One lesson my students had a hard time understanding was the triangle angle sum theorem and the exterior angle sum theorem. When I initially taught this, I first told them the theorem. (I only did this because I was going out of town for a fellowship interview for a few days.) When I went back and retaught it, we did a discovery activity where they had to tear the angles of the triangles off and line them up correctly. I really had hoped that they would gain a better understanding through the discovery, however, that was not the case. The first is when my students did the paper discovery, they were very confused about how to glue the angles of the triangle next to each other. They also were not able to transfer their knowledge from the discovery to the practice problems. They expected the triangles to all look like the ones from the activity.
I chose this GeoGebra discovery activity to combat both misconceptions. I liked the fact that the applets incorporated transformations to help students understand why the angle values don’t change. The best part about the online discovery is that the students play with the triangles for every applet. They can change the size of the triangles. They can make the angles bigger or smaller and slide the slider to see how the theorems always work. This is great for students who need a visual and for those who take a longer processing time. They can drag the vertices as much as they need and slide the slider as many times as they want. They can work at their own pace to understand the theorem on each page instead of me setting the pace of the class. This would be great for my students with an IEP and ELL students. Just like how I retaught it before, I plan to allow students the chance to explore then come together as a class to discuss their findings. I want them to lead the discussion about what they noticed and why or how.
I really like GeoGebra because outside of this explore activity, students can create shapes and angles to explore concepts from class in a blank document. This tool can be used to prove or disprove theorems. I chose these already created activities because not only were they common core aligned, but they had probing questions. My hope is that they are able to transfer what they learn from this online activity to the practice problems and then to other polygons.
A copy of this lesson plan can be view below.