Having done a lot of long road trips, I have often entertained my tired brain by trying to calculate how long it will take me to get to mile marker x, or city y (SPRINGFIELD 400 says the sign) based on how fast I'm going, then how long it would take if I was going 1mph faster or slower, or 5mph, etc. It's relatively simple but to do so entirely mentally seems to take a lot longer for me than I if I could just jot a few notes down. It gets more fun if you try to account for how long it takes for you to slow down for an exit, take a piss and get a snack, then get back up to speed.

I didn't know, for the longest time, what a derivative was. I still don't, not really, though I can bluff my way to a reasonably correct answer using the above analogy and going from dry "rate of rate of change" sort of language into more practical concepts.