Polynomial Sense

In math 3 we’re talking about polynomials, their degrees, and what it means to have imaginary solutions. We just finished doing a ton of work on adding/subtracting and multiplying/dividing complex numbers. I’m feeling confident that if I gave them a page of “multiply these complex numbers” problems, they would definitely know to distribute the real and imaginary parts. Most would draw the box (honestly, I still always use the box). The difficult part is definitely multiplying individual numbers – they know they have to multiply 2i x 4, just not necessarily what it is. To practice, I adapted this game, but made it about 16 times more complicated. I got four 8-sided dice from the RPG club adviser, in different colors to represent positive imaginary, negative imaginary, positive real, and negative real numbers. We soon realized that it would be extremely difficult for anyone to win the game as it was designed, so we improvised.

dice game

This week I showed them second, third, fourth, and fifth degree polynomials and asked them to describe the pattern.

polnomial pattern

Then I told them something like this had 2 imaginary solutions and asked them how they knew:

degree 4 rereimim

That’s not the actual one, but one that was on the very conceptual handout I gave them next. I’m attaching it in case you’re interested. It involves some writing. Click for pdf: matching polynomial equs

I’m realizing we are way ahead, and I’m not sure how I feel about that. I guess I could decide it’s definitely a good thing, because they’re all doing well on assessments and seem to be grasping concepts. I could also decide it’s a bad thing, that we’re rushing through material and not delving as deeply into it as we could. In any event, I’m taking advantage by re-including some polynomial standards I initially rejected because of perceived time constraints. I’ll be doing polynomial long division next week – let’s see how it goes!

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