1. Moving From Multiplicative Comparisons to Proportional Reasoning
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
Thursday October 22, 2015
Format is down...how to give
We got the kids talking...

2. Practicing Multiplicative Thinking
Please have your Multiplicative Thinking Problems homework and the Progression reading about Multiplicative Comparisons available for reference.

3. Card Sort In groups of three: Using Post-It Notes, make three labels –
Compare small unknown
Compare larger unknown
Compare multiplier unknown
Remove one card at a time from the envelope and decide as a group how to classify the problem.
Repeat this process until all the cards have been classified.
Discuss the language and complexity of the various problems in the piles.
Brief – Discussion about the structure of the problem types.
How did the structure of the problem help to determine which category it went to?

4. Homework Sharing Find a new partner across the room:
Share the solution strategies that you used to solve the three homework problems.
As a pair, summarize your understanding of multiplicative comparison problem situations and the solution processes used to solve them.
No debrief needed…

5. Learning Intention and Success Criteria
We are learning how multiplicative comparison problems lay the foundations for proportional reasoning.
We will be successful when we can extend multiplicative thinking to ratio reasoning.

6. Putting Comparison Situations to Work
Amy has 12 times as much money as Mary. What is relationship between Amy’s money and Mary’s money?
If Mary doubles her money, what is the relationship between Amy’s money and Mary’s money?
What if Mary triples her money?
What if Amy doubles her money?
What if they both double their money? Triple?
10 minutes

7. Building Proportional Reasoning
Refer to p. 44 of Marian Small’s Building Proportional Reasoning.
With your table partner, solve the first question at the bottom of the page. Use multiple representations to display your answer.
5 minutes - Look for different entry points that show equivalent ratios.

8. PRR: Building Proportional Reasoning Reading
Read pages of Marian Small’s Building Proportional Reasoning.
Summarize your understanding of multiplicative comparison situations in your notebook.

9. Learning Intention and Success Criteria
We are learning how multiplicative comparison problems lay the foundations for proportional reasoning.
We will be success when we can extend multiplicative thinking to ratio reasoning.

10. 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.