1. River Valley Primary School – Strive for the Best 12 August 2011

2. River Valley Primary School – Strive for the Best 5.45 – 6.00 – Registration 6.15 – 6.30 – Overview of our Primary Mathematics Curriculum 6.30 – 7.00 Heuristic 1 7.00 – 7.30 Dinner 7.30 - 9.15 Heuristic 2 9.15 – 9.30 Q n A Programme

3. River Valley Primary School – Strive for the Best   To familiarise parents with the more challenging heuristics from “Conquer Math”.   To partner with parents so that they can help their children with the approaches the school uses to each problem solving. Objectives

4. River Valley Primary School – Strive for the Best Mathematics Curriculum 1.Concepts Basic mathematical knowledge needed for solving mathematical problems. - Numerical concepts - Geometrical concepts - Algebraic concepts - Statistical concepts

5. River Valley Primary School – Strive for the Best Mathematics Curriculum 2. Skills Topic-related manipulative skills that pupils are expected to perform when solving problems. - Estimation & approximation - Mental calculation - communication - use of mathematical tools - arithmetic & algebraic manipulation - handling data - use of calculator

6. River Valley Primary School – Strive for the Best Mathematics Curriculum 2. Processes The knowledge skills ( process skills) involved in the process of acquiring and applying mathematical knowledge : - reasoning - communication and connection - thinking skills and heuristics - application and modelling

7. River Valley Primary School – Strive for the Best To give a representation - draw a diagram (eg. model), make a list, use equation To make a calculated guess - guess and check, look for patterns, make supposition To go through the process - act it out, work backwards, before-after To change the problem - restate the problem, simplify the problem, solve part of the problem Problem Solving Heuristics

8. River Valley Primary School – Strive for the Best Working Backwards Sharon had some sweets at first. After she gave away 5 sweets to her sister and ate another 3 sweets, she went to buy another 48 sweets. In the end she had thrice as many sweets as before. How many sweets did she have at first ? (P3 - pg 20) At First End 1 unit Extra Extra 48 – 3 – 5 = 40 2 units 40 1 unit 40 ÷2 = 20 (She had 20 sweets at first.) ?

9. River Valley Primary School – Strive for the Best Equal Concept Model (Internal Transfer) Dinesh Melissa 1 u 2 u -$36 +$36 1 u $36 + $36 = $72 Amt. of money each received at first $72 +$36 = $108 Dinesh and Melissa shared a sum of money equally. After Dinesh gave $36 to Melissa, Melissa had twice as much money as Dinesh. How much money did each of them receive at first ? (P3 – pg 15)

10. River Valley Primary School – Strive for the Best Equal Stage There was an equal number of boys and girls at a gathering at first. After 60 boys and 12 girls had left the gathering, there were twice as many girls as boys that remained behind. Find the number of boys at first ? (P4 – pg 30) Boys 1u 60 Girls 1u 12 Left left 1u = 60 – 12 = 48 48 + 60 = 108 There were 108 boys

11. River Valley Primary School – Strive for the Best Equal Stage Type 1 (Beginning) Boys Girls 1 unit  60 – 12 = 48 48 + 60 = 108 60 12 P4-page 30

12. River Valley Primary School – Strive for the Best Equal Stage Raymond and Rauf had a total of 224 marbles at first. After Raymond had bought another 12 marbles and Rauf had given away 30 of his marbles, both had the same number of marbles left. How many marbles did Raymond have at first ? (P4 – pg 34)

13. River Valley Primary School – Strive for the Best Equal Stage Type 2 (End) Ray Rauf 224 – 30 = 194 194 – 12 = 182 182 ÷ 2 = 91 12 30 224 P4-page 34

14. River Valley Primary School – Strive for the Best Equal Stage There was an equal number of boys and girls at an exhibition. After of the boys and 42 girls had left the exhibition, there were 12 more boys than girls at the exhibition. How many students were there at the exhibition at first ? (P4 – pg 96)

15. River Valley Primary School – Strive for the Best Equal Stage - Fraction (Type 1) Boys Girls 3u  42 – 12 = 30 1u  30 ÷ 3 = 10 10u  10 x 10 = 100 12 42 P4-pge 96

