The first two days of this week, I had students work on an activity designed to help them arrive at the formula for the sum of interior angles. The first day, I passed out this great worksheet from Great Math Teaching Ideas which has all the regular polygons from triangles to decagons already done and ready to go.
I printed off the three page activity put only passed out pages two and three with the polygons.
The first step is to have students use a protractor to measure one angle and use that to find the sum of the interior angles. This step has them learning to use and reinforce the use of a protractor.
For the next step, I had students divide the shapes into smaller triangles with the lines starting from the same vertex. This provides students a chance to create the 180 degree part of the formula. When everyone had this completed we discussed using the knowledge that triangles have 180 degrees with the number of triangles to calculate the sum of the interior angles.
I asked students to compare their answers which lead to a discussion on why there might be differences between their answers with the protractor and the calculated answer. It was a great discussion.
I passed out the first page with the chart for names of the polygon, number of sides, and sum of interior angles. I added two more columns, one for number of triangles and one for each individual interior angle. One column was added in front on the left side and one at the end on the right.
Once the chart was completed, I asked questions which lead to the (n-2)180 formula. They added it to their notes and finished class by answering three of the four questions at the bottom.
Yesterday, they had a chance to apply the actual formula with a worksheet. Let me know how you teach this. I prefer activities to introduce topics. Thanks you all.