Proof Puzzles

Proofs are one of the most dreaded things in my Honors Geometry classroom.  It is difficult to start thinking about justifying each step of what you are doing in order to "prove" something.  To get my students started thinking about proof, I use the "Peanut Butter and Jelly Activity".

I give my students pieces of paper in an envelope with the steps listed for making a peanut butter and jelly sandwich.  I then have them put the steps in order that would successfully create the sandwich.  Once we agree upon an order, we talk about how the ingredients are like the "given" information in a proof and how the sandwich is what we are trying to make, or what we are trying to "prove".  There is a logical order in which the steps get us from the ingredients to the sandwich, but sometimes we have some flexibility in this.  

In order to continue guiding my students along, I have put together "proof puzzles".  In order to create this, I write out a two-column proof.  I then cut apart the statements and reasons.  It is the students' job to reorganize the proof into a valid logical argument.  Once they get the hang of this, I start adding in some distractor statements that are not necessary to add to the proof or might lead to an invalid logical argument.  It gets the students thinking about the necessary steps and they start to evaluate their thinking.  I call these "proofs with training wheels" and I have found it helps students to start moving in the right direction.