16. River Valley Primary School – Strive for the Best Equal Stage There is a total of 620 apples and oranges at a stall. of the oranges is equal to of the apples. How many apples are there at the stall ? (P4 – pg 105)

17. River Valley Primary School – Strive for the Best Equal Stage - Fraction (Type 3) Oranges Apples Oranges  16u Apples  15u Total  31u  620 1u  620 ÷ 31 = 20 15u  20 x 15 = 300 P4- Page 105

18. River Valley Primary School – Strive for the Best Equal Stage – Fractions (Type 3) Unitary Method: 3 2 8 5 6 16 15 Oranges  16u Apples  15u Total  31u  620 1u  620 ÷ 31 = 20 15u  20 x 15 = 300

19. River Valley Primary School – Strive for the Best Equal Stage At the graduation ceremony, there were 30 less boys than girls. After of the boys and of the girls had left the hall for recess, there was an equal number of boy and girls that remained behind. Find the number of boys who were present at the graduation ceremony (P4 – pg 106)

20. River Valley Primary School – Strive for the Best Equal Stage – Fractions (Type 3) Unitary Method: 2 3 5 8 6 15 16 Boys  15u Girls  16u Difference  16u – 15u = 1u 1u  30 15u  30 x 15 = 450 P4- Page 106

21. River Valley Primary School – Strive for the Best Internal Transfer Two classes,3A and 3B, had an equal number of pupils. After 12 pupils left class 3A to join class 3B, there were twice as many pupils in class 3B as in class 3A. Find the number of pupils in each class at first ? (P3 – pg 23) 3A 1u 12 3B 1u 1u = 24 24 + 12 = 36 There were 36 pupils in each class

22. River Valley Primary School – Strive for the Best Internal Transfer Esther has 86 more stickers than Jane. How many stickers must Esther give to Jane so that Esther will have 40 more stickers than Jane ? (P3 – pg 26) Esther 86 Jane Esther 40 86 - 40 = 46 462 =23 She gives 23 stickers

23. River Valley Primary School – Strive for the Best Equal Stage (Internal Transfer) David had 5 times as many marbles as Serene. After David had given 32 of his marbles to Serene, they had an equal number of marbles in the end. Find the number of marbles each of them had at first. (P4 – pg 38)

24. River Valley Primary School – Strive for the Best Equal Stage Type 3 (Internal Transfer) David Serene 4u  32 + 32 = 64 1u  64 ÷ 4 = 16 Serene: 16 David: 16 x 5 = 80 32 5u 4u P4- Page 38

25. River Valley Primary School – Strive for the Best Linear Formation Trees were planted along each side of a square garden so that an equal number of trees are formed along each side of the garden. If there were 60 trees planted, how many trees were there along each side of the garden ? 60 ÷ 4 = 15 (because of 4 sides)..Nope.. Let’s pick a smaller number - 12. So 12 ÷ 4 = 3 trees per side. Right? WRONG! As you can see, when sets of 3 were put along the sides, some trees be part of ANOTHER side. It is 3 + 1 = 4 trees on each side of the garden. So, it is 15 + 1 = 16 trees on each side of the garden.

26. River Valley Primary School – Strive for the Best Linear Formation Trees were planted along each side of a square garden so that an equal number of trees are formed along each side of the garden. If there were 60 trees planted, how many trees were there along each side of the garden ? Since the 4 corners are repeated, we take 60 – 4 = 56 Then 56 divided equally by 4 sides = 14 per side 14 + 2 ( 2 corners ) and we get 16 trees per side.

