## Polydoku!

08 Dec

I’m trying out CPM’s Algebra 2 book and so far it’s pretty much fantastic.  I don’t want to give away many details of the lesson plan I used today, since they asked me not to reproduce it.  But I have to tell you about the basic mechanic: polydokus.

A complete polydoku has 4 main sections – one for each of two polynomial factors, one for the product of said factors, and another area for the work.  You can figure it out from this already-solved puzzle:

Of course, much of this data is redundant.  Try your luck at this unsolved puzzle:

These puzzles are fun and satisfying.  I tried it in class today and students had the perfect amount of difficulty with them.  I explained the puzzles only as much as I explained them here, and the students seemed to enjoy figuring them out.

The payoff comes in when the puzzle looks like this:

Have your kids solve this polydoku, and then ask them, “Hey, by the way, what’s ?”

The CPM lesson went on to have the kids discover remainders, and even connected it to the factor theorem for finding roots of an equation, but I’ll let you ask CPM about that.

You know who’s a polydoku convert?

[pointing emphatically at myself with my thumbs] This guy.

1. December 8, 2009 at 3:46 pm

That reminds me of these: http://illuminations.nctm.org/LessonDetail.aspx?id=L798

That page just has numbers, but the associated documents have variables too.

• February 1, 2012 at 8:56 pm

I love poly-doku. I thinks its the best way to connect operations with integers and factoring. But for some who are still struggling with both topics, I guess there is really no royal road to math. Just trea it like ‘DOTA’ …” NO experience, NO skill.” Keep it up!

2. December 8, 2009 at 3:50 pm

The grid pattern for the distributive property is really brilliant. You could teach multiplication this way too, with 1s, 10s, 100s places replacing 0th, 1st, 2nd degree places.

Too bad those bags of fluid look totally gross!

3. December 8, 2009 at 7:51 pm

I think they are supposed to be rocks, or bones, or something. Wait, bones is gross too.

4. December 31, 2009 at 2:38 pm

Yes, you can teach multiplication the same way–that’s basically what lattice multiplication is.

5. June 16, 2010 at 4:12 pm

Curios, how do you deal with polynomials with missing terms?

6. June 5, 2011 at 4:45 pm

My terrible Algebra 2 teacher taught me with this equally terrible book: tell me, why is it that the Guided Practice section doesn’t help me ONE FUCKING BIT? And how exactly are we being “taught” when the first questions we get only give the final term, which is usually a 4th degree/5th degree polynomial with no other information? Long Division > Polybullshit x 10000000. Yeah, everyone using this book or even just this stupid method is fucked for life.

• June 6, 2011 at 11:04 pm

I’ve taught this method and I liked it – after years of using area models to multiply polynomials and factor polynomials, my students quickly figured out how to use an area model to divide polynomials. Had I tried to teach them polynomial division using long division or synthetic division, I wouldn’t have had the advantage of building on the same models and methods they’d been using since Algebra I.

That said, I was a little uneasy about CPM’s presentation of this method as “polydoku,” a game. I was afraid that some students would interpret this “game” as some sort of mathematical trick that wasn’t “real” mathematics. I don’t know — maybe this is what happened in your classroom, or maybe your teacher hadn’t helped you and your classmates grasp a greater understanding of the area model and why it works.

Regardless of the reason, it sounds like you’ve found a method (long division) that works for you, and that’s what counts. Congrats!

• June 7, 2011 at 5:15 am

You’re frustrated with this book. You’re frustrated with this teacher. I’m so sorry. I often struggled with my math classes, textbooks, and teachers too. What kind of options do you have to get help?

7. June 6, 2011 at 9:52 pm

My kids call these the “magic box method.” I like the connection to sudoku, though, to make it a bit more of a game.

For missing terms, I suspect you’d put 0x or similar.