I’ve been given 2 missions from Exploring The MTBoS regarding blogging and twitter usage and to be honest, I’ve been trying to find the motivation to go after it. The last thing I want is for one of my blog posts to be forced. I want my blog to be a written record of “things that work well”. Ya know when you go home and say to yourself, “Dang, that was a good day today. What made that work so well?” So here’s something that went right in my class this week. It involved a new twist to an old lesson that I’ve been doing for years. The concept is graphing sine and cosine functions. We’ve gone through all of the transformations and today we are just tying up loose ends. The old version of this lesson goes something like this: As students walk in there is a hand drawn graph up on the screen and for a warm up the Ss are to write an equation for the graph in their notebook. After a minute or two I ask them to compare answers with the people around them in the hopes that there could be some interesting conversations. I go over the answer(s), we talk about how there could be more than one answer, and we move on to another graph and another equation. Repeat a few times and Voila, call it a day.
The challenge, I say, is to use desmos.com to recreate the graph. I think it’s important for me to say here that we have been using chrome books, and desmos.com pretty frequently in class so there’s not much of a learning curve here. Kids log in and off they go. They start out with some random guessing and they are getting instant feedback from the graph which then leads to more guessing and more feedback. It becomes addictive and they start noticing patterns on how the graph changes when the input bigger and smaller numbers. Most are using guess and check and some of them decide that this strategy can only get them so far. One girl gets so close but can’t quite bring it home. She is losing interest and calls me over. I tell her that she is one digit away from striking gold and ask her to figure out the period of my graph and then look at the period of her graph. Click…the light bulb goes on and she’s off and running again. Okay, after 10-15 minutes of “play time” I announce that we need to debrief so we can proceed with the days lessons. NO NO NO NO…how dare I make such a statement. They’re asking me for more time because they are soooooo close. I give them a 5 minute extension. One kid has been sitting there a while with a content look on his face. He got it, he’s ready to move on so I walk over, celebrate his knowledge, and then offer him the next challenge. Now, find another equation that makes the same graph – use sine instead of cosine. He looks at me with a confused but confident face and he’s back on task.
A debrief with classroom discussion followed. Before we start I asked them to take out a notebook to jot down anything that would be helpful for them. Nothing was forced as they are now taking notes for themselves, not just “copying” notes off the board. I just asked some questions and it became a student led discussion. I have desmos.com up on the screen and they still have chrome books on their desk. Someone got the equation to work using an “a” value of 2 and another student got the equation to work using an “a” value of -2.
What? Is that possible? Prove it. Why does that work?
Are we convinced that there are 2 answers here? Are there more? How many more?
How do you know? Play lawyer and convince us that you’re correct.
I’m changing numbers in the equation and so are they making great observations and connections along the way. The homework assignment goes something like this…Click the link on my website for another graph. Use desmos.com to write as many equations as you can that will lead to the same graph. Good luck, I’m curious to see which one of you will get the most equations. See you Monday.