My math class is doing derivatives via basic differentiation rules after suffering through doing them "the long way" (the limit process that apparently produces many groans and bad test grades).
So Mr. Riley taught us a cute math rhyme for doing the derivative of (u/v):
Lo-dee-hi minus hi-dee-lo,
Over the square of what goes below.
So totally awesome.
When I learned the quadratic equation, my teacher taught it to the tune of "Pop Goes the Weasel":
x is equal to minus b plus or minus the squaaaare root of b square minus four ac all! over two a.
Clearly, I still remember it to this day. Mnemonics rule!