1. A warm welcome to our… Mathematics Model Drawing Grade 4 Workshop October 10, 2015 1

2. 2 INTRODUCTION Ms. Audrey Pang Presenter Mr. Alexander Ho Co-Facilitator

3. AGENDA 1. About Model Drawing 2. Types of Models 3. Hands On 4. Q & A 3

4. Objectives To equip you with the necessary tools to help your child/children in problem- solving using models To align you with the school’s approach in educating your child/children 4

5. Why Model Drawing? Models help us to organize pieces of information into a system Models provide visual aids that are more concrete Model drawing can often help us to cut short the number of steps Model drawing bridges the gap between the concrete and the abstract (Algebra) 5

6. 6 Do’s of Model Drawing Deal with one piece of information at a time Include all pieces of information in the model (including the question) It’s okay to redraw or rearrange the model If two things are different, make sure the difference is clearly shown in the model For comparison, align the model bars properly

7. Disclaimers There are different ways to draw models Model drawing is not always easy Model drawing is not the only method Model drawing is not the best method all the time There are different ways to represent brackets or braces 7

8. Key Teaching Points Before attempting to solve the word problems, teach your child to think through them by asking them questions Examples: Read the following word problems, do you find any similarity between the questions? What values are given and what is needed to solve the problem? If you were to draw a model, where would you start? 8

9. 9 1.Part-Whole Models for Addition 2.Part-Whole Models for Subtraction 3. Comparison Models (involving More than / Fewer or Less than) 4. Multiplication Models 5. Division Models Different Types of Models

10. 10 1. PART-WHOLE MODELS – Addition ? Pears 40 + 80 = 120 There are 120 fruits in the box. There are 40 apples and 80 pears in a box. How many fruits are there in the box ? 80 Apples 40

11. 11 Georgina has 990 stamps. Her father gives her 112 stamps. How many stamps does she have in total? 990 + 112 = 1102 She has 1102 stamps in total. 990 ? 112 PART-WHOLE MODELS – Let’s try using magnets

12. 12 There are 432 fruits in some baskets. 178 of them are oranges. The rest are bananas. How many bananas are there? 432 – 178 = 254 There are 254 bananas. 178 ? 432 2. PART-WHOLE MODELS – Subtraction BananaOranges

13. 13 There are 362 marbles in a box. 139 of them are blue. The rest are yellow. How many yellow marbles are there? 362 – 139 = 223 There are 223 yellow marbles. 139 ? 362 PART-WHOLE MODELS – Let’s try using magnets

14. For the difference between 2 quantities, write down the difference in whole numbers in the model. boys Example: There are 24 more girls than boys 3. COMPARISON MODELS – More / Less than girls 24 14 Difference

15. 15 Devi has 202 stamps. She has 69 more stamps than Siti. How many stamps did Siti have? 202 – 69 = 133 Devi Siti ? 202 69 COMPARISON MODELS – More / Less than Siti had 133 stamps.

16. 16 James had 168 stickers. He had 87 less stickers than Kenny. How many stickers did Kenny have? 168 + 87 = 255 168 ? James Kenny COMPARISON MODELS - Let’s try with magnets! Kenny had 255 stickers. 87

17. 17 4. MULTIPLICATION MODELS (Basic) Mina has 5 fish tanks. She has 8 goldfish in each fish tank. How many goldfish does she have altogether? 8 x 5 = 40 Mina has 40 goldfish altogether. 8 ?

18. 18 Desmond gave 7 marbles to each of his 6 friends. How many marbles did Desmond give to his friends altogether? 4. MULTIPLICATION MODELS- Let’s try drawing a model. 7 x 6 = 42 He gave 42 marbles altogether. 7 ?

19. 19 A teacher divided 18 colour pencils equally between 3 groups of students. How many colour pencils were there in each group? 5. DIVISION MODELS (Basic) 18 ÷ 3 = 6 Each group had 6 colour pencils. 18 ?

20. 20 Nina used 375 cm of fabric to make 5 similar cushions. How much fabric did she use for each cushion? 5. DIVISION MODELS – Let’s try drawing a model 375 cm 375 ÷ 5 = 75 Nina used 75cm of fabric for each cushion. ?

21. 21 COMPARISON MODELS (Combined) Key words: x times as many as / x times as much as a b e.g. a is four times as many as b

22. 22 1650 pupils took part in a parade. There were twice as many boys as girls. How many boys were there in the parade? COMPARISON MODEL - Example 1 unit Boys Girls ? 1650 3 units 1650 1 unit 1650  3 = 550 2 units 550 x 2 = 1100 There were 1100 boys in the parade. 22

23. 23 645 pupils were at a carnival. There were twice as many girls as boys. How many girls were there at the carnival? COMPARISON - involving multiples – Let’s try! 1 unit Girls Boys ? 645 3 units 645 1 unit 645  3 = 215 2 units 215 x 2 = 430 There were 430 girls at the carnival. 23

24. 24 COMPARISON Multiple Individuals Key words: more/fewer/less than/times e Sum a b d c

25. 25 Ali, Bob and Tom have 48 stamps altogether. Ali has twice as many stamps as Bob. Bob has 4 more stamps than Tom. How many stamps does Bob have? COMPARISON Multiple Individuals- Example 4 units 1 unit Bob has 13 stamps. Ali Bob 48 Tom ? 48 + 4 = 52 52  4 = 13 1 unit 4

26. 26 Alice, Belle and Cindy have a total of 49 stamps altogether. Alice has twice as many stamps as Belinda. Belinda has 7 more stamps than Cindy. How many stamps does Belinda have? COMPARISON Multiple Individuals-Let’s try! 4 units 1 unit Belinda has 14 stamps. Alice Belinda 49 Cindy ? 49 + 7 = 56 56  4 = 14 1 unit 7

27. 27 Numerator Denominator (Number of equal parts the whole is divided into)

28. 28 1If this bar is a whole, draw of this bar. 2 If this bar is of a whole, draw the whole bar.

