Whenever I teach a theorem, I always prefer to lead my students to discover it on their own. I’d like for them to not only know the theorem and how to use it, but also where it comes from. This week, my seventh grade students were working on discovering the sum of the interior angles of a polygon. It’s a pretty straight forward theorem so the worksheet I created is also pretty simple. Students could easily find the theorem without a worksheet. I created it to add structure because my students still need that, but eventually I would prefer if they could do something like this with less of my input. A nice extension activity would be to have students investigate the sum of the exterior angles.
In years past, I have had students draw the polygons and measure the angles with a protractor. This year I was able to check out a classroom set of laptops so we used GeoGebra. Helpful GeoGebra tip: To get the interior angles displayed, you must create your polygon by plotting points counterclockwise. Then select the angle icon from the menu and click inside the polygon. If you build your polygon clockwise, the exterior angles will be shown. Some student work is shown below:
Confessions of a Middle School Math Teacher 