I work with an amazing group of dedicated, talented teachers. One of the great joys of my position is seeing how they put the things we learn about together into practice. This guest post was from one such classroom.

In Math 3, we are learning about parent functions and translations.  The functions students struggle with the most are exponential functions.  We had been working with all of the function families for a few days. I really wanted to see how the students were doing with the exponentials, so I gave an exit ticket, which is pictured below.

I collected their work as the students left the class and looked through the cards.  About half the class got the problem wrong. It was a little discouraging, but I felt everyone could learn from the mistakes.  The next day when they came into class, I started out by saying  that there were a lot of misconceptions with exponential functions. I told them that we would be using everyone’s cards as our warm-up and learn from some of my “favorite mistakes”.  I had pre-sorted the cards into piles of correct and incorrect answers. I started by projecting a card with a wrong answer. In groups, I had them talk about the answer and figure out what was right and wrong. As I circulated I reiterated it was important to find out what was right and wrong in the problem and that everyone had done something right.  After giving them a minute or so in their groups, I had them popcorn out what the student did correct. We then talked about what was wrong. I put up another wrong card, and repeated the same instructions. We did this a few times, also including an answer that was correct. Suddenly, there was a shift in the class, and they could quickly see what was right and wrong in the graphs. It was amazing! We begin moving rapidly through every student’s card in the class.  All of a sudden, students could quickly see the translation and asymptote (or lack thereof) and were able to state why the graph was correct, and/or why the graph was incorrect. It was such an awesome experience for all of us, and so much better than going over a homework problem together as a whole class! It took about 10-15 minutes, but the time spent was well worth it. I gave a quiz that day and no one missed the exponential function graph!!  Here are a few pictures of the students cards (I am sharing mostly incorrect responses that gleaned more discussion than the correct answers).