27. River Valley Primary School – Strive for the Best Internal Transfer There are 25 more passengers on Bus A than Bus B. If 7 passengers transferred from Bus A to Bus B, how many more passengers will there be in Bus A than in Bus B ? (P3 – pg 25) ABAB 25 7 7 25 – 7 – 7 = 11 There will be 11 more passengers in Bus A

28. River Valley Primary School – Strive for the Best Regular Gaps Fig 1 Fig 2 Fig 3 4 dots 7 dots 10 dots Fig 1 – 4 dots Fig 2 – 4 + 3 Fig 3 – 4 + 3 + 3 Fig 5 – 4 + 3 + 3 + 3 + 3 = 16 Fig 20 – 4 + 19 x 3 = 61 109 dots -- 109 – 4 = 105 105 3 = 35 35 + 1 = 36 figure (P3 – pg 37)

29. River Valley Primary School – Strive for the Best Equal Distribution without Remainder Mrs Singh has a certain number of sweets to distribute to her class. If she gives each of them 5 sweets, she will have 54 extra sweets. If she gives each of them 8 sweets, she would need another 33 more. How many pupils does she have in her class? (P3 – pg 45) 555554 extra 5555 333 33 needed Sets of 5 is the same (number of students fixed) 54 + 33 = 87 sweets needed to form extra sets of 3s. Hence, 87 ÷ 3 = 29 pupils in her class. 54 extra

30. River Valley Primary School – Strive for the Best More than / Less than (External Unchanged) Joshua had 45 more stickers than Melvin at first. After Melvin had used up 15 of his stickers, Joshua had thrice as many stickers as Melvin in the end. Find the number of stickers Joshua had at first. (P4 – pg 21)

31. River Valley Primary School – Strive for the Best More / Less than (External Unchanged) Joshua Melvin 2u  15 + 45 = 60 1u  60 ÷ 2 = 30 3u  30 x 3 = 90 45 15 2u P4 – Page 21

32. River Valley Primary School – Strive for the Best More than / Less than (External Unchanged) There were thrice as many swimmers as non- swimmers at a swimming carnival. After 40 non-swimmers had left the carnival,there were 5 times as many swimmers as non-swimmers at the carnival. How many swimmers were there at the carnival ? (P4 – pg 24)

33. River Valley Primary School – Strive for the Best More/ Less than (External Unchanged) Swim Non-swim 2u  40 x 3 = 120 1u  120 ÷ 2 = 60 5u  60 x 5 = 300 5u 40 1u P4 – Page 24

34. River Valley Primary School – Strive for the Best Internal Transfer Ryan and Aaron had 156 bottle caps. After Ryan gave 40 bottle caps to Aaron, Ryan had twice as many bottle caps as Aaron. How many bottle caps did Ryan at first ? (P3 – pg 69) Ryan Aaron 40 40 40 156 3u = 156 – 120 = 36 1u = 12 24 + 120 = 144

35. River Valley Primary School – Strive for the Best External Change Concept Mrs Tan and Mrs Lim had an equal number of pies at first. After Mrs Tan bought another 12 pies and Mrs Lim gave away 4 pies, Mrs Tan had twice as many pies as Mrs Lim. How many pies did each of them have at first ? (P3 – pg 77) Mrs Tan Mrs Lim At first 12 4 : from equal amount, decrease by 4 (gave away) bought 12 + 4 = 16 ---- forms 1 unit Each of them had ---16 + 4 = 20 pies at first.

36. River Valley Primary School – Strive for the Best External Unchanged There were as many men as women at a concert. Halfway during the concert, some of the men left the concert and the number of men became of the number of women. Given that there were 80 more women than men at first, find the number of men who left the concert halfway ? (P4 – pg 110) Men women 5u = 80 1u = 16 3u = 48 48 men left the concert left

37. River Valley Primary School – Strive for the Best External Unchanged During a class gathering were boys and the rest were girls. Halfway, 22 more girls joined in the gathering and there were as many boys as girls. Find the number of students at the class gathering in the end. (P4 – pg 113) Boys Girls + 22 3u 3u 3u 3u 3u 3u 3u 4u 4u 4u 4u 4u 4u 4u 4u 20u – 9u = 11u 11u = 22 1u = 2 32u = 64 There are 64 students in the end.

38. River Valley Primary School – Strive for the Best External Unchanged Johnson had as many red marbles as blue marbles. If he bought another 12 red marbles, he would be left with as many red marbles as blue marbles. How many marbles did he have altogether ? (P4 – pg 114) Red Blue + 12 5u 5u 5u 3u 3u 3u 3u 3u 6u 5u 1u = 12 20u = 240 He had 240 marbles.

