I try to present math topics four ways: verbally, algebraically, graphically, and numerically. There is more than one way to think about a problem and there is often more than one solution. By teaching this way I'm frequently surprised and delighted about how my students solve problems.
The picture above is an example of this. This is a question on a recent test. We've been studying properties of integrals and this is a straight forward question.
I expected the solution outlined below and the solution in the picture above was presented to me. This makes me smile!
"Your only as good as your record collection." -DJ Spooky