I use this activity to bridge the gap between the students' prior knowledge and the new concepts of properties of regular polygons.
I print two copies of the chart double sided and give one to each student. On one side, the students are to focus on polygons with 3 to 12 sides (a key is provided). I ask the class to fill in as much as possible. When all possible boxes have been filled in as a class, I guide the class into focusing on trends and patterns until formulas become apparent. This can also be done in small groups.
On the back of the chart, I ask for the students to fill in the boxes using polygons with many, very many, sides (a sample key is provided). There is additional room if you wish to extend the chart to an unhealthy level.
I have created a constructed response assessment to gage how the students understood the information from the chart and discussion.