1. Ratio Reasoning in 6th Grade The Road to Proportional Reasoning
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
December 3, 2015

2. Learning Intentions & Success Criteria
We are deepening our understanding of ratio concepts and ratio reasoning, their place in the Eureka Math curriculum, and their connections to the Common Core State Standards for Mathematics (CCSSM).
Success Criteria:
We will be successful when we can plan an introductory unit of instruction on ratio and proportion, paying attention to both the overall progression of these ideas in the CCSSM and the precise details of the mathematics involved in our unit.

3. Proportional Reasoning
Proportional reasoning has been referred to as the capstone of the elementary curriculum and the cornerstone of algebra and beyond.
It begins with the ability to understand multiplicative relationships, distinguishing them from relationships that are additive.
Van de Walle,J. (2009). Elementary and middle school teaching developmentally. Boston, MA: Pearson Education.

4. Proportional Reasoning vs Proportions
Proportional reasoning goes well beyond the notion of setting up a proportion to solve a problem—it is a way of reasoning about multiplicative situations.
In fact, proportional reasoning, like equivalence is considered a unifying theme in mathematics.

5. 6.RP.1
Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Fill in standards Progression

6. What is a ratio? Re-read 2 paragraphs from the RP Progression.
How would you define the word ratio?
A pair of non-negative numbers a:b which are not both zero. (CCSSM glossary)
An ordered pair of numbers that express a multiplicative (relative) comparison.
Uses of ratios
Part-to-Part Comparison: number of girls to number of boys
Part-to-Whole Comparison: number of girls to number of
children in the family
Read the progressions p. Ratios, Rates Proportional Relationships 2-3
Make this handout.
Read 2 paragraphs starting at bottom of page 2 and complete the top paragraph on page 3.

7. Ratios and Ratio Reasoning
We should discuss how participants interpret these terms before the next slide, which leads to the Springboard interpretation. 7

8. Exploratory Challenge
Work in pairs to complete Exercises 2 & 3 from the Exploratory Challenge in Eureka MathTM Grade 6, Module 1, Lesson 2
Need student copies of the Exploratory Challenge (pages 4-5 in the student edition)

9. Using Ratio Reasoning to Solve Problems
Work in pairs to complete Exercise 1 from Eureka MathTM Grade 6, Module 1, Lesson 5
How did the use of tape diagrams help to surface ratio reasoning?

10. Using Ratio Reasoning to Solve Problems
Work in pairs to complete Exercise 2 from Eureka MathTM Grade 6, Module 1, Lesson 5

11. Using Ratio Reasoning to Solve Problems
Work in pairs to complete Exercise 2 from Eureka MathTM Grade 6, Module 1, Lesson 7

12. Using Ratio Reasoning to Solve Problems
Work in pairs to complete Exercise 1 from Eureka MathTM Grade 6, Module 1, Lesson 11
How did the use of ratio tables help to surface the concept of equivalent ratios?

13. Learning Intentions & Success Criteria
We are deepening our understanding of ratio concepts and ratio reasoning, their place in the Eureka Math curriculum, and their connections to the Common Core State Standards for Mathematics (CCSSM).
Success Criteria:
We will be successful when we can plan an introductory unit of instruction on ratio and proportion, paying attention to both the overall progression of these ideas in the CCSSM and the precise details of the mathematics involved in our unit.

14. 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.