1. Developing an Understanding of Multiplication
Thursday, June 23, 2011 Common Core Leadership in Mathematics (CCLM) Summer Institute Melissa Hedges & DeAnn Huinker

2. Learning Intentions & Success Criteria
We are learning to…
Understand how the CCSSM views the development of multiplicative thinking.
Apply strategies that promoting fluency with single-digit multiplication and division.
We will be successful when…
We can help students apply properties of operations as strategies to multiply.

3. What is Multiplication?
Respond in writing in your notebook…
What is multiplication?
Check with a neighbor to see:
How is your thinking similar?
How is your choice of language similar or different?
What is Multiplication?

4. Standards…
Reflect on homework reading: Third Grade Critical Area and Standards 3.OA: 1 – 6
Share with your shoulder partner a few ideas that struck you as critical to developing a sound understanding of multiplication and division.

5. From Counting by Ones to 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?
You were just unitizing!

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

9. Image 1
Put an equation with that.

10. Image 2

11. Image 3

12. Grounding thinking in CCSSM
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.”

13. Reflect back on 3.OA.5.
Think about how the images were described.
Where do the properties show up in the reasoning?

14. Group:
Pick a “color.”
Individually:
Quickly glance at the dot image and determine the number of dots.
Jot down using “language” how you saw it.
Write an equation that matches your image and your description.
Identify the property or properties you used.
Turn and share.

15. Image 4

16. Image 5

17. Image 6

18. 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?

19. Revisiting Learning Intentions & Success Criteria
We are learning to…
Understand how the CCSSM views the development of multiplicative thinking.
Apply strategies that promoting fluency with single-digit multiplication and division.
We will be successful when…
We can help students apply properties of operations as strategies to multiply.