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:
- Upload a picture into GeoGebra.
- Place points around all the outlines making sure to hit critical points
- Fit functions to the outlines.
- 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!)