Observing Student Representations
 Introduction | Building Viewpoints | Student Work Reflection #1 | More Building Viewpoints | Student Work Reflection #2 | Observe a Classroom | Classroom Practice | Your Journal

Now let's look at how a middle school student solved the following problem:

 This is the floor plan (or top view) of a structure made from cubes. The numbers in the squares indicate the number of cubes in that stack. Construct this building on the Building Mat.

Reflect on the problem and think about some questions you would ask this student. Then look at the questions listed below. For each question, think about an answer the student might provide, then select "Show Answer" to reveal a sample response.

As you read these questions and answers, analyze the student's representation. How does this representation help the student identify relationships among the different views of the building?

 Teacher: Can you draw what you would see if you were in front of the structure, looking at it from eye level? Show Answer
 Student: Yes:
 Teacher: That is what the building would look like if you were looking down at it from the sky -- what we call a "bird's eye view." If you, get down and look at the front view of the building, at your eye level, can you draw what you see then? Show Answer
 Student: (observes the building from eye level) Oh, okay:
 Teacher: What would you see if you were in back of the structure, looking at it from your eye level? Can you draw that? Show Answer
 Student: Yes:
 Teacher: How is the view from the back different from the view from the front? Show Answer
 Student: It is reversed.
 Teacher: What would you see if you were on the right side of the structure, looking at it from your eye level? Can you draw that? Show Answer
 Student: Yes:
 Teacher: And now can you draw what you would see if you were on the left side of the structure, looking at it from your eye level? Show Answer
 Student: Yes:
 Teacher: How is the view from the right side different from the view from the left side? Show Answer
 Student: It is reversed.
 Teacher: Is there another name for this relationship? Show Answer
 Student: It's a mirror image, or symmetrical.
 Teacher: If you were under the building and looking straight up, what would you see? Show Answer
 Student: It would be the same shape as from the top. (Note: The orientation of the shape would depend on where the student was standing: at the front of the building, at the back, at an angle, etc.)

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