1. Understanding Ratios as Percents
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
March 17, 2016

2. Matching Representations
In Pairs… Lay out the pieces from your bag. There are 6 ratio relationships in the bag. Match the equation, table, and graph that represent the same relationship. Identify the Unit Rate for each. Record your reasoning on a sticky note.

3. Is this a proportional relationship? How do you know?
What is the Unit Rate? How did you “see” that on the graph?

4. Learning Intentions & Success Criteria
We are deepening our understanding ratios and percents and their connections to the Common Core State Standards for Mathematics (CCSSM).
Success Criteria:
We will be successful when we can use visual representations and ratio reasoning to solve percent problems.

5. Percents Working with percents is no different from
working with other ratios because percents are
ratios.
Small, M. (2015) Building Proportional Reasoning, p. 71

6. Standard
Standards
Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP. 3 Use proportional relationships to solve multi- step ratio and percent problems.

7. It’s just 40%...
Choose a large number. Then draw a diagram that would show what 40% of that large number is.
2. Next, choose a large number that you decide to be 40% of some other number. Draw a diagram that would show that other number.

8. How many balloons?
Joey inflated 24 balloons for decorations at the middle school dance. If Joey inflated 15% of the total number of balloons for the dance, how many balloons are there in total?

9. How much fuel?
A furnace used 40% of it’s fuel in the tank in March, then used 25% of the remaining fuel in the month of April. At the beginning of March there were 240 gallons of fuel in the tank. How much fuel was left at the end of April?

10. Use and Connect Mathematical Representations
Turn and talk…how is your work represented in the star model? Why would it be important for students to explore all of these representations?

11. Learning Intentions & Success Criteria
We are deepening our understanding ratios and percents and their connections to the Common Core State Standards for Mathematics (CCSSM).
Success Criteria:
We will be successful when we can use visual representations and ratio reasoning to solve percent problems.

12. 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.