I wonder, for all those who teach multiple levels, how your preparation differs based on the composition of the class.

I teach high school students, undergraduates, advanced undergraduates and graduate students. But what I do for each class to prepare is quite similar. The major difference is that I have two or three back-up plans if I’m teaching high school, one or two if I’m dealing with undergrads, and I’m usually confident that my graduate classes will be over-planned.