1. Guest Presenters: Susan Gebhart and Julie Dill

2. Model drawing is a strategy first used in Singapore to solve word problems. Bar models or tape diagrams, as they are sometimes called, are visual models or graphic organizers of the information that is in the word problem. Model drawing involves “translating” the words in the problem to a visual model. Model drawing is a good match for many of the Math Practices described in CCSS (Common Core State Standards) and can be used by students from grade 1 through algebra.

3. Model drawing makes a strong connection to algebra. In model drawing the rectangular bars represent the relationship between quantities in the problem. The question mark indicates the unknown. In algebra these same unknowns would be represented with a variable like “x”. Students are engaged in algebraic thinking even before they are ready to handle formal algebra.

4. What Is Model Drawing? Jim has 2 Lego sets and Lin has 5 Lego sets. How many sets do they have altogether? Jim’s Lego sets Lin’s Lego sets 2 + 5 = 7 Jim and Lin have 7 Lego sets altogether. 2 ? 5

5. Betty, Jill, and Chris shared $78.75. Betty had 1/2 as much money as Jill, and Chris had 4 times as much money as Betty. How much money did Jill have? Give It a Try

6. An Example of Model Drawing Here’s the model… what’s the problem?

7. Progression of Solving Word Problems 7 4 3 Concrete Objects Picture Number Bond Number Statement Story (oral or written) There were two trees. One had 3 apples and the other had 4 apples.

8. Shanice has _____ cards now. ? Monday’s Cards Tuesday’s Cards 5 3 53 ? Monday’s Cards Tuesday’s Cards 3 5 ? Part-Whole Shanice got 5 cards on Monday and 3 cards on Tuesday. How many cards does Shanice have now?

9. 80% of word problems for grades 1-6 can be solved using bar models! You still need to teach your students other heuristics so after they read a problem they are equipped with the skills to choose which strategy would be most efficient for solving that particular word problem.

10. 1.Read the problem. 2.Rewrite the question in the problem as a complete sentence leaving space for the answer. 3.Identify the “who” and the “what.” 4.Draw a unit bar to model each variable. 5.Chunk the problem and adjust your unit bars to match your information. Fill in your question mark. 6.Work your computation. 7.Write the answer in your sentence. Step-by-Step Model Drawing Method

13. Give students “Attack Time”. They need to read the problem, think to themselves, and talk or think about where they will begin.

14. Part – Whole James got 158 cards on Monday and 331 cards on Tuesday. How many cards does James have now? 1

15. James got 158 cards on Monday and 331 cards on Tuesday. How many cards does James have now? James has _______ cards now. ? 158 331 Monday’s cards Tuesday’s cards

16. James got 158 cards on Monday and 331 cards on Tuesday. How many cards does James have now? James has _______ cards now. ? 331158 489 331 158 ? Monday’s cards Tuesday’s cards

17. Part – Whole Giles read 24 books in the first part of the year. If he read 59 books in the entire school year, how many books did he read in the second part of the year? 2

18. Giles read 24 books in the first part of the year. If he read 59 books in the entire school year, how many books did he read in the second part of the year? 24 ? 59 ? 24 59 first part second part A.59 – 24 = 35 P. 35 + 24 = 59 Giles read 35 books in the second part of the year.

19. Part – Whole Calvin had $575 in his savings account. He bought a bow for $125 and a package of arrows for $90. How much money did he have left in his savings account? 3

20. Calvin had $575 in his savings account. He bought a bow for $125 and a package of arrows for $90. How much money did he have left in his savings account? 575 ? 90 575 bow A.$125 + $90 = $215 $575 – $215 = $360 P. $125 + $90 + $360 = $575 Calvin had $360 left in his savings account. 125 ?90 125 arrows savings

21. Part – Whole Deidra was in a 72-mile bike race over the course of 3 days. How many miles would she need to ride the third day to finish the 72-mile bike race if she rode 23 miles the first day and 29 miles the second day? 4

