1. One example of "chocolate covered broccolli" math would be the television show Lost. In the show, there is a series of numbers (4, 8, 15, 16, 23, 42) which constantly appear, and each one is assigned to one of the characters. To avoid setting off an alarm, the characters have to punch the numbers into a computer once every 108 minutes, 108 being the sum of all the numbers. While this series of numbers affects the characters, the math behind it takes a backseat to the significance of the assignment, rather than the assignment itself.
2. One movie where math is the central idea is The Number 23. This movie is heavily based on numerology, as the main character believes he is haunted by the number 23 in all of his actions. His paranoia drives him crazy, and the more he thinks about it, the more he sees the number everywhere, and looks for increasingly complex ways to derive the number 23 out of anything. This man bases his story off of his math and plays off the numbers.
I think of "There Was An Old Lady Who Swallowed A Fly" as a nursery rhyme involving math. Here's a bit of it: