Saturday, February 19, 2011

Open Lesson at Junior High School Attached to Tsukuba University

I had a chance to teach a reserach lesson in a Japanese junior high school. It was for a graduating class waiting to sit for their final examinations next week. Thus, I chose a general problem that allows for review of several concepts.

The problem was to use the geoboard to form polygons with (a) no dots inside the polygon and (b) 4 dots on the sides of the polygon. The ideas was to find how the area is related to the number of dots in both cases with the hope that some students will make a conjecture for the general relationship. Would they try to find a proof too?

The lesson went through four parts. Part 1 involved students finding the area of a 5 square unit square. This introduces students to the key variables, area, x and y where x is the number of dots inside the polygon and y is the number of dots on the perimeter. Part 2 involved a problem shown in the photograph - draw a polygon with no dots inside the polygon. This is a platform for students to look for some relationship involving area. Part 3 is another problem - draw a polygon with 4 dots on the perimeter. This was the point where one student gave a general relationship involving area (S), x and y. I ended the lesson by asking students to find cases that does not satisfy the general relationship given. One girl did and I urged the class to check if the girl was right and to find other figures where the relationship does not hold.

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