1. Ratio and Proportion Part 1 Tuesday January 17, 2012 Common Core Leadership in Mathematics (CCLM) Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

2. Short Readings Homework Grade 3 2 nd narrative p. 21 Grade 4 2 nd narrative p. 27 Grade 5 1 st narrative p. 33 Grade 6 2 nd narrative p. 39 What did you notice? Give some examples of key advances from one grade to the next. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

3. Learning Intentions Deepen conceptual understanding of ratio and rates Unpack the 6 th grade CCSSM standards about ratios. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

4. Success Criteria We will know we are successful when we can  Use various strategies to solve ratio and proportion problems.  Justify our thinking when solving problems involving ratio and proportion.  Clearly explain and provide examples for specific CCSS standards Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

5. Launch Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year Consider this phrase Two pounds of potatoes for $1.00 What does this mean?

6. Making Sense Read the statements on the handout. Which ones make sense? Why? What distinguishes those that make sense from those that don’t make sense?? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

7. Five Minute Exploration Time

8. If the small gear turns clockwise, which direction does the big gear turn? Why? If you turn the small gear a certain number of times, does the big gear turn more revolutions, fewer, or the same amount? How can you tell? Have You Discovered?

9. Suppose you have turned the gears until they have returned to their original positions. How many revolutions does the small gear make? How many revolutions does the big gear make? (Find a way to keep track of the number of revolutions both gears make until they return to their original positions.) Gear Up! Part I

10. Students need to make a transition from focusing on only one quantity to realizing that two quantities are important. Shift from One Quantity to Two Quantities

11. Someone found out that when the small gear turns 5 times, the big gear turns 3 times. What are some other rotation pairs for the gears? Gear Up! Part II

12. From Additive to Multiplicative Comparisons Students need to distinguish between an additive and multiplicative situation. Students need to make a transition from making additive comparisons to forming a ratio between two quantities. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

13. Oh no! What’s the answer? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

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

15. Grade 6 Ratio Standard Representing and reasoning about ratios and collections of equivalent ratios 6RP1 Divide your slate in 2 parts. On one side, rephrase the standard. On the other side, explain how this standard was illustrated in the gear problems. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

16. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year Consider this phrase Two pounds of potatoes for $1.00 What does this mean? (Express as a ratio statement.) Launch

17. Success Criteria We will know we are successful when we can  Use various strategies to solve ratio and proportion problems.  Justify our thinking when solving problems involving ratio and proportion.  Clearly explain and provide examples for specific CCSS standards Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year

18. Homework Read pp. 15 – 22 in Developing Essential Understanding: Ratios, Proportions and Proportional Reasoning. How did the examples and discussions of the problems help you understand how students develop understanding of ratios? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011- 2012 School Year