This has been such a crazy week. From tons of students re-testing and being displaced and floating, I am surprised I have any hair left. I disappointed my students by our continued work in practicing factoring towards solving quadratics. :-) "Why yes...I DO have work for us..."
In interest of looking at the flow of my lessons differently, it has been interesting, With our Algebra 2 team, we have always talked about properties of parabolas, refresh factoring separately, then start talking about solving quadratics with the factoring. I have tried to keep the emphasis throughout the entire unit on the critical points on the parabola and ways we can find them. I have been working heavily with multiple representations and factoring in context of solutions as x-intercepts.
I know for many, this is a no brainer. But looking at how we were teaching and the disconnect between the major ideas we try to weave in isolation.
So, today I started with this question: If the solutions of my parabola are 3 and -2, what is the equation? Of course this was to tie in applying what we had been learning upto now, We discussed how we can take the factoring and solving ideas to re-create the equation. How does the graph look? What is the minimum value?
The activity that facilitated the discussion I had was this: each group of students were given a problem on a quadratic (either an equation, a description of the solutions, or a table) and were asked to show the solutions and vertex from the equation, a table where they were to show the vertex and solutions (labeled), and the graph with the pertinent information. They were to show the work on grid poster paper. So far, it looks promising.
My goal is to keep all of this tied together and not about one representation without the others. I am trying to look at how to teach the skills with the context of why we need it. Maybe this might not seem like much...it is just what is coming from the mind of a quarky math teacher, :D
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