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Some days are just good, ya know? At the end of it, when all the kids leave, you just feel like good stuff happened. Perhaps some of it was due to diligent planning, but heck, sometimes it just seems to happen. Today, it just kind of happened.

In Algebra 2 we have been studying polynomial functions; to this point we are really just getting started, so everything is in factored form. We completed this investigation (graph_polynomials) last week to introduce the students to end behavior and degree, root behavior, and general graphing (I did not create this, and have no idea where I found it. If it’s yours, shout out and I’ll credit ya. If you make it, thanks, BTW. Great job.) I got them started on Thursday, then had to be out Friday so they worked on it without me. That generally leaves me a little queasy to my stomach, but this time it worked out pretty well. When I returned on Monday, I recapped the investigation, asking them what they thought they thought they should have gotten out of the activity and, while I’m not sure any one student came out of it with everything, as a class they were able to generate the same list of goodies I would have lectured to them about. (Hallelujah chorus is playing in my mind right now).

I flashed an equation on the screen and asked them to tell me anything and everything they could about it and, again, no one knew it all, but together, they did. Instead of harping on what they didn’t get, I chose to credit all the stuff they did know, and really highlighted the fact that while they might not have known it all on their own, TOGETHER, they totally rocked. Then, we filled in this Graphing polynomials foldable. Actually I only guided them through the layout…they already knew what needed to go in it. Today, I pulled out the mega-white boards and gave each pair of students a set of equations to graph. It took them a little longer to get going than I expected, but once they did, they took off with it. I was able to get around to the students who needed the most help, and the others really communicated well and worked through the process together. I heard great conversations about finding x-intercepts, knowing how the ends were supposed to act, and putting it all together to come up with a complete graph.

I guess the real test will be tomorrow when I ask them to do it on their own. For now, I’m just going to enjoy what appears to be a successful set of lessons. Now, to figure out how to get from real roots to complex roots and standard form…the challenges never end.

Oh, and we got to throw inflatable globes at each other in AP Stats class. Yep, today was a good day to be in room 413.

Fawn Nguyen

said:I needed to read something positive tonight. And I’m glad I found it in room 413!! Go, Rachel!! May tomorrow be even better.

Emily

said:I am a little late on this post, but I have a class that is going to start graphing polynomials on Tuesday. They have a quiz Monday over classifying, adding, subtracting, multiplying, factoring, and dividing polynomials. They are not at all firm on the idea of relationships between factors and zeroes, even though we have talked about it in relation to quadratic functions. How do you suggest I proceed with the investigation you gave here? I like it…I am just unsure how to do it. Also, can you give me so details on how you filled in that foldable? I like it but I’m not sure what information goes in it. Thanks!

rachelrosales

said:I just gave them the investigation and a calculator and had them start graphing and filling in the chart. They seemed to catch onto it all pretty quickly without much guidance from me. The payoff was when I started making a list of all the stuff they though they should have learned. Amazingly the group as a whole gave me every single thing I would have lectured over (how the graph behaves at the roots, how the ends behave, how it all connects to the degree, etc).

For the foldable, T: tails (how the end behave based on the degree and the sign of the leading coefficient

I: Intercepts (we found all the x- and y- intercepts)

RB: Root Behavior (we used “pass through” for linear factors, “bounce off” for all even power factors, and “squiggle through” for all higher order odd factors)

I hope this is helpful. Holler back if I can offer any more help. Good luck to you!