Primary 3/4 Mathematics Workshop For Parents

1. Primary 3/4 Mathematics WorkshopFor Parents 14 April 2012 Endeavour Primary School Mathematics Department 2012

2. Workshop Outline • Introduction to Problem-Solving • Model Method • 3 Different types of Models • 4 different Heuristics • Format of assessment

3. Problem-solving Approach • Understand the Problem (Understand) • Devise a Plan (Plan) • Carry out the Plan (Do) • Review and discuss the solution (Check)

4. Problem-solving Approach • Understand the Problem (Understand) • Read to understand. • If at first not clear, read again. • Still don’t get it? Read chunk by chunk. • Explain the question in another way. • Use visualisation tool – model, timeline, diagrams, table etc.

5. Problem-solving Approach • Devise a Plan (Plan) • Have I seen a similar or related question before? • Do I have a ready plan? • Do I have all the data? What data is missing? • Can I find the missing data? • Can I use a smaller number to try first? • Use a heuristics?

6. Problem-solving Approach • Carry out the Plan (Do) • Are all my steps accurate? • Are there traps I need to be alert of? • Have I used all the data given? • Do my steps make sense?

7. Problem-solving Approach • Review and discuss the solution (Check) • Does the answer make sense? • Did I answer the question? • Could this problem be solved in a simpler way?

8. Model Method Draw a diagram

9. Why Model Drawing? • Visual representation of details • Majority of our children are visual learners • Helps children plan the solution steps for solving the problem • Useful in fractions, ratio & percentage

10. WhyModel Drawing? • Teaches mathematical language • Provides foundation for algebraic understanding • Empowers students to think systematically and master more challenging problems

11. Model Drawing does NOT • Work in every problem • Specify ONE RIGHT model • Specify ONE RIGHT operation

12. Concrete-Pictorial-Abstract Approach Concrete – Manipulatives: Base-Ten Blocks Pictorial - Models: 100 30 ? Abstract – Symbols: 100 – 30 = 70

13. Concrete-Pictorial-Abstract Approach 4 + 2 = 6

14. Types of Models • Part-whole model a) Whole Numbers b) Fractions 2. Comparison Model a) Comparing 2 items b) Comparing 3 items c) Other Comparison Models • Before-After Model a) Total unchanged b) Total changed

15. 1. Part-whole Model Find value of unknown part Find value of whole

16. Part-whole Model: Whole Numbers Calvin earns $2000 every month. He pays $300 for food. He also spends $200 on his car, $500 on housing and saves the rest. How much does he save every month? Calvin earns $2000 every month. He pays $300 for food. He also spends $200 on his car, $500 on housing and saves the rest. How much does he save every month?

17. $2000 $300 $200 $500 ? food savings car housing Part-whole Model: Whole Numbers Calvinearns $2000 every month. He pays $300 for food.Healsospends $200 on his car,$500 on housingandsaves the rest.. How much does he saveevery month?

18. $2000 $300 $200 $500 ? food car housing saving Used $300 + $200 + $500 = $1000 Savings $2000 - $1000 = $1000 He saves $1000 every month.

19. How can we check if $1000 is a reasonable answer? What is another way to solve this problem?

20. Part-whole Model: Whole Numbers Qi Ying bought some sweets. She ate half of them and gave 5 sweets to Joy. She had 7 sweets left. How many sweets did Qi Ying buy?

21. Ate 5 (Joy) 7 (Left) 1 unit (half) 1 unit (half) Part-whole Model: Whole Numbers Qi Ying bought some sweets. She ate halfof them and gave 5 sweetsto Joy. She had7 sweets left.How many sweets did Qi Ying buy? ?

22. Ate 5 (Joy) 7 (Left) 1 unit 1 unit Part-whole Model: Whole Numbers ? 1 unit 5 + 7 = 12 2 units 2 × 12 = 24 Qi Ying bought 24 sweets.

