Sunday, January 22, 2012

FOIL, Factoring and Quilting

I've spent my whole long weekend (Thursday, Friday, Sat and Sun.  We got a day an a half off due to rain.  I'm feeling guiltily giddy at having so much time to prep and to play) working on my next algebra 1 unit.  I've specifically been thinking about how to introduce FOIL and factoring.  I don't like the acronym FOIL very much either, but it is a better name than "multiplying binomials."

I've been trying to come up with a new way to introduce it.  I've played with using algebra blocks and I like the connection to area, but I find them a bit unwieldy.  The last two years I've just introduced it using this solid worksheet I found online somewhere (but I can't remember where.) Intro to FOIL Guided Notes I think working through this worksheet with my students has gotten the job done, but it's a little bit dull and unconnected to reality. Why would we be trying to find the area of random rectangles that we don't actually know the dimensions of so we have to write the dimensions as x+2 and x+3?  I know it's just a way to introduce the logic behind FOIL, but I find it a bit unsatisfying.  I do think it does a great job of showing how  and why the process works and my students have enjoyed learning FOIL this way.

So I threw together some ridiculous replacement activities modeled on this worksheet and on algebra blocks.  Mostly, I am just trying to give a tiny bit of context and some humor and silliness to this topic.  I may, though, have just confused the point.  The beauty of the above worksheet is  its simplicity and what I've thrown together is much more complicated.

I thought I'd start with the following algebra blocks that I made myself: Algebra Tiles for Teaching FOIL V2 I'd let the kids cut them out and play with them a little, then I'd have them work through the following "quilting activity" in pairs.

Algebra Tiles for Teaching FOIL Quilting Ws I've already changed the third rule of quilting to "all quilts must be formed with exactly four rectangular pieces of cloth" because I realized that without this rule, the kids would probably get pretty confused.

The purpose of this is just to try to introduce them to the idea of having rectangles with dimensions that have variables and to see if they can intuit FOIL for themselves.  I would follow this activity with a more conventional multiplying binomials lesson with some notes and some homework.  I'm unsure about this lesson.

The advantage is though that I was able to make a follow up activity for when the students start factoring that follows the same pattern, so doing FOIL this way, then factoring this way may help students connect the two processes with one silly context problem.  Here's the factoring worksheet: Algebra Tiles for Teaching FACTORING Quilting Ws I think I like this one a little bit more than the first one, but I'm still not sure if this is the best way to go about teaching these two topics.  Oh no, and I just noticed on the last page I put it's, not its.  I like to have correct grammar, I really do, but I can't hold good grammar and math together at the same time.  I'll go fix it on my originals...

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