Modeling Quadratics: First Attempt

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I’ve had trouble with getting students to model a quadratic function since forever. Apparently I’m not the only one, as it comes up often in the MTBoS. Last year, I made a step in the right direction by starting with the vertex form of the function. Well, actually let me go back one more step. We started our quadratics unit with absolute value functions. Check it out:

Now that we have a good idea of how to shift around a parent function, it’s time to try building a quadratic from scratch. (Side note: try patterns 106 and 108 at visualpatterns.org when you start your quadratics unit, some of your students will amaze you, or your money back guaranteed!) Anyway, so here’s my plan:
Actually, first a quick word about my schemes for next year. I plan to run my class like a game, so there’ll be quests, XP, leveling up, no grades, and other stuff I haven’t figured out yet. And I think I’ve got my theme. Wait for it… “Hitchhiker’s Guide to Algebra” (not sure about the name, but you get the idea). Total credit for this idea goes to Jessica Anderson (@triscicurious). Check out her blog, especially if you’re thinking about gamifying too, since she’s already doing it.

With that in mind, I am trying to write tasks around that theme so that I’ll have some ready to go for next year. The more I get done before the year starts, the more self paced and non-linear my class game can be. So I tried to make this task fit with a Hitchhiker’s Guide theme. Hence the “Intergalactic Lower Appendage Ball League”. Get it?
Anyway, when students come in to class, they’ll get into groups and each kid will receive 16cm of string and this handout:

Inspiration credit for this idea goes to Scott Hills (@Planting_ideas). Thanks Scott!
As they wrap up measuring and recording, I’ll put the Desmos graph (woot images!) shown below up on the smart board and ask everyone to come up and enter their results. Go ahead, click it and put in your results and see what you think, I’ll wait!

If they haven’t already, they should notice (once we’ve got enough up on the board) that the points are forming a parabola. BAM!! Quadratic Modeled!! Well, almost. Each kid will then complete a summary report of their findings where they’ll have to write a function and think about key parts of the graph. Then they’ll share their thoughts with their group, and then each group will make a whiteboard to display for the class. If we have time, I’ll have them blog the results at our class blog.

What do you think? Got any ideas for improvements? Have you done something similar before, any tips?

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