This is exactly what I did as a grad student when I taught classes for my prof. She preferred bottom up and I preferred top down. I wanted to give people a reason for learning what they were getting ready to learn rather than "let's start from first principles" that almost all my professors wanted to do.
I prefer the exact same approach for learning to play board games too. Your 20 minutes of rules explanation will go completely over my head unless you start with "the goal/win condition of the game is to get more points/reach the end faster/collect all the macguffins".
