I wrote about this project back on Sam’s blog this summer when Sam gave me reign of his kingdom for a month or so, but I wanted to share the student work that I got this year from it, because it was much better than last year, and some of the work is actually really beautiful/cool/interesting (Math Art, MArTH anyone?).

The basic premise of the project is to RECREATE A PICTURE USING INTEGRALS by doing the following:

1. Upload a picture into GeoGebra.
2. Place points around all the outlines making sure to hit critical points
3. Fit functions to the outlines.
4. Use integrals to shade in the areas between the outlines.

I initially waffled about whether this was a worthwhile problem or just an exercise in integrals, but having taught AP Calculus this year, I realize how these problems of just finding the area of a weird shape are interesting and important for deep understanding of the connection between a Riemann sum and how the integral actually calculates area. So basically, if you think that this is a worthwhile problem…

Find the Area of R and S given that f(x) is blah blah and g(x) is blah blah blah squared.

…then this project is just a glorified, more interesting, more complex version of that problem. If you don’t think that problem is worthwhile, well, then you probably wont like this either. Regardless, it was a great thing to do to hammer in ideas about finding the area between curves, and a great learning mode while AP’s were occurring because attendance did not really matter all that much. It took most students 3 and a half 45-minute class periods (so about 2.5 hours), though I think that more efficient students not freaking out about standardized tests, and consistently present in the classroom, might be able to do it a little quicker.

SOME OF MY FAVORITES:

ALL OF THE STUDENT WORK:

(the good, the bad, the ugly!)

GEOGEBRA INSTRUCTION SHEET: