Math teachers at a community college are not paid to create new mathematics. We are not supposed to invent math but teach what exists. This does not mean we can’t be creative, we can. But the creativity should be confined to how we teach, not what we teach.
I give my creativity freely to anyone who teaches. I not only give worksheets to whoever asks, I’ve put up a few of them on this website. I will describe my examples freely–so freely I suspect that I bore people. Some of my favorite examples may be pretty common:
When teaching exponential growth I use credit card interest and figure out how much a student will owe on his credit card if he doesn’t pay it off.
I introduce logarithms by asking how to determine the number of rounds left in a single elimination tournament if the number of teams is known.
When teaching the mathematics of apportionment, I discuss how many teachers will be assigned to each school, based on the student population.
One example of Newton’s law of cooling, has a cast of characters including Victor “Vic” Timm, who dies, his fiancee Mary Ritch, His sister Molly Gunn (although no one seems to know what a gun moll is any more) and her son, Carey A. Gunn. The body is found by Tom Peepers. Unfortunately, these jokes are totally lost on the non native English speakers in my class. This is the only case I use terrible jokes in a problem.
I enjoy finding interesting examples. I hope I never have to teach a problem starting “Seven years ago, John was twice as old as Mary.” Who cares?