One of the fun activities we bandied about in the Talk Less session at TMC16 was to ask students to create the best mistake for a particular problem. Each year in my Algebra I classes, my students (9th graders) have had some portion of Algebra I the year before. Many have had courses that didn’t take them all the way through, some experienced all of it but didn’t do so well, and some had PreAlgebra. We are a private 9-12 school, so we are in charge of placing them after an assessment. This is all to say that while my students need a year of Algebra I, many of them also need a fresh look at the subject–especially the intro topics that they most definitely hit last year. This activity is perfect for this situation.
Introducing this activity was as simple as can be. I gave them one equation to solve and asked them to create the best mistake they could. I had each table (3 or 4 students per table) put their mistake worked out on the board. After they were all done, a representative needed to explain their mistake. Here were all the results from one period.
I’ll tell you what, as happy as I was with these results, the next period wasn’t so great. As much as I don’t want to degrade or judge a mistake that a student thinks is relevant, they started going down a road of simply dropping numbers or introducing new ones. Responses weren’t as thoughtful. A lot of that is on me. Maybe the setup required more work than I indicated before. Maybe I need to respond to the specific combination of students in that room. Regardless, I’ll be coming back to this activity.