1. The Importance of SMP5 Use appropriate tools strategically Double Number Lines Common Core Leadership in Mathematics (CCLM) Tuesday January 21, 2014 This material was developed for use by the project staff and participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

2. Today’s Learning Target By the end of the session, participants will: Understand the importance of SMP 5 Use appropriate tools strategically in Claim 2, and demonstrate this knowledge by using double number lines to solve problems.

3. 6.RP.3 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.

4. Double Number Lines They are used for understanding the equivalence of two related numbers. It’s called “double” because each mark on the line has two sets of numbers matched to it. The top row of numbers describes the whole represented by the line in one way and the bottom row describes the whole in another way. Because the whole line is the same, it’s possible to see the equivalences between the rows of numbers at any point on the line.

5. Yummy Fruit Punch A simple example To make Yummy Fruit Punch, use two cups of grape juice for every three cups of apple juice. If you already have 12 cups of apple juice, how many cups of grape juice will you need? Work with your partner to solve this problem. Use two models and one must be a double number line.

6. Various strategies

8. Use a Double Number Line to Represent This Problem The local dairy farmer is selling 20% of his herd of 150 cows. How many is he selling? What do you know? What do you want to find?

9. How do we use the lines to get the answer? 0% 20% of cows 100% of cows  cows 150 cows 20 x 5 = 100 150 divided by 5 = 30 0% 20% 100%  150 cows Find 10% of 150 cows: 150 divided by 10 So 10% of 150 cows = 15 cows So 20% of 150 cows = 30 cows 0 cows

10. What do students need to know so they can do this? Have a sound understanding of percent. Recall of multiplication and division facts. Know that the answers must in in context with the correct units. Common factors and least common multiples.

11. On your own 30% of the swimming team are girls. If there are 18 girls, how many are in the team altogether? What do you know? What do you want to know? Use a Double Number Line to solve this problem.

12. Sarah went shopping for a new bike which cost $350. When she got to town there was a sale and she got 20% off the price. What did she pay? Did she pay more or less than the original price? How much less? So instead of paying 100% she only paid ____ %. Show all this on the number lines.

13. Winter Fun At the ski park each lift holds 3 people, and there are 5 lifts. The lift takes 10 minutes. There are still 150 people in the line, and the lift closes in exactly one hour. Will all the people be able to ride the lift? Justify your answer.

14. Today’s Learning Target By the end of the session, participants will: Understand the importance of SMP 5 Use appropriate tools strategically in Claim 2, and demonstrate this knowledge by using double number lines to solve problems.