We've been solving quadratic equations in my Math 3 classes for the past couple of weeks.
After starting with solving by factoring, I segued into radicals, completing the square, and quadratic formula (with a detour to show graphing).
(The word segue looks so weird.)
I've been very careful to emphasize the choice that the kids have to make when solving and haven't told them when to use which method. (Except for last night's assignment on the Quadratic Formula, when I wanted to make sure they used it for practice.)
Today's work was a chart - the kids were given 16 quadratic equations and told to assign 4 to each of our 4 solving methods (then solve 2 of each). I really wanted them to think about how to solve each one.
And you know, for as much as kids want to complain that they don't get a choice in life, they don't like it. They want to be told what to do when (wish my kids at home were like that!). They want to be spoonfed, and I'm refusing to do that. I want them to be able to rationalize which method makes the most sense, and if they use the quadratic formula on an equation that will factor, so be it.
I'm hoping that will work out better for them (and me, honestly) in the long run.