Applying Representation
 Introduction | Taking a Sample | Problem Reflection | Classroom Practice | Representation in Action | Classroom Checklist | Your Journal

Reflect on each of the following questions about the woodpecker's habitat simulation you saw in Mr. Sears's class, and then select "Show Answer" to reveal our commentary.

 Question: What are some types of representation that are present in this lesson? Show Answer
 Our Answer: The cubes represent elements in the woodpecker's habitat. Drawing the cubes represents the rate of occurrence of that element. For example, drawing more green cubes means that more pine trees are present in the habitat. Students used a variety of representations to communicate their results, including checklists and tallies.
 Question: How do students create and use representations to organize, record, and communicate mathematical ideas in this lesson? Show Answer
 Our Answer: Students represent their work by organizing the way that they will record each draw from the bag of blocks (i.e., by making checklists and tallies).
 Question: How is the classroom discussion enhanced by students' representations? Show Answer
 Our Answer: The representations of the results of drawing 10 blocks help the students draw conclusions about what is in the bag. For example, their work is a visual record that green and yellow were drawn most often. From these representations, they predict that green and yellow are the colors that occur most often in the bag. Within the groups, the representations help students clarify their thinking and explain their reasoning to one another.
 Question: Could this be a good time to introduce the use of bar graphs to represent data? Explain your reasoning. Show Answer
 Our Answer: Yes, it could be. The students are using their own methods for keeping track of the data. The blocks themselves, when lined up, are a physical representation of a bar graph, since it's a natural extension to show students that a bar graph is another strategy for recording their outcomes.
 Question: How does this problem show how each of the Process Standards can be integrated into a single activity? Show Answer
 Our Answer: Students communicate their thinking in the follow-up class discussions. Problem solving is integral in the entire task. Students make conjectures about what is in the bag and support their ideas with the use of their written work. Finally, the outcomes are represented by students in the form of tallies and organized lists.

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