39. River Valley Primary School – Strive for the Best Repeated Identity The mass of a container with 7 glasses is 2 500 g The same container with 3 glasses is 1 500g. What is the mass of the container ? (P3 – pg 101) (Container+7 glasses) – (Container+3 glasses) = (No container + 4 glasses) 2 500 – 1 500 = 1 000 1 000 ÷ 4 = 250  1 glass 250 x 3 = 750  3 glasses 1 500 – 750 = 750  container

40. River Valley Primary School – Strive for the Best Repeated Identity The mass of a container with 7 glasses is 2 500 g The same container with 3 glasses is 1 500g. What is the mass of the container ? (P3 – pg 101) 4u = 2500 – 1500 = 1000 1 u = 250 3 u = 750 OR 7u = 1750 1500 – 750 = 750 (g) 2500 – 1750 = 750 (g) 2 500 1500

41. River Valley Primary School – Strive for the Best Repeated Identity Serene had as many chocolates as Melvin. Melvin had as many chocolates as Esther. If Esther had 38 more chocolates than Serene, find the total number of chocolates that was shared among these 3 children at first. (P4 – pg 117) Serene Melvin Esther 4u 4u 4u 4u 4u 4u 4u 4u 4u 7u 7u 7u 7u 35u 35 – 16 = 19 19u = 38 1u = 2 79u = 158 There are 158 chocolates.

42. River Valley Primary School – Strive for the Best Repeated Identity Inside a bag, there were twice as many red balloons as blue balloons and 15 more blue balloons than green balloons. If there was a total of 141 balloons of these colours, how many green balloons were there in the bag at first ? (P4 – pg 56) Red Blue Green 15 4u = 141 – (3 x 15 ) = 96 1u = 24 There were 24 green balloons.

43. River Valley Primary School – Strive for the Best Internal Transfer (No change in total) Ryan and Aaron had 156 bottle caps. After Ryan gave 40 bottle caps to Aaron, Ryan had twice as many bottle caps as Aaron. How many bottle caps did Ryan at first ? (P3 – pg 69) Ryan Aaron 156 3 units 156 1 unit 156 ÷3 = 52 No. of bottle caps Ryan had at first 52 x 2 + 40 = 144 40 ?

44. River Valley Primary School – Strive for the Best Repeated Identity There are 180 blue and green balls in bag A. There are 320 green and red balls in bag B. Given that there are thrice as many red balls as blue balls, and the number of green balls in both bags is the same, find the total number of green balls in both bags ? (P4 – pg 59) ABAB Green blue 180 320 Red 2u = 320 -140 = 140 1u = 70 180 – 70 = 110 110 x 2 = 220 There were 220 green balls.

45. River Valley Primary School – Strive for the Best Repeated Identity Serene and Tommy have a total of 130 sweets. Tommy and Clara have a total of 141 sweets. Serene and Clara have a total of 99 sweets. How many sweets does Serene have ? (P4 – pg 60) S + T = 130 T + C = 141 S + C = 99 S + T + C = (130 + 141 + 99) = 185 2 185 – 141 = 44

46. River Valley Primary School – Strive for the Best Fraction (Part-Whole Relationship) At a swimming event, of the students were boys. Given that of the girls and of the boys did not know how to swim, how many students were there altogether if there were 154 swimmers at the event ? (P4 – pg 88) 5u 5u Boys girls 2u 3u 6u 9u 11 u = 54 1u = 14 20u = 280

47. River Valley Primary School – Strive for the Best Parents’ Help with Child At Home Talk to your children about mathematics and help them to see the usefulness of math in our daily life. Be observant to improve their visualisation. Real life application of measurements Math in real life

48. River Valley Primary School – Strive for the Best Reference Conquer Problem Sums (Primary 3 and Primary 4 ) -Published by onSponge Pte Ltd -Mathematics Syllabus Primary 2007

49. River Valley Primary School – Strive for the Best Kathleen_lee_mui_hwa@moe.edu.sg

50. River Valley Primary School – Strive for the Best