1. Looking Deeper Into Ratios Tuesday March 20, 2012 Common Core Leadership in Mathematics (CCLM) Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

2. Learning Intentions Review additive and multiplicative comparisons. Use a variety of representations to solve ratio tasks. Form ratios as measures of real-world attributes Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

3. Success Criteria We will know we are successful when we can Use and justify various strategies to solve ratio problems and make connections to CCSSM. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

4. Let’s review Standard 6RP1 Domain RP: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems. Standard 6RP1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

5. What happens at recess…. The students in Mr. Hill’s class played games at recess. 6 boys played soccer 4 girls played soccer 2 boys jumped rope 8 girls jumped rope Afterward, Mr. Hill asked the students to compare the boys and girls playing different games. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

6. And the class said 6 boys played soccer2 boys jumped rope 4 girls played soccer8 girls jumped rope Mika said, “Four more girls jumped rope than played soccer.” Chaska said, “For every girl that played soccer, two girls jumped rope.” Mr. Hill said, “Mika compared the girls by looking at the difference and Chaska compared the girls using a ratio.” Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

7. Your Turn 6 boys played soccer2 boys jumped rope 4 girls played soccer8 girls jumped rope Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did. Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did. Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

8. Abby’s Paint Problem Abby’s orange paint is made by mixing 1 cup red paint for every 3 cups yellow paint. Zach’s orange paint is made by mixing 3 cups red paint for every 5 cups yellow paint. Whose mixture is ‘orangier’? Use ratio tables to prove your answer in at least two ways. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

9. Abby’s Paint Problem

10. Standard 6RP3 6RP3a Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a) Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Refer to your work from Abby’s Paint Problem to illustrate the meaning of this standard. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

11. Ratio Wars: Who Has More Red? Player 1: Ratio of 2 white to 6 red Player 2: Ratio of 6 white to 4 red Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

12. Standards for Mathematical Practice Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

13. Connecting to the Practice Standards MP #2: Reason abstractly and quantitative ly MP #3 Construct viable arguments and critique the reasoning of others In what ways did our ratio work engage you in Math Practice #2 and #3?

14. Success Criteria We will know we are successful when we can Use and justify various strategies to solve ratio problems and make connections to CCSSM. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year