War on Bad Lessons: More Approximation

The sequel to my introductory activity. This time we went all the way up the ladder, as they say.

Step 1:

Present a set of quadratic situations. I grabbed a few stills from "Will it hit the hoop?" 3ACTS and Angry Birds.

Step 2:

Each group is given a set of the pictures. Each kid is responsible for approximating the situation for two of them. They should make a first order determination of the release point and vertex. Sketch a version of the picture in your notebook.

Step 3:

Use y = a (x - h)^2 + k as a template to insert the vertex for h and k. Use the estimate for the release point for x and y in order to solve for a. Before solving for a, what should you expect the value of a to be? What about the situation tells us this? Upon finding the value for a, append your sketch with the final equation model. The values of a should be tiny, negative numbers. Assign each group a sketch that should be officially presented via iPad. I dumped full versions of the pictures into the iPad Photo Stream and they've already seen how to bring photos into SketchBook Express.

Notice a few of them have a very funky sense of scale. I provided a base assumption that the Angry Birds slingshot is 6ft tall and yet those birds don't seem to be flying very far, do they?

Step 4:

A few discussion items. How well would this process work for the tennis ball videos we made? What affects the accuracy of our result? Watch this crazy video. What's different about that situation versus the ones we looked at?

Conclusion:

Interesting activity. Probably missed a bit of its potential because it was facilitated by my student teacher* and as always, sharing 9 iPads with 32 kids isn't the best thing in the world. This activity would also work quite well in a whiteboarding situation. I can hear Frank Nochese screaming this at me. One day, Frank, one day! All in all, I learned a lot working through this lesson and I think it will be of use when we get to quadratics in Algebra II.

The one where Dan chucks it underhand drew a lot of questions ("that looks wrong!"), and produced this gem:

*My student teacher is quite good. Considering I threw this at him on his second full day in charge, he did admirably.

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