22. Deidra was in a 72-mile bike race over the course of 3 days. How many miles would she need to ride the third day to finish the 72-mile bike race if she rode 23 miles the first day and 29 miles the second day? ? 29 72 miles A.23 + 29 = 52 72 – 52 = 20 P. 23 + 29 + 20 = 72 Deidra will need to ride 20 miles on the third day. 23 29 ? 72 first day second day

23. Part – Whole Jim had 901 baseball cards. He gave 283 to Sue and then bought 155 new cards. How many cards did Jim end up with? 5

24. Jim had 901 baseball cards. He gave 283 to Sue and then bought 155 new cards. How many cards did Jim end up with? baseball cards A.901 + 155 = 1,056 1,056 – 283 = 773 P.901 + 155 = 1,056 1,056 – 283 = 773 Jim ended up with 773 cards. 901 29283 155 to Sue new cards ?

25. Part – Whole Oliver decorated 70 cupcakes for dessert. 45 cupcakes were eaten. How many cupcakes were left? 7

26. Oliver decorated 70 cupcakes for dessert. 45 cupcakes were eaten. How many cupcakes were left? ? 45 70 cupcakes A.70 – 45 = 25 P. 25 + 45 = 70 There were 25 cupcakes left. 45 ? 70 eaten

27. Carl has ____ candies. He ate ____ candies. How many candies does he have left? Differentiating (10, 8) (25, 17) (6, ) 2323 ? # #

28. Additive Comparison Sharon had 5 stuffed animals. Lola had 3 more stuffed animals than Sharon. The girls put their animals in one basket. How many animals are in the basket? 8

29. Sharon had 5 stuffed animals. Lola had 3 more stuffed animals than Sharon. The girls put their animals in one basket. How many animals are in the basket? 5 8 ? Sharon’s animals A.5 + 5 + 3 = 13 P. 13 – 10 = 3 There are 13 animals in the basket. 5 Lola’s animals 5 3 ?

30. Additive Comparison Josh and Aaron went to collect golf balls. Together they found 11 golf balls. Josh found 3 more balls than Aaron. How many golf balls did Aaron find? 9

31. Josh and Aaron went to collect golf balls. Together they found 11 golf balls. Josh found 3 more balls than Aaron. How many golf balls did Aaron find? ? + 3 ? 11 Aaron’s golf balls A.11- 3 = 8 8 ÷ 2 = 4 P. 4 + 4 + 3 = 11 Aaron found 4 golf balls. ? Josh’s golf balls ? 3 11

32. Additive Comparison Justin has 18 fewer swimming ribbons than Nathan. Altogether, they have 110 swimming ribbons. How many swimming ribbons does Justin have? 10

33. Justin has 18 fewer swimming ribbons than Nathan. Altogether, they have 110 swimming ribbons. How many swimming ribbons does Justin have? 18 + ? ? 110 Justin’s ribbons A.110 – 18 = 92 92 ÷ 2 = 46 P.46 + 18 = 64 64 + 46 = 110 Justin has 46 swimming ribbons. 46 Nathan’s ribbons ? 110 18

34. Additive Comparison The third grade class raised $350 for their field trip. The girls raised $30 more than the boys. How much did the girls raise for the field trip? 11

35. The third grade class raised $350 for their field trip. The girls raised $30 more than the boys. How much did the girls raise for the field trip? 30 + ? ? 350 Girl’s $ raised A.$350 - $30 = $320 $320 ÷ 2 = $160 $160 + $30 = $190 P.$160 + $160 + $30 = $350 The girls raised $190 for the field trip. 46 Boy’s $ raised $350 30 ?

