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By Smith M.S., Silver E.A., Stein M.K.

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On my way back to the front of the room, I passed by Tommy’s group and stopped quickly in my tracks. The group was very engaged again. ” She suggested that maybe they could make a circle. Beatriz reminded the group that it had to be a rectangular pen. Michael said maybe the pen could be 125 × 50. Tanya asked where those numbers came from. Michael explained that he was just trying out different numbers that would add up to 300. Beatriz said that if the side of the building was 100 yards you would be using only half of the side.

My first stop was the group that included Robert, Kenneth, Ty, and Cassandra. 5). I asked them to explain what they were doing. As I recalled, the last time I visited this group they had built a square pen that was 8 × 8. Like most groups, they had decided on one configuration and wouldn’t budge. Cassandra explained that they were trying to see if what Michael said was true. She went on to say that they decided to draw the pens on graph paper because then they could count the distance around the outside and count the squares on the inside.

Jr. (1996). Visual mathematics: Course II, Lessons 1–10. Salem, OR: The Math Learning Center. Of particular interest in Lesson 2 (Shape and Surface Area) are Actions 8–10 in the Focus Teacher Activity (pp. 24–25). Students explore the effects of changing 20 the unit with respect to linear measurement, surface area, and volume. , Fey, J. , Fitzgerald, W. , Friel, S. , & Phillips, E. D. (1998d). Looking for Pythagoreas: The Pythagorean theorem. Menlo Park, CA: Dale Seymour. 1 (p. 17), in which students determine the areas of regular and irregular figures drawn on grids.

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