1. Core Mathematics Partnership
Tape Diagrams Part 1
Core Mathematics Partnership
Thursday, September 4,2014
4:30 – 7:30
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success

2. Learning Intentions and Success Criteria
We are learning to:
understand how tape diagrams builds coherence, perseverance, and reasoning abilities in students.
understand how using tape diagrams shift students to be more independent learners.
Success Criteria
We will be successful when we can solve problems that use tape diagrams throughout the K-8 modules.

3. Mathematical Shifts Focus
Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the Standards.
Coherence
Teachers carefully connect the learning within and across the grades so that students can build new understandings on foundations built in previous grades.
Deep Understanding
Students deeply understand and can operate easily within a math concept before moving on. They learn more than tricks to get the right answer. Their learning is built on conceptual understanding.

4. What Is A Tape Diagram?
A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as strip diagrams, bar model, fraction strip, or length model.
(CCSSM Glossary, p. 87)

5. East Meadow School District October, 2013
Tape Diagrams
What is a Tape Diagram?
Grade 1: Math Drawings (1.OA.1, 1.OA.2)
Grade 2: Math Drawings (2.OA.1, 2.OA.2, 2.MD.5)
Grade 3: Visual Fraction Model (3.NF.3a-d)
Grade 4: Visual Fraction Model (4.NF.3, 4.NF.4, 4.OA.2)
Grade 5: Visual Fraction Model (5.NF.2-4, 6, 7)
Grade 6: Tape Diagrams (6.RP-3) Visual Fraction Model (6.NS-1)
Grade 7: Visual Model for Problem Solving (7RP1-3)
Number Line Diagram (7.NS-1)
Why are they important?
Next level of abstraction

6. Progression of Tape Diagrams
Students begin by using concrete objects and drawing pictorial models
Evolves into using bars to represent quantities
Enables students to become more comfortable using letter symbols to represent quantities later at the secondary level (Algebra) 15 7 ?

7. Students make use of concrete objects (or picture cut-outs) to make sense of the part-whole and comparison concepts. Then, they progress to drawing rectangular bars as pictorial representations of the models, and use the models to help them solve abstract word problems

8. Problem Set 1

9. Example A: Connor has toy 6 cars
Example A: Connor has toy 6 cars. He gets 8 more toy cars for his birthday. How many toy cars does he have now? = 14 He has14 toy cars altogether.

10. East Meadow School District October, 2013
Tape Diagrams
Example B: Rose has a vase with 13 flowers. She puts 7 more flowers in the vase. How many flowers are in the vase? ?
Number of flowers in the vase 13 7
= 20
There are 20 flowers in the vase.
“We do” problem
What category? Add to result unknown
ENY G1 M4 L19

11. Example C: 174 children went to summer camp
Example C: 174 children went to summer camp. If there were 93 boys, how many girls were there?
93 + ? = 174
174 – 93 = ?
There were 81 girls.

12. Example D: Caleb brought 4 pieces of watermelon to a picnic
Example D: Caleb brought 4 pieces of watermelon to a picnic. After Justin brings him some more pieces of watermelon, he has 9 pieces. How many pieces of watermelon did Justin bring Caleb?
9 pieces of watermelon 4 ?
4 + ? = 9
9 – 4 = ?
Justin brought 5 pieces of watermelon.

13. East Meadow School District October, 2013
Tape Diagrams
Example E:
Some yellow beads were on Tamra’s bracelet. After she put 14 purple beads on the bracelet, there were 18 beads. How many yellow beads did Tamra ’s bracelet have at first?
18 beads on the necklace ? 14
Yellow beads
Purple beads
? + 14 = 18
18 – 14 = ?
Tamra had 14 yellow beads at first
ENY G1 M4 L20

14. East Meadow School District October, 2013
Tape Diagrams
Example F: The students were playing with 7 balls on the playground. They accidentally kicked some of the balls into a big puddle and now some are muddy! What is one way the balls might look?
ENY GK M4 L18

15. East Meadow School District October, 2013
Tape Diagrams
Example G: Kiana found some shells at the beach. She gave 8 shells to her brother. Now she has 9 shells left. How many shells did Kiana find at the beach?
8 shells
9 shells
? shells
ENY G1 M4 L21

16. East Meadow School District October, 2013
Tape Diagrams
Stop to Reflect:
What did you notice about the structure of the problems in Problem Set 1?
They were all addition or subtraction problems, and were all conducive to use of the Part-Whole model.
Ask participants to turn and talk. Gather a few ideas from the group. Then display the summary bullet on the slide

17. Part-Whole Model Addition & Subtraction
Part + Part = Whole Whole – Part = Part

18. K, 1st and 2nd Grade Addition and Subtraction Problem Situations

19. Problem Set 2

20. East Meadow School District October, 2013
Tape Diagrams
Example A: Rose wrote 8 letters. Nikii wrote 12 letters. How many more letters did Nikii write than Rose?
Number of letters Rose wrote
Number of letters Nikii wrote 8 12 ?
= 4
Nikii wrote 4 more letters than Rose.
ENY G1 M6 L1

21. East Meadow School District October, 2013
Tape Diagrams
Example B: Rose saw 14 monkeys at the zoo. She saw 5 fewer monkeys than foxes. How many foxes did Rose see?
Number of monkeys
Number of
foxes 14 ? 5
= 19
Rose saw 19 foxes at the zoo.
ENY G1 M6 L17

22. Example C:
Anthony has 5 baseball cards. Jeff has 2 more cards than Anthony. How many baseball cards do Anthony and Jeff have altogether?
5 + 2 = 7
7 + 5 = 12
They had 12 baseball cards altogether.
Anthony
Jeff 5
2 more ?
This example required two computations in order to answer the question. This is an example of a two-step problem as called for in the standards beginning in Grade 2.
For ms teachers, represent this problem with x and y and a system of equations.

23. East Meadow School District October, 2013
Tape Diagrams
Stop to Reflect:
What did you notice about the structure of problems in Problem Set 2?
They were all addition or subtraction comparison problems, and were all conducive to use of the Additive Comparison model.

24. The Comparison Model Addition & Subtraction
larger quantity – smaller quantity = difference smaller quantity + difference = larger quantity

25. 1st and 2nd grade Comparison Problems

26. Write Your Own Problem
Using the OA Addition/Subtraction Story Problem Sheet:
Write your own addition/subtraction problem on an index card that is appropriate to your grade level.
Draw the tape diagram on the back of your index card.
Trade problems with your neighbor and solve the new problem.

27. Key Points
When building proficiency in tape diagraming skills, start with simple accessible situations and add complexities one at a time.
Develop habits of mind in students to reflect on the size of bars relative to one another.
Part-whole models are best used ___________________________________
Compare models are best used when ___________________________________
When building proficiency in tape diagraming skills start with simple accessible situations and add complexities one at a time.
Develop habits of mind in students to continue to ask, ‘is there anything else I can see in my model’ before moving on to the next sentence in the problem.
Develop habits of mind in students to reflect on the size of bars relative to one another, by asking, ‘who has more’ type questions.
Part-whole models are more helpful when modeling situations where you are given information relative to a whole.
Compare to models are best when comparing quantities.

28. Learning Intentions and Success Criteria
We are learning to:
understand how tape diagrams builds coherence, perseverance, and reasoning abilities in students.
understand how using tape diagrams shift students to be more independent learners.
Success Criteria
We will be successful when we can solve problems that use tape diagrams for addition and subtraction situations.

29. Disclaimer Core Mathematics Partnership Project
University of Wisconsin-Milwaukee,
This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors.
This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.