## Monday, April 16, 2012

### Conic Sections: Parabolas

Much like with circles, I need some major help in the area of teaching parabolas (through the lens of conic sections).  Maybe I'm just not cut out to teach geometry.  It's quite possible.

In any case, here are a couple of things that I found/made that did work nicely:

1. This graphing paper from MathEdPage.org is awesome.  It gives a very nice low-tech option for discovering the geometric definition of a parabola.  I split the class into groups of two or three and gave each group a sheet of this graphing paper with one of the lines darkened (which is to be the directrix).  I told the students to plot seven or so points that are equidistant from the point in the middle and the darkened line.  We found a couple together, and then they were good to go for the rest.  When I gave them the following definition, they were able to fill in the  blanks no problem:

2. I made a little graph with sliders that shows what happens to a parabola in the form x^2=4py when you change p.  It wasn't a ton of work, but I'm still pretty proud.  Plus, I continue to absolutely adore Demos graphing calculator at abettercalculator.com.  I also love their new "Projector Mode" under Settings.

 I got to borrow one of these from my college.  I really want one.  Unfortunately they're a little pricey.

So, those are two things that worked.  The 5-10 minute intro.  But once we got to working examples, I wasn't too pleased.  I feel like I jump all over the place when I work these problems.  "What's the vertex?!  How do we find the focus from there?  And the directrix?"  I think students get it during class, but that's with me asking all the right questions at all the right times.  Ideas for making them do more of the work?