1. Work the Following on Your Own Paper… Luis mixed 6 ounces of cherry syrup with 53 ounces of water to make a cherry-flavored drink, Martin mixed 5 ounces of the same cherry syrup with 42 ounces of water. Who made the drink with the stronger cherry flavor? Give mathematical evidence to justify your answer.

2. Let’s Discuss What was challenging about this problem? What was routine about this problem? Looking at some responses… What is the mathematical evidence? What makes “good” explanation?

3. Solving a Simpler Problem Create a set of 4 related, but simpler problems Each group should work one problem ◦ Work together ◦ Make sure everyone in the group can solve the new problem Be ready to share the solution and solution strategy

4. Solving a Simpler Problem Share the solution and solution strategy with your new group Look back to the original problem and discuss with the group ◦ Was your thinking correct on the original problem? ◦ Did you use a similar strategy on the simpler problem and the original problem? ◦ Can you apply a new strategy?

5. Grading Rubric A grading rubric is used to show students exactly what the expectations are for a task that is being assessed. Rubrics help provide some credit for correct thinking even if the answer to the task is not exactly right. Typically, a rubric scores with points ranging from 0 to 4 and includes a description of the characteristics of a response that ranks at each levels.

6. Create Your Own Guidelines 4 (Everything was perfect and exceeds beyond just a correct answer) 3 2 (Something in between) 1 0 (No attempt was made or response was nonsensical)

7. Share Your Rubric Share your characteristics for each level beginning with level 0 Record each groups’ ideas in one list Decide upon a rubric for the whole class

8. How did you do? Assess the following student responses using our rubric. As you assess other student work, think about ◦ What constitutes a complete justification? ◦ Why is the justification important?

9. NAEP Scoring Guide Compare the rubric your class created to the scoring guide from NAEP Compare your scoring of student work to the score NAEP would assign

10. Multiple Choice Question Abby found a recipe for humming bird nectar. The recipe called for 2 cups of sugar and 3 cups of water. Abby only had 1 ½ cups of sugar. What amount of water should she use to make the nectar? a) 1 cup b) 2 ¼ cups c) 2 ½ cups d) 2 cups

11. Choice a.) Abby found a recipe for humming bird nectar. The recipe called for 2 cups of sugar and 3 cups of water. Abby only had 1 ½ cups of sugar. What amount of water should she use to make the nectar?

12. Choice b.) Abby found a recipe for humming bird nectar. The recipe called for 2 cups of sugar and 3 cups of water. Abby only had 1 ½ cups of sugar. What amount of water should she use to make the nectar?

13. Choice c.) Abby found a recipe for humming bird nectar. The recipe called for 2 cups of sugar and 3 cups of water. Abby only had 1 ½ cups of sugar. What amount of water should she use to make the nectar?

14. Choice d.) Abby found a recipe for humming bird nectar. The recipe called for 2 cups of sugar and 3 cups of water. Abby only had 1 ½ cups of sugar. What amount of water should she use to make the nectar?

15. “Good” Wrong Answers Abby found a recipe for humming bird nectar. The recipe called for 2 cups of sugar and 3 cups of water. Abby only had 1 ½ cups of sugar. What amount of water should she use to make the nectar? What other answer choices might distract someone from the correct answer?

16. Back to Cherry Drinks Luis mixed 6 ounces of cherry syrup with 53 ounces of water to make a cherry-flavored drink, Martin mixed 5 ounces of the same cherry syrup with 42 ounces of water. Who made the drink with the stronger cherry flavor? What answer choices would make good distractors?

17. Time to Reflect On a scale of 1 to 5 (1 being extremely confident, 5 being not at all confident), rate your level of confidence in solving a problem involving a proportion. Explain your rating. What are the important understandings necessary for solving a problem involving quantities that relate in proportion to one another?