We've been learning about sequences and series in Precalc (along with a foray into mathematical induction, which is always fun) and for the past couple of days have been investigating Pascal's Triangle. I got a neat exploration from Ann Gregson (who has since left the math world for elementary tech) and also gave the kids this activity from the Math Forum where you color the triangle according to a specific rule. (Because you use 5 colors, it's mod 5 arithmetic. Neat.) I ended up with a bunch of neato triangles that I taped together, laminated, and am about to hang on the wall. Or at least I'll hang it once my student aide cuts 'em out and assembles next period!
There was some confusion with the coloring because it appeared that the pattern would continue to be a series of identical-ish triangles. Like this:
But instead there was a funny block at the bottom all the same color:
(I can't figure out why this picture is sideways. Oh well.)
Here's the arrangement of the correct ones:
The best quote of the day was from a student who was looking closely at the correct triangle. "That makes sense... it would just be a giant fractal." YAY! :)
(And then another favorite quote from today, "Did you get my email? (Me: No.) Good, because I didn't sent one." Oh, teenagers.)