Going Off on Tangents

I don't know why, but that picture cracks me up.

The other day, I had my Algebra 2 Honors students work on a "story" problem as a long warmup.

We had been working on quadratics, but hadn't done any examples of word problems using quadratics yet.  My goal was just to see how they would do on their own (They are usually rock stars.).  I created this multi-question problem to help them baby step along the way.  It's about a girl throwing a rock in the air.

They did quite well.  At the maximum of the parabola, I asked the kids whether the rock was going up or down when the parabola was at it's maximum (worded in terms of the problem).  Most of the kids said "neither, it's changing direction".  I was so excited that I actually did a little happy dance in class.  we have not talked about that at all (yet), and I'm excited that this feels intuitive for them.  We got into a huge discussion that lasted for the rest of class about tangent lines, secant lines, slopes of tangent lines, etc.  We didn't finish anything else that I had prepared for that class period, but I still consider it super successful.  In my honors class, it seems like the best class periods are the ones where we go off on some tangent (haha) talking about other things.

I usually show this video by the National Science Foundation before we start the lesson on quadratics.  I'm kicking myself because I forgot this year.  I still showed it, but it didn't have the same effect.

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