Ratios and Proportions

1. Ratios and Proportions Grades 6/7 Sara Anaya AyşeŞahin Diana White

3. An example of how to introduce the notion of a ratio: • Illustrative Mathematics6.RP.1 Task example: • Games at recess 6.RP.1: The language of ratio and proportion Anaya, Şahin, White

4. This recipe has a ratio of 3 cups of flour to 4 cups of sugar. • How many cups of flour would you use for 1 cup of sugar? • Answer this question using as many different methods as possible. 6.RP.2 and 7.RP.1 Anaya, Şahin, White

5. Tape Diagram Representation 1 cup of flour 1 cup of flour 1 cup of flour ¾ cups of sugar Author's Name IM&E CCSSM National PD

6. Table x 2 x 2 x 3 x 3 x 4 x 4 x ½ x ½ x¼ x¼ Author's Name IM&E CCSSM National PD

7. 1 2 3 Cups Cups 1 2 3 4 1 2 3 Cups of flour Cups of sugar 1 2 3 4 Double number line representations don’t work as well when the units are the same. Author's Name IM&E CCSSM National PD

8. Changing the problem slightly, a double number line becomes an appropriate representation: This recipe calls for 3 tablespoons of butter for every 4 cups of sugar. How many tablespoons of butter would you use for 1 cup of sugar? 0 tbs 3 tbs Tablespoons Cups 4 c 0 c Author's Name IM&E CCSSM National PD

9. Using double number lines we directly translate the problem into asking: what is 3 /4? (Standard 5.NF.3) ¾ tbs of butter for every cup of sugar. 0 tbs ? tbs 3 tbs Tablespoons Cups 4 c 0 c 1 c Author's Name IM&E CCSSM National PD

10. This recipe has a ratio of 3 cups of flour to 4 cups of sugar. • How many cups of sugar would you use for 1 cup of flour? Solve this problem using a method you did not use for the previous question. Anaya, Şahin, White

11. This recipe calls for ¾ cup of flour for every ½ cup of sugar. How many cups of flour would you use for every 1 cup of sugar? Answer this question using as many different methods as possible. 7th Grade Unit Rate Problem Anaya, Şahin, White

12. This recipe calls for ¾ cup of flour for every ½ cup of sugar. How many cups of flour would you use for every 1/4 cup of sugar? Answer this question using as many different methods as possible. Anaya, Şahin, White

13. Suppose Abby’s orange paint is made by mixing 1 cup red paint for every 3 cups yellow paint and Zack’s orange paint is made by mixing 3 cups red for every 5 cups yellow. Whose paint is yellower? 6.RP.3 and 7.RP.3 Anaya, Şahin, White

14. Suppose Abby makes orange paint by mixing 1 cup red paint for every 3 cups yellow paint. She can only find 100 cups of the red paint, and as much of the yellow paint as she likes. How many cups of orange paint can she make? Answer this question using as many different methods as possible. 7th Grade Extension Anaya, Şahin, White