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The following questions refer to the Largest Container problem that you watched Ms. Duncan's class work on. Reflect on each question, then select "Show Answer" to reveal our commentary.
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Question: What previous knowledge do students need to bring to this task?
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Our Answer:
Understanding of volume and surface area, how they are similar, how they are different, and what they actually measure.
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Question: What are some strategies the students employ to solve the problem?
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Our Answer:
Making a model, writing an equation, guessing and checking.
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Question: How do Ms. Duncan's questions lead students to think about their approaches to solving the problem?
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Our Answer:
Her questions help students to clarify their thinking –– especially when they are explaining their ideas to their classmates. She purposely leaves the task open-ended so that students need to bring their own understanding to the task.
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Question: How does this problem help students solidify their understanding and application of mathematical formulas?
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Our Answer:
Students need to apply a variety of formulas to the three-dimensional shapes they construct and then analyze whether those shapes are the largest they can make.
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Question: What characteristics make this a rich mathematical task?
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Our Answer:
Students need to understand the task before they begin. The solution process is not immediately apparent, so students need to consider which strategies they can use to solve the problem. The problem encourages reflection and discussion among the students after it is solved.
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