Sometimes My Problems Solve Themselves in Unexpected Ways

My gen-ed class this semester is the BEST CLASS EVER. Never before have I had such a group of well-behaved and highly motivated students with a positive attitude towards mathematics and an open-minded demeanor. Super-fantastic.

I had built an extra day into the November schedule so that if I got behind I wouldn't have to leave out things at the end of the semester. As of right now I'm exactly on schedule, and I didn't know what I was going to do with the extra day. In fact, I feared that I would get ahead because the material that we're doing right now (basic probability) is stuff that they should have seen before.

What I forget sometimes is that many of them come from really weak math backgrounds.

Today we got HORRIBLY DERAILED on what I thought was going to be a basic problem: You flip a penny, a nickel, a dime, and a quarter. What's the probability of seeing exactly two heads?

The method I directed them to use was to list all 16 possibilities and to count. (We will do it in a more elegant, less brute-force way in the future, but I wanted them to do it this way today.)

Less than 10% of the class was able to make the list. Once we had the list, all was good. But making the list? Major digression.

On the bright side, I now know something that I can devote more time to on Wednesday.