1. Making Sense of math with tape diagrams
Marisa Aoki

2. Goals Address what makes word problems difficult for students
Experience strategies that support student engagement and understanding during word problems
Explore tape diagrams as a sense-making and problem solving tool
Discuss ways to help students connect ideas across various topics in mathematics

3. Age old question:
Why do students struggle with word problems? - Robert Kaplinsky Video -

4. Student Hat

5. Facts, Inferences, and What is Relevant?
Beth has some red beads
She has 3 fewer yellow beads than red beads
She has 4 more green beads than red beads
What is the question?
(Answer statement)
Do we have all the information we need to solve it?
1 min: Quick sketch - NO OPERATIONS! 
Share with partner – justify sketch and answers, partner critiques (switch roles)
Make a number sentence to match your drawing
Targeted share out
Adapted from Steve Leinwand

6. Teacher Hat

7. Strategies that slow answer-getting
Deleting numerical values (words only)
Leaving off the question (students can create questions)
3 Reads/Math Stories (will demonstrate)
Notice and Wonder from Annie Fetter (if time)
Giving the answer in context and having students create the word problem(s) that produce it
Teach math comprehension like you would reading comprehension
AVOID: Key words and “follow these easy steps” techniques.

8. Why not key words?

10. Umm…Why haven’t we done tape diagrams yet?

11. Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE
Math Stories – 3 Reads
Problem-Solving Recording Sheet

12. Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE
Math Stories – 3 Reads
Problem-Solving Recording Sheet

13. Umm…Why haven’t we done tape diagrams yet?
Just a tool
Not the ONLY way to draw out thinking
Without comprehension, tape diagrams just become another senseless procedure to students
Problem-Solving doesn’t progress in stair-like steps

18. Examples: Addition and Subtraction Problem Types
9 boys and 8 girls were in the class. How many children were in the class altogether?
17 children are in the class. 9 are boys and the rest are girls. How many girls are in the class?
17 children are in the class. There are some boys and 8 girls. How many of the children are boys?

20. Student Hat

21. Math Stories – 3 Reads
30 seconds
Remember!
Tell Back to me

22. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?

23. 20 seconds to reread and check accuracy
Math Stories – 3 Reads
Chart response
20 seconds to reread and check accuracy

24. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?

25. Final check – leave in view
Math Stories – 3 Reads
Chart changes
Final check – leave in view

26. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?

27. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
QuestionAnswer Statement

28. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
QuestionAnswer Statement

29. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
Total? Part? Comparison?

30. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
30 second sketch

31. Partners: Justify - Critique
Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
Partners: Justify - Critique

32. Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
Number Sentence

33. Share out-complete chart
Math Stories – 3 Reads
There are 295 children at a school. 127 stayed for extracurricular activities after school. How many did not stay for an activity?
Share out-complete chart

34. Teacher Hat

35. Process:
Present word problem (pick strategy that slows answer- getting and focuses on comprehension)
Write answer statement
What are we looking for – Total? Part? Comparison?
Who/what has more/less?
Sketch and label diagram/model
Use diagram to solve problem
Check reasonableness/justify
Write expression/equation (justification good here too – often multiple correct answers)
Compare/make connections

36. Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE
Math Stories – 3 Reads
Problem-Solving Recording Sheet

38. Resources: Tape Diagrams 3-5 Solving Word Problems Article Packet TCOE
Math Stories – 3 Reads
Problem-Solving Recording Sheet

39. Pg. 5

40. Pg. 7

41. Pg. 8 - COMpare

42. Pg #3
Alan bought a bag with 29 jelly beans. He gave 13 to his little brother. How many jelly beans did Alan keep for himself?

43. Pg #4
Carl has 13 games in his collection. Daniel has 7 more than Carl. How much do they have altogether?

44. Pg #7
Seven friends went out for a nice dinner. They decided to split the bill evenly amongst themselves and paid $21 each. What was the total money left by the seven friends?

45. Pg #8
The grand prize for a contest was $270. Five winners came forward to claim the prize. Their claims were legitimate and it was decided to split the prize amongst the five winners. How much did each winner take home?

46. Pg #9
A box containing 96 pencils is opened and shared equally among some children. Each child receives 8 pencils. How many children shared the box of pencils?

47. Pg #10
Eric has saved $ His sister, Fiona, has saved 3 times as much. How much has Fiona saved?

48. Pg #11
Gabriel harvested 124 lemons from the large tree in his yard. This was four times as much as he harvested from the small tree in hi yard. How many did he collect from the small tree?

49. Pg #12
Hermione was able to catch 90 fireflies. Ingrid was able to catch 18 fireflies. How many times as many fireflies did Hermione catch compared to Ingrid?

50. Pg #13
Jerry bought a large gummi bear weighing 64 ounces. He and his friends ate ¾ of it. How many ounces did they eat?

51. Pg #14
Kendra bought a batch of cookies, 2/3 of which were chocolate chip. If 30 of them were chocolate chip, how many total cookies did Kendra buy?

52. Pg #15
Lily spent 2/5 of her cash on a CD which cost $15. How much money did Lily have to begin with?

53. Notice and Wonder
Pg. 21

54. Need support?
I am more than happy to meet with/explain further/help plan lessons using these strategies during the “unconference” times
Interest in this???

55. Citations and resources
Based on information presented by TCOE (Kim Webb)
Book: Bar Modeling A Problem-solving Tool (Yeap Ban Har)
Information and Strategies from
Robert Kaplinsky:
Steve Leinwand:
Annie Fetter:
Article: ”Solving Word Problems” (Randall I. Charles)
Problem-Solving Recording Sheet (shown in article)
Problem Set Packet (TCOE)
Math Stories Instructions (TCOE)