Back-to-Back Pictionary!

Last week in my highest level class (Calculus A, a class for juniors that combines all of Precalculus and the first half of AP Calculus AB) I was astonished to see how abysmal my kids are at describing graphs using the kind of terminology that their tests and exit tickets would *indicate* they understand - words like increasing, decreasing, concave up or down over the interval ... , symmetric about ... , etc. This occurred to me as I was having a student review a Do Now with the class and when he called on a student to describe the graph of f(x)=x^(2/3), the student described it as "the bird." It was clear then that we had a problem. Students could define the terms above and use them in the context of multiple choice test questions, but they are far from fluent in graphical lingo.

Enter Back-to-Back Pictionary.  I played this today in one of my regular Precalculus classes and it turned out to be a blast and also extremely productive. Partners sat back-to-back, each of them with a different sheet of nine graphs each. Some of the graphs were recognizable based on the types of functions we've studied, and others were strange piecewise concoctions. They also had their mini whiteboards. Students took turns choosing a graph to describe to their partner, the caveat being that they could only use sentence starters from the word box: "The graph is increasing/decreasing over ...", "The graph is concave up/down over ...", "The graph is symmetric about ..." etc. I told students that they weren't even allowed to reference the name of a parent function in their description (let alone make bird noises, as one student asked). The sketcher listened to his partner and drew the graph on his board; when he thought he was finished, he'd show to graph to his partner. The team got a point if the graph on the whiteboard matched the graph on the sheet.

I modeled one with a student, and then they played for around 15 minutes. The room was loud and slightly chaotic, but it was exciting to hear students screaming at each other "I TOLD you it was MONOTONICALLY INCREASING!!!" Not something you hear every day (but hopefully something I'll hear more often, going forward).