36. Additive Comparison Ryan and Sharie had the same amount of money. Ryan lost $10 while his friend Sharie collected another $25. How much more money does Sharie have than Ryan? 12

37. Ryan and Sharie had the same amount of money. Ryan lost $10 while his friend Sharie collected another $25. How much more money does Sharie have than Ryan. Ryan’s $ A.$10 + $25 = $35 Sharie has $35 more than Ryan. 46 Sharie’s $ 10 ? 25

38. Additive Comparison Blaine is 8 years older than Jade and 2 years younger than Ramel. The total of their ages is 63 years. How old is Ramel? 13

39. Blaine is 8 years older than Jade and 2 years younger than Ramel. The total of their ages is 63 years. How old is Ramel? ? + 8 + 2 ? 63 Blaine’s age A.8 + 8 + 2 = 18 63 – 18 = 45 3u = 45 u = 15 15 + 8 + 2 = 25 P. $125 + $90 + $360 = $575 Ramel is 25 years old. ? + 8 8 Ramel’s age Jade’s age 82 ? 63

40. Multiplication Ling put 3 photos on each page of her album. If there were 6 pages, how many photos did Ling put in her album? 14

41. Ling put 3 photos on each page of her album. If there were 6 pages, how many photos did Ling put in her album? Ling’s photos A.6 x 3 = 18 P. 3 + 3 + 3 + 3 + 3 + 3 = 18 Ling put 18 photos in her album. 3 ? 3 3 3 3 3

42. Multiplication Luis ran 2 miles each day during the month of September. How many total miles did Luis run in September? 15

43. Luis ran 2 miles each day during the month of September. How many total miles did Luis run in September? miles run A.30 x 2 = 60 P. 30 + 30 = 60 Luis ran 60 miles in September. 2 X 30 2 ? Do you really want your students to write “2” thirty times? Is that working efficiently????

44. Division Devi saved $40 in 5 weeks. She saved the same amount each week. How much did Devi save each week? 16

45. Devi saved $40 in 5 weeks. She saved the same amount each week. How much did Devi save each week? money saved each week A.$40 ÷ 5 = $8 P. $8 x 5 = $40 Devi saved $8 each week. 40 ? week 1 week 2 week 5 week 4 week 3

46. Multiplicative Comparisons Deana had 3 times as many books as Hilary. If they had 16 books altogether, how many books did Deana have? 17

47. Deana had 3 times as many books as Hilary. If they had 16 books altogether, how many books did Deana have? books A.16 ÷ 4 = 4 3 x 4 = 12 P. 4 + 4 + 4 = 12 Deanna had 12 books. 46 Deanna’s Hillary’s ? 16 ?

48. Multiplicative Comparisons Wyatt had 4 times as many stamps in his collection as Shannon. If they had 45 stamps altogether, how many more stamps did Wyatt have than Shannon? 18

49. Wyatt had 4 times as many stamps in his collection as Shannon did. If they had 45 stamps altogether, how many more stamps did Wyatt have than Shannon? Wyatt’s stamps A.45 ÷ 5 = 9 9 x 3 = 27 P.5 x 9 = 45 3 x 9 = 27 Wyatt had 27 more stamps than Shannon. 46 Shannon’s stamps 45 ?

50. Choose one of the models and write a problem to go with it.

51.  Reads the problem.______ (1)  Rewrites the question in the problem as a complete sentence, leaving space for the answer.______ (1)  Identifies the “Who” and the “What.”______ (1)  Draws a unit bar for each variable.______ (1)  Chunks the problem and adjusts the unit bars to match the information. Fills in the question mark.______ (3)  Computes and solves problem correctly. ______ (2)  Writes the answer in the sentence.______ (1) Total ______ (10) Scoring Model Drawing

55. Multiplication Bar Modeling Solve Length Word Problems Using a Bar Model Solve Comparison Problems Using Bar Models Interpret Division as an Unknown Factor Problem Using a Bar Model

56. Online and now also an app!

57. Singapore Math Bar Models App from Houghton Mifflin Harcourt

58. Evaluations Enjoy your lunch!