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Mathematics Upper Primary Problem Solving

Mathematics Upper Primary Problem Solving. Objectives. To share on some common problem solving methods To highlight some problematic areas/common misconceptions in pupils. Ratio. 3. difference. Unchanged data. Ratio.

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Mathematics Upper Primary Problem Solving

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  1. MathematicsUpper Primary Problem Solving

  2. Objectives • To share on some common problem solving methods • To highlight some problematic areas/common misconceptions in pupils.

  3. Ratio 3

  4. difference Unchanged data Ratio 1) Mr Lim is 4 times as old as his son, Andy. 8 years ago, the ratio of Mr Lim’s age to Andy’s age was 10 : 1. Find Mr Lim’s age now. Now Mr Lim Andy 8 Years ago Mr Lim Andy

  5. difference Unchanged data Now Mr Lim Andy 2 units  8 yrs 12 units  48 yrs Mr Lim is 48 yrs now. 8 Years ago Mr Lim Andy Checking

  6. Unchanged data to be same Drop of 13 units cos gave away 26 marbles each X 3 = 6 15 21 X 2 = 6 2 8 Ratio 2) Jim and Venus had some marbles in the ratio 5 : 7. After they both gave away 26 marbles each, the ratio became 1 : 4. Find the number of marbles Jim had at first.

  7. 13 units  26 marbles 15 units  30 marbles Jim had 30 marbles at first. X 3 = 6 15 21 X 2 = 6 2 8 Checking

  8. Unchanged data – no. of adults Drop of 4 units cos 32 chn alighted from the bus X 3 X 3 = 9 = 3 Ratio • The ratio of the number of adults to the number of children in a bus was 9 : 7. After 32 children alighted from the bus, the number of adults left in the bus was 3 times the number of children. How many children were on board the bus at first?

  9. 4 units  32 chn 7 units  56 chn 56 chn were on board at first. Unchanged data – no. of adults Drop of 4 units cos 32 chn alighted from the bus X 3 X 3 = 9 = 3 Checking

  10. spent V C $32 $112 4) Veronica and Clement went shopping with a total of $112. After Veronica spent a quarter of her money and Clement spent $32, the ratio of Veronica’s money to Clement’s money became 1 : 4. What was the ratio of Veronica’s money to Clement’s money at first? 16 units  112 – 32 = 80 4 units  $20 Veronica had $20 at first. $112 - $20 = $92 Clement had $92 at first. Ratio of Veronica’s money to Clement’s money at first was 20 : 92 or 5 : 23.

  11. Share of bill G H Amt left $84 Share of bill 5) Gabriel and Huiling shared the cost of a dinner in the ratio 2 : 3. Gabriel used up half his money to pay for his share. After paying for her share, Huiling had $84 left. The ratio of the amount of money that Gabriel and Huiling brought along for the dinner was 3 : 4. How much was the bill for the dinner? Amt bought along 7 units  $84 15 units  $180 The bill for the dinner was $180.

  12. Percentage 12

  13. 6) Sarah has 20 % more than Ji Wei. When she spent 45 % of her money, she had $68 less than Ji Wei. How much did she have left? Had Ji Wei 100 % Sarah 120 % Sarah spent 45 % of her money = 45% of 120 = 45 x 126 = 54 % 100 Had 120 – 54 = 66% of Ji Wei’s money left 100% – 66% = 34 % 34 %  $68 66 %  $132 She had $132 left.

  14. 80 % 1120 pupils  100 % 1344 pupils  120 % 120 % - 100 % = 20 % The enrolment increased by 20 % compared to the enrolment in 2003. 7) The enrolment of a certain school was 1400 pupils in 2002. In 2003, the enrolment decreased by 20%. If the enrolment in 2004 is 1344, what was the % increase in 2004 compared with the enrolment in 2003? 1120 pupils 1344 pupils

  15. x 7 280 x 7 420 x 6 180 x 6 420 8) In a class, 40 % of the pupils wore spectacles. After 5 pupils who wore spectacles left the class, the percentage of pupils who wore spectacles dropped to 30%. How many pupils in the class did not wear spectacles? 70 %

  16. x 7 280 x 7 420 x 6 180 x 6 420 70 % 100 units  5 pupils 420 units 5/100 x 420 = 21 pupils 21 pupils do not wear spectacles.

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