Park City Mathematics Institute
Secondary School Teacher Program

Reflection on Practice Class: Day 4
Akihiko Takahashi

"The reason why we divided into three groups is that we are going to have a discussion. Yesterday we were talking about how to find the area of a parallelogram. In our role as a teacher we don't want to explain to the student how to find the area. We expect students to find out this idea. Then the student will explain. We don't want to help students."

"What we are going to do today is basically the same idea."

"Our focus today is finding the formula for the area of a trapezoid. There are three things I am asking each group to do:"

  1. Anticipate students' solution methods to finding the area of a trapezoid. Find as many ways as possible.
  2. Derive the formula for finding the area of trapezoid from each anticipated solution methods.
  3. Discuss how you would like to lead students' discussion in order to help students derive the formula for finding the area of trapezoid.

"At the end, each group will summarize their ideas."

We spent the rest of the hour on this task. Photos were taken of the 12 flip charts.

Here are some samples:

Click on the thumbnail image to view the larger version.



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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.