1. Multiplication Concept Development & Word Problem Structures
Pathways to Teacher Leadership in Mathematics
Wednesday, July 9, 2014

2. Learning Intentions & Success Criteria
We are learning to…
Understand the development of multiplicative thinking.
We will be successful when we can …
Identify and describe “unitizing” as a key understanding needed for the development of multiplicative thinking.

3. What is Multiplication?
Respond in writing…
What is multiplication?
Record your thinking.
Check with a neighbor to see how your thinking is similar. How is it different?

4. The Meaning of Multiplication

5. From Counting by Ones  Thinking In Groups
Place a large amount of counters in the middle of the table.
On the word “go” grab as many groups of two that you can before we say stop.
Don’t count the total number of sets, just concentrate on making groups of two.
We will transition to grabbing 3’s and 4’s very quickly. (This is meant to go REALLY fast!)

6. Return the counters to the middle of the table.
On the word “go” grab as many sets of ________ that you can before we say stop.
We will transition to grabbing 3’s and 4’s very quickly. (This is meant to go REALLY fast!)

7. Making groups: What did you notice?
What kind of thinking were you doing as you were making groups?
What would this activity tell you about students’ thinking?

8. Big Idea That Surfaces Thinking in Groups Unitizing
Moving beyond counting by 1’s

9. Pre-requisites to Thinking Multiplicatively
Cardinality: Understand that the last counting word indicates the amount of quantity of the set of objects
Subitize: Perceive an amount (1-7) without counting
Unitizing: Counting sets of objects, rather than single objects

10. A Purposeful Push to Unitizing Thinking in Groups

11. Dot Images
How many dots so you see?
How do you see It?
Draw what you see in your notebook.

12. Image 1

13. Image 2
Put an equation with that.

14. Image 3

15. Grounding Thinking in CCSSM 3.OA.7 & 3.OA.5
Read 3.OA.7.
Read 3.OA.5: Apply properties of operations as strategies to multiply and divide.
Commutative
Associative
Distributive
With your shoulder partner, use an example, remind each other how these “rules of numbers work.”

16. As a group, pick one card
Individually:
Quickly glance at the dot image and determine the number of dots.
On your white board, jot down how you saw the image using words.
Write an equation that matches your image and your description.
Identify the property or properties you used.
Turn and share.

21. Revisit Standard 3.OA.5 and 3.OA.7
Take turns with a Shoulder Partner to summarize:
Reflecting on our “dot image” work, what are the main messages of these standards?
How do dot images promote multiplicative thinking?
skip counting, doubles, unitizing, repeated addition, relationship between rows and columns, sets and # of sets, thinking in groups

22. Big Idea behind Dot Images
Reinforces thinking in groups
Unitizing
Subitizing
Promotes multiplicative thinking

23. Definition of Multiplication
Look back at your definition of multiplication.
Modify your definition based on this morning’s work.
Share with a shoulder partner how you adjusted your definition and why.

24. Rigor of Understanding
What questions might
you have after
reviewing this work?

25. 3.OA.3
Divide your whiteboard in half. On one side rephrase 3.OA.3 in your own words. On the other side provide an example. Turn and share

26. Students’ struggles with context
Students’ struggles with context. Grade 5  Tell a story problem for 6 x 8
I can get them from 6th grade, too.

27. Learning Intentions & Success Criteria
We are learning to…
Understand the development of multiplicative thinking.
We will be successful when we can …
Identify and describe “unitizing” as a key understanding needed for the development of multiplicative thinking.

28. Disclaimer Pathways to Teacher Leadership in Mathematics Project
University of Wisconsin-Milwaukee,
This material was developed for the Pathways to Teacher Leadership in Mathematics 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 Improving Teacher Quality Program.