Proof puzzles

If your students are anything like mine, the mere mention of the word proof is enough to bring on severe anxiety attacks. Despite moving significantly more slowly this year than last, my students still struggle to write their own proofs. So I thought I’d throw a matching activity at the problem and see what happens.

Most students finished two proofs today, which included cutting time. Hopefully we’ll be able to finish all six by the end of the week. From the conversations I had, this really helped students start to piece together the flow of a proof. It also gave those students who are struggling a great entry point, because all the relevant theorems were listed there for them to simply look up in their notes or the textbook.

Basic outline of the day:

  1. Give students a Randomized packet. Tell them to cut out the steps for the first proof. Make sure they keep the part of the page that says what information is given and what they’re supposed to prove.
  2. As students finish cutting, explain that these are complete and correct proofs whose statements and justifications have been jumbled up. The students’ job, of course, is to put the proof back together in the correct order.
  3. I let students work together in pairs so that they had someone to bounce ideas off of. As students worked, I circulated around to (1) verify answers and (2) help steer thinking.
  4. After verifying that a student has a correct proof, have them write the correct order down in their notes. Each card has a number and a letter in the corner that identifies it. I chose to do it this way so that students could reuse these proof puzzles for studying. You could also have students tape down the completed proof. Or just throw out the cards. Or make a class set and reuse them. The world is your oyster!
  5. Once the correct order is transferred to their notes, have students paper clip the cards together and put in another one of these handy-dandy envelopes.
  6. Repeat the process until all proofs are completed.

Here are the files. Note that there are multiple correct ways to write the proofs, so this is just one possibility. I accepted any correct proof, even if the steps were in a different order. And some proofs have multiple “Given” cards, so those might be mixed up too :)

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