The following demonstrates why I don't do "formal" lesson plans before my lesson. Well, this and the fact that I'm a last-minute (post-last-minute?) person. I eventually do get the plans down on paper, since I use them the following year to see what works and doesn't work.
I was introducing piecewise functions to my precalculus class. I started with an example of a power company in town and suggested that they may offer incentives to people who use less electricity, so if you use less than or equal to 500 kW per month, they charge you 10 cents per kW, and if you use more than 500 kW per month, they charge you 15 cents per kW. I then gave them the disclaimer that I had no idea how much a kW was and if this was at all reasonable. (future assignment for the class and me: find out how many minutes of light that is). Then to make sure they got it, I asked them to put on paper in calculator-ready form, how much my bill would be if I used 600 kW last month. I wasn't even thinking about the ambiguity, but a great question came up: is it 15 cents for everything since you went over, or is it only 15 cents for the 100 kW over? (we went with the 2nd option).
Then we started drawing the graph, and decided that there would be an initial service fee of $20 even if you didn't use any kW. I asked them to discuss in their groups the axes labels and what the left part of the graph would look like (before 500 kW). We also did the right side. Now here is where in the past I would have breezed through this and shown how it was piecewise and then went on with another "math-class" piecewise function to work with. But a student pipes up with, "ooh! I know the equation of the left part of the graph". This got us on the path of finding the 2 line equations, and seeing what and why the slopes are what they are, and discussing point-slope form (the forgotten quiet nice guy in the class of line equations) vs. the ever-popular-player-guy "slope-intercept" form of the line equation. We set them up and discussed that those equations go on forever, so how do we show someone where it's restricted to. We then got it into an f(x) piecewise format and worked with finding f(32) and f(701) and describing what they mean.
Yea! For unexpected improvements to my as-yet-unwritten lesson plans.