Algebraic Topology, Barcelona 1986 by J. Aguade, R. Kane

By J. Aguade, R. Kane

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First, they must reason that the area of each 1-centimeter square would be 10 millimeters × 10 millimeters, or 100 square millimeters. To successfully complete the problem, then, they will need to multiply the total area of the irregular shape as measured in square centimeters by 100. I think that the tasks I assigned will provide the basis for lots of good discussion. I have found that the routine of explaining your thinking and asking questions sometimes can lead to pretty superficial interactions.

He paced off a square that was 10 × 10 and asked Tanya, Beatriz, and Michael to each stand in one of the corners. He said that each square of the linoleum counted as 10 yards, so each side was 100 yards and the area was 10,000 square yards. The group agreed. He then suggested that they build the rectangle that Michael had suggested at the end of the class. 5 linoleum squares) by 50 yards (5 linoleum squares). Michael then proceeded to count linoleum squares in the area. He got confused while counting, but Tanya was ready to step in.

To give students the opportunity to struggle in order to learn that perseverance would lead to satisfying conclusions. ” I began to realize that even this question appeared to be too remote to steer the students in the right direction. Most of the students insisted that their particular construction covered the most area. ” I returned to Tommy’s group after stopping to check on each of the other groups. They appeared not to have made much progress since my first visit. I again asked the group how they knew that the pen they had built provided the largest amount of room possible with 300 yards of fence.

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