Practicum - Sharing a Lesson

The lesson objective was to have students discover that the length and width of rectangles are inversely related in regard to a constant area. Students were expected to come up with 5 dimensions of rectangles with a constant area of 350. (Examples, 1 X 350, 2 x 175) Students created a table and then plotted these points on a graph. The end result was a curve that is symmetric about the line y = x.

Prior to assigning this problem, students were asked for the general formula for area of a rectangle (L x W = A). They also tried solving dimensions of rectangles with area of 24. Overall, the class had a good idea how to do this and there were hardly any questions. They came up with all possible dimensions using whole numbers. The "AHA!" moment did not come until later.

I assigned the problem and required that students work with their elbow partners. The only students who struggled with the problem had their general equation mixed up ( Some of them solved for W or L and had the area on the bottom instead of the top). I stopped the class, asked for everyone's attention, and cleared up the problem since more than a couple groups had done the same thing. I had to stop later to talk to the class about their graphs because several groups did not have incremental changes on their axes. Each line must go up by the same amount in order to draw the graph properly. Some students also connected their lines to the axes, which could never be true for dimensions of a rectangle. Neither dimension can ever be zero. This was our final discussion right before the bell rang. The student's attempts and failures allowed them to learn more about the concept of inverse relationships.

If I were to re-do this assignment, I would not have changed a thing. It is OK for the students to struggle and somewhat necessary for them to learn. If I gave them ALL of the answers upfront, I do not think they would feel the same sense of pride and ownership over their work when they figured out the right answer.