I started by having groups up at the board working on this Would You Rather problem.

This was the first time we've worked at the board in a little while. There were a number of people who were quite off task. Others got to work right away but the group dynamics were not what they should have been. Once they were done the activity I sent them back to their seats and we talked about contributing effectively to a group and how it benefits everyone in the group.

The main event for today was some geometry, specifically interior and exterior angles of polygons. I put the image below up on the board and asked students to work at the whiteboards to see how they would do without any instruction.

The group work was much better this time around and all groups were able to answer all of the questions. A few groups needed some reminders about supplementary angles and a couple asked about opposite angles. They were doing great.

I brought them back together as a group and we summarized the different types of triangles, supplementary angles, opposite angles and began exploring the sum of interior angles. Everyone knew that the interior angles in a triangle sum to 180° so we began looking at other polygons. We did this by looking at the number of triangles in each polygon:

From this they were able to determine the sum of the interior angles. Next I had them fill out the table below to come up with an equation.

We've done enough visual patterns that to many this process came easily. They had no trouble finding the rate but had to think a bit about the initial value. I had a couple of different results which was neat. The most common was that the sum of the interior angles = 180n-360 and the other was that the sum of the interior angles = 180(n - 2). It was exciting to see these different results.