29. 29 3If this bar represents 1 whole, draw 1 bars. 4 If this bar represents 1 bars, draw 1 bar.

30. 30 After spending of his money on a badminton racket, Andrew had $14 left. How much did the badminton racket cost? Step 1: Look for the WHOLE (usually appears after the word ‘of’). Box it up. Step 2: Check the denominator. It indicates the number of equal parts the WHOLE is to be divided into. Example:

31. 31 After spending of his money on a badminton racket, Andrew had $14 left. How much did the badminton racket cost? Step 3: Draw a bar to represent the WHOLE. Divide it into the required number of equal parts given by the denominator.

32. 32 After spending of his money on a badminton racket, Andrew had $14 left. How much did the badminton racket cost? Step 4: Shade the required number indicated by the numerator.

33. 33 After spending of his money on a badminton racket, Andrew had $14 left. How much did the badminton racket cost? Step 5: Relate known and unknown ? (Spent) $14 (left) Badminton racket 1 unit

34. 34 After spending of his money on a badminton racket, Andrew had $14 left. How much did the badminton racket cost? ? (Spent) $14 (left) Step 6: Solve the problem. It cost $21 Badminton racket 2 units$14 1 unit $14  2 = $7 3 units3 x $7 = $21 1 unit

35. 35 Thank You For Your Attention Kindly complete the Evaluation Form & drop it into the box on your way out. Thank you for your valuable feedback

36. 36

37. 37 Practice 1 Esther baked 145 butter cookies and 157 chocolate cookies. How many cookies did she bake altogether? Draw a model and label it correctly. Solve the problem.

38. 38 ? 145 157 butter chocolate 145 + 157 = 302 Esther baked 302 cookies altogether. Practice 1 - Answer

39. 39 Practice 2 Jason had 350 stickers. He gave his sister 205 stickers. How many stickers did he have left? Draw a model and label it correctly. Solve the problem. 39

40. 40 350 - 205 = 145 Jason had 145 stickers left. 350 Left Gave away ? 205 Practice 2 - Answer

41. 41 A coat costs $152. A dress costs $200. How much more does the dress cost than the coat? Draw a model and label it correctly. Solve the problem. Practice 3 41

42. 42 $200 - $152 = $48 The dress costs $48 more than the coat. Practice 3 - Answer $152 Coat ? Dress $200

43. 43 There are 7 children at a party. Each child is holding 4 balloons. How many balloons are there altogether? Draw a model and label it correctly. Solve the problem. Practice 4

44. 44 7 x 4 = 28 There are 28 balloons altogether. Practice 4 - Answer ? 4

45. 45 Lily and her 2 friends shared 24 apples equally. How many apples did each of them get? Draw a model and label it correctly. Solve the problem. Practice 5

46. 24 ? 24 ÷ 3 = 8 Each of them got 8 apples. Practice 5 - Answer 46

47. 47 A baker baked 130 strawberry cakes. He baked 23 more mango cakes than strawberry cakes. (1) How many mango cakes did he bake? (2) How many cakes did he bake altogether? Practice 6 (2-Part Word Problem)

48. 48 130 Strawberry 130 + 23 = 153 He baked 153 mango cakes. Practice 6 – Part 1 Answer (1)? 23 Mango

49. 49 130 (2)? 153 130 + 153 = 283 He baked 283 cakes altogether. Practice 6 – Part 2 Answer

50. 50 A fruit seller sold 937 apples on Saturday and Sunday. If he sold 387 of them on Saturday, how many apples did he sell on Sunday? Practice 7

51. 51 937 – 387 = 550 The fruit seller sold 550 apples on Sunday. 937 SaturdaySunday ? 387 Practice 7 - Answer

52. There are 450 balls in container A. There are 27 more balls in container B. How many balls are there in container B? 52 Practice 8

53. 53 450 +27 = 477 There are 477 balls in container B. Container A 450 Container B 27 ? Practice 8 - Answer

54. 54 Jasmine has $35. She has $7 less than Peter. How much do they have altogether ? Practice 9 (2-Step Word Problem)

55. 55 Step 1: $35 + $7 = $42 Step 2: $35 + $42 = $77 They have $77 altogether. Step 1 (?) $7 Peter Step 2 (?) Jasmine $35 Practice 9 - Answer

56. 56 Mr. Lin earns $1230. He earns 3 times as much as Mr. Wang. How much does Mr. Wang earn? Practice 10

57. 57 Mr. Lin earns $1230. He earns 3 times as much as Mr. Wang. How much does Mr. Wang earn? 3 units ------ $1230 1 unit ------- $1230  $410 Mr Wang earns $410. $1230 1 unit ? Mr Lin Mr Wang Practice 10 - Answer

58. 58 Online Resource: www.mathplayground.com/thinkingblocks.html