It's that time of the year in algebra, and I'm processing the right sequence that works for me on how to teach this. I have block classes, and even though that seems like, "whoa! 1.5 hours! You can cover HEAPS." It turns out that this is still a multiday process for me. Here's what I've done so far and where I'm going.
Previously on As the Algebra Turns:
Quadratics bla bla bla
Factoring bla bla bla
Finding Zeros of Quadratics by factoring
Linking Zeros of equations to graphs of parabolas.
TEST on some stuff
START of our Program:
Day 1: start the class with reviewing one problem of finding zeros by factoring and link it to the graph. Start them on the 2nd problem of trying to find the zero by factoring, and BOOM, falls apart. Ask them if they think this means it DOESN'T cross the x axis. Show them it does but the numbers aren't "nice". Show them a slow step by step process of how to use the never-fail quadratic formula to solve. Have time for 1 "nice" problem.
HWK: can't involve simplifying of radicals (haven't done that yet). Can't have the equation in a weird form yet ... must be in ax^2+bx+c=0 form.
Day 2: now they have a reason for simplifying of radicals. Spend most of the period on simplifying (just the stuff they need for the quadratic formula). Then have time for one quadratic formula problem where they solve AND simplify. I also threw in a problem to solve that looked like: ax^2 + c = bx to get them used to this.
HWK: mixed radical problems (some with and without denominators) and some quadratic formula problems.
This is where I am so far.
Now I'm thinking, they need practice of both radicals and more quadratic formula. I still want to link it to the graph. I'd like to throw in some word problems. I'm probably forgetting something, but that seems about it. So, sheesh, 4 block days on this. Why am I stressing about that? Better to do it well than just to rush through it. .... I guess I'm stressing because I still have/want to cover: more radicals (adding multiplying...), Pythagorean theorem use of radicals and to refresh their memory, midpoint and distance formulas .... more geometry and radicals. Will I have time for rational expressions?
Stay Tuned for the Next Episode.