Low-Tech Group Approach to Proofs with CPCTC

This week in my Honors Geometry class we looked at proving two triangles congruent.  Today we built on this to prove that parts of congruent triangles are congruent using CPCTC.  We started class by watching a quick video from Brightstorm that introduced CPCTC.

We then took a look at last night's homework where we were proved that we had two congruent triangles.  We talked about what the proof would look like if we were trying to prove that two of the sides were congruent.  We kept our proof exactly as we had constructed it, but we added that we knew that we had two congruent sides because of CPCTC.

Since my students seem to dread proof, every year I look for new ways to get my students to gain understanding.  This year I tried a new activity with my students that seemed to work really well.  In order to set up this activity, I needed some whiteboards and a wet-erase marker.  On each whiteboard I wrote out the "given", what we needed to prove, the diagram, and the outlined structure for a two column proof.  

I then had my students break up into groups of 4-5 students.  The students used dry-erase markers to mark up the diagram and complete the two column proof.  I was really amazed at all of the great conversations going on in the classroom today.  The students were engaged and focused!  They talked about the differences between the different congruence shortcuts (SSS, SAS, ASA, SAA and HL congruence) and they argued with each other about when it was time to bring in CPCTC.  They weren't just focused on getting the problems done, they were worried about understanding the problems!

Once students were finished with their proof, they checked in with me to see if they had completed it correctly.  Once the proof was done correctly I erased their work that was done with dry erase marker and the original problem written in wet erase marker was left behind.

Students then traveled to the other whiteboard stations.  Each time a new person in the group was in charge of writing on the whiteboard.

This activity really got the students to communicate and I think we gained some great understanding.  I had a couple of students who were struggling tell me that they now understand proofs!  It was a great day in Geometry!