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Download Algebraic topology. Errata (web draft, Nov. 2004) by Hatcher A. PDF

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Extra info for Algebraic topology. Errata (web draft, Nov. 2004)

Example text

He went on to say that the rectangles that had a 1 or 2 had the smallest area. Liz explained that the biggest area was the rectangle that had a width that was half the length. I indicated that this was an interesting observation and wondered if it would always be true. I encouraged them to continue to explore the problem and consider other lengths of fence. I visited a few more groups, noting that most were making progress. Unlike yesterday, students were definitely exploring—some were building pens with tiles, some were drawing configurations on graph paper, and others were just sketching pens freehand.

Michele said she thought that Michael’s group picked a number that was too high—it would be hard to do all the pens. They wanted one that was smaller. I asked what they had found out from the table. Michele said that they found out that the 20 × 10 pen had the biggest area. Jamal added that the wall lengths decreased by two each time and the side length increased by one. Jessica said that if you look at the area it keeps getting bigger and bigger until you get to the biggest, then it starts going down.

We will discuss additional connections to your own practice at the end of the chapter. Exploring Area and Perimeter—The Case of Isabelle Olson THE CASE OF ISABELLE OLSON 1. 2. 3. 4. Isabelle Olson teaches at Roosevelt, a middle school located in a large urban school district. She left a position at Lakeview, a more affluent suburban district, 3 years earlier to teach at Roosevelt. She had been using a new curriculum in her classes at Lakeview but found no support within her school for her efforts.

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