Friday, October 12, 2012

3rd Degree

I Love Charts, constant source of fun graphics, had a fun temperature comparison chart. temperature graph, complete with fun. I did share my graphs finally. I used GeoGebra to make them, of course, because that's the best accurate mathematical image maker. Easy enough to make all three variations. Which, of course, lead to wondering what features would you put in a dynamic sketch for it? How could you make the sketch switch between the three ranges?
But it wasn't to scale, so I started thinking about what that would look like. Just lengths? What's the norm? Then Shawn Cornally shared his oneupped

So I had to make it then. Obviously. It's on GeoGebraTube: for download or use as an applet.

Instead of checkboxes, I knew I wanted a slider to switch amongst Kelvin, Fahrenheit and Celsius as the input. I thought about adding an input box for conversion, but those still don't work on the iPad, and I'm trying to think about that more.

The idea came to make the segments for the 0 to 100 degree temperature range where the endpoints were a function of the slider. Then I just needed a particular value for three different inputs, so it would only have to be a quadratic. I started to go to Wolfram|Alpha to do the regression, when I realized that, of course, GeoGebra would do it more easily. So with the slider at values 0, 1 and 2, the range for Fahrenheit, for example, is just determined by
F0(x)=FitPoly[{(0, -459.67), (1, 0), (2, 32)}, 2]
F100(x)=FitPoly[{(0, -279.67), (1, 100), (2, 212)}, 2]
a=Segment[(3, F0(n)), (3, F100(n))]
I was struck again by how nice GeoGebra is as a source of activities for students, but also how rich the task of making things in GeoGebra is, and wonder: how do I encourage more sketch creation from students?

Having sunk the time into making the sketch, I did think about what activity could go with it, and whipped this up:

I'd be interested in feedback on the sketch. Does it have the features you'd want for your students to use? Should it have more cute doodads? What do you think about the design of such a sketch as a task? How far should the students be past the material before trying to design the sketch?

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