Variety of areas with fixed perimeter: Difference between revisions

After learning the concepts of perimeters and areas, it is easy for students to think that figures with larger perimeters would also have larger areas, and vice versa. This applet helps teachers to explore with students the variety of the areas of a rectangle with a fixed perimeter. Together with the complementary applet [Variety of perimeters with fixed area], teachers can clarify with students that a figure with a larger perimeter may have a smaller area, and areas and perimeters are two different concepts.

Ask students to record the dimensions, perimeters and areas in the table of the applet;

Remind students that when the longer side and the shorter side are shortened and lengthened by the same amount, the perimeter is unchanged;

Guide students to visualize that the area would always be increased if the longer and shorter sides are changed by the same amount until they become equal;