Which One Doesn't Belong? ... for Calculus

In February, Christopher Danielson released his shapes book: Which One Doesn't Belong? It is fantastic for all ages and if you haven't downloaded it yet, do that now. I'll wait... I put the link up there...

More recently, Chris Hunter wrote this blog post after tweeting out some really cool Which One Doesn't Belong? (henceforth known as WODB) graphs like this:

and this:

He also had graphs of functions and that made me think that I could create some of my own for my calculus classes. We are doing curve sketching right now so it would be perfect! The more time I spent on this, the more value I could see in having students do this so here is what I have so far.

1. WODB? Student have to figure out which graph is the odd one out using characteristics of graphs that we study in calculus like asympototes, max/min, points of inflection, non-differentiable points, etc. The key here is that there is a correct answer for each of the four graphs in each set. I have, so far, made two of these. Making them has been so much fun, but also quite challenging. 

2. I have them work in groups to create one or more sets from these graphs. Many of these are the "crazy" ones I found along the way when I was trying to create something specific. They will cut them out and see if they can make it work. 

3. They will create their own WODB? from scratch, in groups. This adds another level as they have to come up with the equation for each graph (and there will be heavy use of Desmos, of course). The level of thinking required to get a particular characteristic given the other constraints is great! If they are like me, they will encounter a lot of cool graphs along the way that they may not have ever seen before. They will undoubtedly be making or deepening connections between graphs and their equations in such a cool, different way. Instead of starting with the equation and finding out what the graph will look like, they have to create the equation based on very specific characteristics.

I am so excited to try this out with my students after March break! The discussions should be really rich and interesting. A huge thank you to Chris and Christopher for inspiring me. This is why I love the MTBoS!