Contrasting Cases

A few years ago after an informal observation, an administrator suggested I call on more students who answered problems wrong and invite them to share their work with the class.  This seemed counter-intuitive to me, but I decided to try it anyway.  I had a student explain their incorrect answer before he knew it was wrong and another student chimed in right away explaining to his peer his misconception.  The light bulb went off – the student correcting the mistake really must understand it if he can find an error, and other students who answered it wrong are receiving instant feedback and correction.  It was a simple suggestion that is now embedded in my instruction on a daily basis. 

So I was delighted when I found this free resource packed with problems where students have to decide who is right. I love using these for Warm Ups and Exit Tickets. I project this on the board and have students respond on a small piece of scratch paper. 

Each problem has Alex and Morgan explaining their work. Sometimes they get the same answer, and sometimes they don't. When one of the two gets it wrong, it's always a mistake I have seen my students make, so it's a great way to address common misconceptions. When they get the same answer, it's a great way to reinforce that there are multiple approaches to a problem and have students justify why either way works.

I used this particular problem as a Warm Up after we had reviewing multiplying polynomials, and here is what a few of my students had to say:

Sometimes I take a few of my favorite answers and put them on the document camera, so that students can see what a strong answer looks like. I want them to not only be able to recognize who solved the problem correctly, but also use math vocabulary to explain their work and be able to correctly work out the problem to further justify their response.

I took the sharing one step further by picking out some of my favorite responses and having one of my early-finishers create this poster. It hung by my door, so that students could check it out when they had a few extra minutes or when they needed to disguise the fact that they were lined up at the door before the bell ;)