...or Quadratics Unit (continued)
So once we got all the graphing out of the way, it became about solving quadratic equations. We took a lot of time developing the concept of being able to identify key points/characteristics of a parabola by examining the two forms of the equation. (ie. Graphing (vertex) Form and Standard Form)
The one thing that isn't easily identified by examining either equation is the x-intercept(s). So we started solving quadratic equations. We got out of sync really quickly, though. So I threw out a tweet asking for what you all had in regards to solving quadratics and Sam shot me this.
So I took Sam's hard work and re-mixed it to fit what my students need and came up with this (and the corresponding Notebook file). Most of Sam's problems were perfect so I just added a little to bridge the gap between what we had already done and where we were headed.
This "Quadratic solving" boot camp lasted three days and culminated with the kids deriving the quadratic formula. Realistically, I would have about four or five students who could actually derive it. The rest can follow the steps, which is what they will be expected to do on our CST's.
(the quadratic formula derivation is part of the Notebook file above)
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2 comments:
I love the video. I especially like that the students were clearly looking at the steps and trying to make sense of what would come next. One person wasn't doing all the work...they were checking each other and making corrections as needed. Awesome.
Have you seen a geometrical approach to completing the square like this one:
http://www.helpalgebra.com/articles/completingthesquare.htm
I think it is much better motivated, and once students get good with it they can prove the quadratic formula themselves. It is also great because you can try to have the students come up with the fundamental insight of cutting the rectangle in half.
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