Applying Problem Solving
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Reflect on each of the following questions about the Fish Derby problem, and select "Show Answer" to see a sample response.

 Question: What evidence does the teacher look for to see if the students are moving from stage to stage in the problem? Show Answer
 Sample Answer: Ms. Cho asks to see if they have been able to find the inequalities and know what to do next; in particular, whether they understand what the equations mean. When it's clear that a number of groups are struggling with finding the area of feasibility, she addresses the whole class and asks about strategies for this.
 Question: How did the teacher respond to the varying interpretations of graphs in the class? Show Answer
 Sample Answer: More than one student is invited to present graphs to the whole group and to explain them. The teacher has created an environment where students productively critique one another's work rather than mainly relying on the teacher to do so. One example of this is when she asks whether people agree or disagree with an interpretation without in any way revealing her view.
 Question: How does the context of the problem effect problem solving? Show Answer
 Sample Answer: The requirement that the results of the problem solving be presented in a letter to a fictional board of supervisors adds richness and complexity to the problem situation. This brings communication more fully into the problem, since students must explain their thinking and process in a narrative that relies on mathematical accuracy to be persuasive. Although this may not seem to be central to the problem-solving task, the ability not only to apply mathematical problem-solving strategies but to also be able to communicate effectively about results is a crucial skill.

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