My school has Chromebook carts that I’ve been using more and more recently. It’s great to have some more tools to provide my students, but also a bit of a pain to get everyone logged on and troubleshoot different issues. Luckily, I came upon a great warm-up to engage kids in purposeful practice while we get everyone logged on. This already exists in the form of Daily Desmos, but my focus is on simpler graphs that are accessible for all of my students, possible through pretty simple trial and error, and don’t require advanced knowledge or an “a-ha” moment. I definitely stole this iteration of the idea from somewhere on the internet, but I forget where, and I’m sorry I’m not giving appropriate credit.
Match My Desmos
Real simple. Give students, either digitally, on paper, or projected, an image of a graph, like this one:
Students’ job is to match the graph in Desmos. That’s all.
I think this is really useful practice for a few reasons. It’s a lot of “touch time” with features of graphs, in this case, slope, intercept, and maybe alternate forms of linear equations, although the graphs can emphasize any concept you like. It requires attention to precision in order to match each part of the graph. I try to design graphs that have patterns within them for students to notice and take advantage of. And it has a low barrier for entry — my students have used Desmos enough that they are willing to dive in and start trying things without much prompting. I can also use it to introduce new ideas or ideas students have forgotten by strategically choosing certain features of graphs.
But more than that, I think this is a great place for students to experience the practice of mathematics. They get immediate feedback on their ideas, and feel much safer trying things and making mistakes in this format. It mostly takes me out of the picture, as they don’t need me to validate that they matched the graph correctly, or to tell them something is wrong. Almost all of my hints are along the lines of “what have you tried so far?” and “what else could you try?” — and just pushing students to a place where they are willing to try things can lead to genuine success. Oh, and my students love getting their graph exactly right.
I had a really interesting experience one day when I was starting class with a Match My Desmos activity, and another math teacher was in the room to check in with a student about something. Another student was struggling a bit, and the teacher immediately jumped in and started asking leading questions — what’s the slope here, what’s the y-intercept, etc. I actually got a little mad. I want students to struggle here — they need to experience that, and the bridge from struggle to success needs to be their willingness to try something and see if it works, not a series of questions from a teacher telling them which piece to look for and how to find it each step of the way.
Anyway, if you have access to Desmos and want to try this, below are all of the Match My Desmos graphs I’ve done so far, I have a pretty good mix, and there’s obviously infinite potential for more.
I’ll leave the solutions as an exercise to the reader.
Questions I still have:
First, who did I steal these from? I feel bad that I forget what blog I took it off of.
What are the best ways to facilitate discussion here? I’d love to share alternate approaches, but it’s tough without a quick way to share each students set of equations with the class.
How far can this be extended? I’ve had trouble generating interesting examples with exponential functions, but there’s definitely a lot of potential with conics, and it reminds me of Heather Kohn’s take on Des-Man.
What are effective topics that could be introduced with a graph that can be more effectively created with a new piece of knowledge? I’m thinking of vertex form for quadratics, or function transformations in general.