For the first couple of weeks in precalc we review a lot of the topics they learned last year in Algebra 2. Domain, range, even, odd, increasing, decreasing, constant, compositions, parent functions, piecewise functions, linear regression. Just typing all of those words bore me. :)
My goal is to review those in ways so that the kids are reviewing them as they apply them.
One of my newly-favorite activities (that I got out of this book) is called "A Taxing Problem". It leads them through writing and graphing several different piecewise functions with different conditions. First is a strict percentage on what you make (depending on your income). Then comes a little bit of an ease so that you pay smaller percentages on the smaller amounts of money but then as you make more you pay more. (For example, you'd pay 15% on your money up to $22,100, 28% on your earnings from $22,100 to $53,500, 31% on anything $53,500 to $115,000, etc.) That's a fun function to write!
The next step is adding in a standard $6950 deduction. The kids want to start off by subtracting that from their variable in the previous function, but what if that moves them down a tax bracket? Everything's messed up. So they have to figure out how to apply the deduction and still end up in the correct tax bracket.
We've spent two days in class on the problems (one more day than I'd planned) but I've heard so much good conversation and collaboration that I didn't want to stop them. Several girls told me today that I was making their brains hurt, and one of my "smart" kids said he'd been struggling and asked if we were going to go over the functions tomorrow. I'm guessing that these kids haven't really had to *think* in a class for a while (no offense to their previous teachers, of course).
Tomorrow we're moving on. I'm going to have them figure out if Usain Bolt's 100m world record is really as good as people say it is.