23. How can we check if ‘24 sweets’ is a reasonable answer? What is another way of representing this problem? ÷ 2 ? 5 + 7 × 2

24. Part-whole Model: Fractions

25. ? girls 24 boys Part-whole Model: Fractions 24 2 units 24 ÷ 2 1 unit = 12 There are 12 girls.

26. How can we check if the answer is reasonable?

27. Part-whole Model: Fractions ¼ of the fish in an aquarium are goldfish. There are 4 more guppies than goldfish in the aquarium. The remaining 16 fish are carps. How many fish are there in the aquarium?

28. ? goldfish Part-whole Model: Fractions ¼ of the fishin an aquarium are goldfish.There are 4 more guppies than goldfish in the aquarium. The remaining 16fish are carps. How many fishare there in the aquarium? 2 units 4 + 16 = 20 ¼ ¼ ¼ ¼ 4 4 units 2 × 20 guppies = 40 16 carps There are 40 fish.

29. How can we check if the answer is reasonable?

30. 2. Comparison Model Find total sum given between difference and value of an item Find value of an item given difference and sum

31. Comparison Model: 2 items Sven collected 3426 stamps. He collected 841 fewer stamps than Jerome. How many stamps did they collect?

32. ? Comparison Model: 2 items Svencollected3426 stamps. He collected 841 fewer stampsthanJerome. How many stampsdidtheycollect? Who has more? Sven 3426 Whose bar should be longer? fewer Jerome 841 ?

33. ? Sven 3426 fewer Jerome 841 ? Jerome 3426 + 841 = 4267 Total 3426 + 4267 = 7693 They collected 7693 stamps.

34. How can we check if ‘7693 stamps’ is a reasonable answer? What is another way to solve this problem?

35. Comparison Model: 2 items

36. Comparison Model: 2 items ? Smaller Larger ¼

37. ? Smaller Larger ¼ 2 units 1 unit

38. How can we check if the answer is reasonable?

39. Comparison Model: 3 items Kyle, Siti and Alice have a total of 290 stickers. Kyle has twice as many stickers as Siti. Alice has 50 stickers more than Siti. How many stickers does Alice have?

40. Comparison Model: 3 items Kyle, Siti and Alice have a total of 290 stickers. Kyle has twiceas manystickers asSiti. Alicehas 50 stickersmorethanSiti. How many stickersdoes Alicehave? Kyle 290 Siti Alice 50 Note how ‘50’ is represented.

41. Kyle 290 Siti Alice 50 4 units 290 – 50 = 240 1 unit Alice 240 ÷ 4 60 + 50 = 60 = 110 Let Siti have x stickers. Kyle 2x Alice x + 50 4x + 50 = 290 4x = 240 x = 60 60 + 50 = 110 Alice has 110 stickers.

42. Comparison Model: 3 items Kyle, Siti and Alice have a total of 270 stickers. Kyle has thrice as many stickers as Siti. Alice has half as many stickers as Siti. How many stickers does Siti have?

43. Comparison Model: 3 items Kyle, Siti and Alicehaveatotal of 270stickers. Kyle hasthrice as manystickersas Siti. Alicehashalf as manystickersas Siti. How many stickersdoesSitihave? Kyle Siti 270 Alice

44. 9 units 270 Kyle Siti Alice 270 270 ÷ 9 1 unit = 30 2 units 30 x 2 = 60 Siti has 60 stickers.

45. How can we check if the answer is reasonable?

46. Other Comparison Models 2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file.

47. Other Comparison Models 2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file. Files Pens

48. Other Comparison Models 2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file. Files $18 ? Pens

49. 2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file. Files $18 ? Pens 9 units $18 = $2 1 unit $18 ÷ 9 3 units $2 x 3 = $6 1 file costs $6.

50. Other Comparison Models 2 crystal vases and 3 plates cost $161. The cost of 1 plate is half the cost of 1 vase. What is the cost of 1 vase?