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Take some time to reflect on the open-ended questions below. Select "Show Answer" to see our comments or if you need help thinking about the questions.
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Question: What types of representation are present in this activity?
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Sample Answer:
The teacher provided models of specific numbers of blocks to give students a reference point for their estimates. The models are representations of specific quantities of blocks.
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Question: How are the representations of specific quantities helpful to the students in terms of completing the task?
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Sample Answer:
Students compare their container of blocks with the references provided by the teacher and determine whether theirs is greater, less, or about the same. They then use this information to make their estimate.
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Question: What are some ways that students could make their own representations to help them make a good estimate of the number of blocks?
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Sample Answer:
If the referents weren't provided, students could use make their own representations (say, 10, 50, and 100 blocks) and then compare their original set of blocks with the sample sets.
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Question: How would you decide whether you should provide the models or allow students to determine their own representations that can be used to help them make an estimate?
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Sample Answer:
If students have had little experience with this type of representation or with making estimates, it might be helpful to provide the referents. Students who have had previous experience are better able to determine their own strategies for making an estimate.
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 Observe more student work
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