A week ago I had plans for Precalculus. I liked them alright, but I felt they could be better so I did what I always do when I need my brain to percolate over ideas: I start catching up on my reader. I ran across Jason Buell’s post about the IMPROVE model (you should go over there to read the details of that model if you’ve never heard of it). I then scrapped my plans and started re-writing them. That was Sunday night. *shakes fist at Jason and his inspirational posts*

Before we get into the week, let me be the first to say that I have no grandeous dreams of students going forth into the world and using their ability to long divide polynomials or sketch them from factored form by hand. Polynomial Long Division (henceforth referred to as PLD) is a way for me to do the following:

1. Check on and improve student ability to add/subtract positive and negative numbers as well as distribute them

2. Improve mathematical endurance (why yes, those last two problems may take up a whole page each)

3. Improve student understanding of how the equation, the factors and the graph work together with higher order polynomials

4. Create an opportunity for my studens to feel like mathematical Rock Stars

Let me explain that last one. It goes back to my drive to help students see themselves as being ‘good at math’. PLD is impressive looking. I mean, really impressive. Especially when you start with a 5th degree, have students figure out the zeros, create the factors and then do multiple rounds of long division in order to come up with the factored form which they then must graph by hand labeling all intercepts. Then they can check their work with the calculator. Yay for instant feedback.

At the start of last week the kids had only worked a day or two with PLD. By then end of the week, with some group assistance, they were all working through these massive problems. They’ll whine that the problem’s huge and takes up too much space, but they’ll do the whole thing and then just kind of sit back and stare at it with this look of ‘did i actually just do all that!?’ on their faces. There were lots of “got it!” mumblings while they worked. It’s not the crowing cheers you get with, say, WCYDWT problems. I liken it to the satisfaction of a job well done. Because what is the true hold up for a lot of students in math? The concepts, or the grammar? Is it that the kid can’t understand what’s going on, or that they are so hung up on the symbols and the difference between coefficients and exponents and plus’ and minus’ that their brain is spinning? I think it’s the latter much of the time that shuts off the student mind.

So here’s the worksheet given out to each table group. I put them in a plastic slip so the four students in each group would have to share. Maybe even, I dunno, *read* a problem to the group. Work *together*.