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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?

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Work the following on your own paper

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.


Let s discuss

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?


Solving a simpler problem
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


Solving a simpler problem1
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?


Grading rubric
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.



Share your rubric
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


How did you do
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?


Naep scoring guide
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


Multiple choice question
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?

  • 1 cup

  • 2 ¼ cups

  • 2 ½ cups

  • 2 cups


Choice a
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?


Choice b
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?


Choice c
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?


Choice d
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?


Good wrong answers
“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?


Back to cherry drinks
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?


Time to reflect
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?


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