Wednesday, January 11, 2006
Yes, in an instantaneous decision while discussing zeros of polynomials today, I went for the cheap laugh. We were discussing a 5th degree polynomial (most have 5 "wiggles") and they can have at most 5 distinct places they cross the x-axis. We were discussing one that touched/crossed the x-axis only 3 times. There's bad picture above.
I was trying to get them to notice that the last 2 places were "alike" and the first one was different, so that they could generate an equation. ... I hummed (badly) the Sesame Street song, "One of these things, is not like the others. One of these things, just doesn't belong...". I paused, they didn't get it. Then I asked them to notice how the graph was "touching" the x-axis, so I said, "one of them is touching it inappropriately." They finally got it.