distancethat he travelled for the 3 days? $767.40 – 3 x $155 = $302.40$302.40 ÷ 60 cents per km = 504 km Example 7
  15. 15. Mr Tan rented a car for 3 days. He wascharged $155 per day and 60 cents forevery km that he travelled. He paid$767.40. What was the total distancethat he travelled for the 3 days? 767.40 – 3 x 155 = 302.40 302.40 ÷ 0.60 = 504 He travelled 504 km. Example 7
  16. 16. Ministry of Education 2006
  17. 17. Ministry of Education 2006
  18. 18. Parents Up In Arms Said Mrs Vivian Weng: "I think the setters feel itll be faster for them to compute with aOver PSLE calculator. So the problems they set are much more complex; there are more values, more steps. But its unfair because this is the firstMathematics Paper time they can do so and they do not know what to expect!"TODAY’S 10 OCT 2009 … "The introduction of the use of calculators does not have any bearing on the difficulty ofSINGAPORE: The first thing her son did when he came out from paper. The use of calculators has beenthe Primary School Leaving Examination (PSLE) maths paper on introduced into the primary maths curriculumThursday this week was to gesture as if he was "slitting his so as to enhance the teaching and learning ofthroat". maths by expanding the repertoire of learning"One look at his face and I thought oh no. I could see that he felt activities, to achieve a better balance betweenhe was condemned," said Mrs Karen Sng. "When he was telling the time and effort spent developing problemme about how he couldnt answer some of the questions, he got solving skills and computation skills.very emotional and started crying. He said his hopes of getting Calculators can also help to reduce(an) A* are dashed." computational errors." …Not for the first time, parents are up in arms over the PSLE Another common gripe: There was notMathematics paper, which some have described as "unbelievably enough time for them to complete the paper.tough" this year. As recently as two years ago, the PSLE A private tutor, who declined to be named,Mathematics paper had also caused a similar uproar. told MediaCorp she concurred with parentsThe reason for Thursdays tough paper, opined the seven parents opinions. "This years paper demanded morewhom MediaCorp spoke to, was because Primary 6 students were from students. It required them to read andallowed to use calculators while solving Paper 2 for the first time. understand more complex questions, and go… through more steps, so time constraints would have been a concern," the 28-year-old said.
  19. 19. Students in the highest international benchmark are able to apply their knowledge in a variety of situations and able to explain themselves.
  20. 20. Ministry of Education 2006
  21. 21. 1 2 3 4 5 6 7 89 10 11 12 13 14 15 1617 18 19 20 21 22 23 2425 26 27 28 29 30 31 3233 34 35 36 37 38 39 4041 42 43 44 45 46 47 4849 50 51 52 53 54 55 56 Problem 4
  22. 22. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plasticframe that covers exactly 9 squares of Table 1 with the centre squaredarkened.(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?
  23. 23. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plasticframe that covers exactly 9 squares of Table 1 with the centre squaredarkened.(a) Kay puts the frame on 9 squares as shown in the figure below. 3+4+5+11+13+19+20 = 96 3 4 5 96 ÷ 8 = 12 11 13 Alternate Method 4 x 24 = 96 19 20 21 96 ÷ 8 = 12 What is the average of the 8 numbers that can be seen in the frame?
  24. 24. (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
  25. 25.  A figure is formed by arranging equilateral triangles pieces of sides 3 cm in a line. The figure has a perimeter of 93 cm. How many pieces of the equilateral triangles are used? 93 cm ÷ 3 cm = 31 31 – 2 = 29 Problem 2 29 pieces are used.
  26. 26. 40 cm x 30 cm x 60 cm = 72 000 cm372 000 cm3 ÷ 5 x 3 = 43 200 cm343 200 cm3 ÷ 1800 cm2 = 24 cm Problem 3
  27. 27. 40 cm x 30 cm x 60 cm = 72 000 cm372 000 cm3 ÷ 5 x 2 = 28 800 cm328 800 cm3 ÷ 1200 cm2 = 24 cm Problem 3
  28. 28. Rena used stickers of four different shapesto make a pattern. The first 12 stickers areshown below. What was the shape of the47th sticker?            ………?1st 12th 47th Problem 4
  29. 29. Weiyang started a savings plan by putting 2coins in a money box every day. Each coin waseither a 20-cent or 50-cent coin. His motheralso puts in a $1 coin in the box every 7 days.The total value of the coins after 182 days was$133.90.(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins? Problem 5
  30. 30. Weiyang started a savings plan by putting 2coins in a money box every day. Each coin waseither a 20-cent or 50-cent coin. His motheralso puts in a $1 coin in the box every 7 days.The total value of the coins after 182 days was$133.90.(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins?182  7 = 20 + 6 = 26182 x 2 + 26 = 364 + 26 = 390There were 390 coins altogether. Problem 5
  31. 31. Weiyang started a savings plan by putting 2coins in a money box every day. Each coin waseither a 20-cent or 50-cent coin. His motheralso puts in a $1 coin in the box every 7 days.The total value of the coins after 182 days was$133.90.(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins?$133.90 - $26 = $107.90 50-cent 20-cent   There were  50-cent coins.
  32. 32. Suppose each day he put in one 20-cent andone 50-cent coins, the total is $127.40But he only put in $107.90 ..to reduce this by $19.50, exchange 50-centfor 20-cent coins$19.50  $0.30 = 65There were 182 – 65 = 117 fifty-cent coins.
  33. 33. VisualizationJohn had 1.5 m of copperwire. He cut some of thewire to bend into theshape shown in the figurebelow. In the figure, thereare 6 equilateral trianglesand the length of XY is 19cm. How much of thecopper wire was left? Problem 5
  34. 34. John had 1.5 m of copperwire. He cut some of thewire to bend into theshape shown in the figurebelow. In the figure, thereare 6 equilateral trianglesand the length of XY is 19cm. How much of thecopper wire was left?
  35. 35. John had 1.5 m of copperwire. He cut some of thewire to bend into theshape shown in the figurebelow. In the figure, thereare 6 equilateral trianglesand the length of XY is 19cm. How much of thecopper wire was left?
  36. 36. John had 1.5 m of copperwire. He cut some of thewire to bend into theshape shown in the figurebelow. In the figure, thereare 6 equilateral trianglesand the length of XY is 19cm. How much of thecopper wire was left?
  37. 37. John had 1.5 m of copperwire. He cut some of thewire to bend into theshape shown in the figurebelow. In the figure, thereare 6 equilateral trianglesand the length of XY is 19cm. How much of thecopper wire was left? 19 cm x 5 = 95 cm 150 cm – 95 cm = 55 cm 55 cm was left.
  38. 38. Problem 7
  39. 39. 1 2 4 9Problem 7
  40. 40.  Number Sense Patterns Visualization Communication Metacognition
  41. 41.  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.

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