I think the missing link is going from a real world application to a practical teaching problem. A topic that motivates an audience would also depend on the audience.

Trying to think of a good example reminds me of a puzzle game; and how sometimes the contrived puzzles in such games can be obtuse or phrased poorly because they really don't want to give away the answer.

The example should start with an unsolvable problem, then simplify aspects to make it more of an estimation model; which is a useful skill as well.