This investigation uses several important geometric facts. To begin the investigation the students must be familiar with the basic concepts of midpoint, area and perimeter. A review of the congruence and similarity properties along with special properties of polygons is present. These basics can then be further explored to form conjectures and finally lead to proof. The scope of possibilities for this investigation is rather wide and can be used according to the desired level of difficulty.

As the teacher you could choose to use cooperative learning groups. Assign a specific polynomial to each group to explore. Provide students with specific instructions for exploration and the desired questions to be answered. After following the directions to arrive at the answers to the assigned questions, each group should present their results to the class. As a class then discuss the methods used and any relationships or general findings.

Another way to approach the cooperative learning groups is to assign each group a polygon to explore without giving specific instructions. Have students form the interior polygon and create important measurements. As a group the students should then form conjectures concerning their findings which result from their drawings. Each group should share their findings with the class.

A final activity is to form the conjectures and have the students use GSP to prove or disprove their assigned conjecture.