Too easy an algebra bonus? (smile)
Credit and bonuses get people’s attention, right? So here’s a twist (in a sort of boast-y post. Forgive me):
In my freshman algebra class this year I did not teach factoring the sum of perfect cubes. We had a good flow on trinomials, it took some struggle for the last few to master it, etc. I did assign exercises (multiplying to get sums/differences of perfect cubes) at the challenge level that could have made a connection, but the kids that chose those problems did not follow them up with board work, so I assume the connection was not made.
Anyhow, I’m thinking, aha, that would be tough as a bonus, if only a portion saw the reverse. But they can all divide polynomials, even if that is a harder topic, right? And dividing with missing places… hard, right?
So, I give a few hard bonus questions, 2 points each, and then the 2008 challenge. The first bonus:
Divide
OK, I know that this is not that tough for you or me, that I could have chosen more “interesting” coefficients, but still. Half the class picked up those 2 points, including a girl who freaked when she saw long division on the board one month ago, because she had never seen it before (with numbers, not polynomials) in her life.
JD2718 
i suppose it’s *possible* to be “too easy” ..
but instances are seldom observed in the wild.
i *used* to tell beginners to multiply out
$latex( {{-1 + {\sqrt3}i}\over2})^3$
(ooh, gosh-wow: a complex cube root of unity!).
but nobody could ever bloody do it.
so *now* i have ’em do
(s if “factoring out” the 1/2 isn’t *obviously*
the right thing to do to get started)
and at least some small fraction of the class
is able to work out all the details.
that bad code sez
but i actually *meant*
My attitude is that you will at least attempt more challenging manipulations, and that if you cannot perform them, you will follow as other do. But the attempt is required.
Today, first day back since the exam, I taught factoring a sum of cubes (and then pointed out the relationship to the bonus question), and I also taught factoring things that look like:
I know that not everyone will be able to handle the 2 or 3 examples in the homework, but all of them need to try.