# Put The FOIL In The Recycle Bin, Please

by on December 5, 2011

That’s it. I’m done with FOIL. Now and possibly forever, unless someone like Alfie Kohn or JD tells me otherwise.

At first I didn’t have a horse in the race. I mean, who cares so long as kids can multiply binomials right? If they get it one way or another way, then they’ll get it and that’s great. So what prompted me to dump it altogether? After school, two of my best students decided to annoy me about their grades after school. They got on my case so much that I said, “You know what? Fine! I’m gonna see if you can do this!” After having taught them how to multiply monomials and binomials in any order, I gave them a product of two binomials like this: (3x² + 5x)(14x³ – 17x + 12).

One of the kids said in her sweet voice: “Mr. V, we’re just KIDS!” I cracked up and said, “Try it!”

Sure enough, they got to plugging away. They started to multiply the binomial with the trinomial as if they had seen the problem before. I couldn’t believe the gall. Then, they saw the FOIL instructions written on the board from my math colleague and laughed. “Yeah, that’s confusing, Mr. Vilson. If you taught it like that, we’d never get this.”

Eureka!

For those who forgot their 8th and 9th grade math classes, FOIL is a precise method for multiplying pairs of binomials using a handy acronym that, unabbreviated, tells you to multiply the first, outside, inside, and last term in each binomial. Before I dump it into the recycle bin, it’s good for a few reasons:

1. It follows along with the uber-cool acronyms and mnemonics we have for different processes, most popular being PEMDAS.
2. It’s easy to remember.
3. It’s about 80% fail safe for its intention, meaning that teachers who don’t know math or are just picking it up for the first time can teach it readily.

I started looking at the curriculum map we developed in hopes of remembering what I’ve taught / learned for the last 6 years that I’ve come to this point. Multiplying binomials (and factoring) is difficult to teach if you don’t get the concept entrenched within the first few days of the topic. I almost fell into FOILing until I realized my planning simply didn’t allow for it. I was already thinking about the training I received on math pedagogy. I’d like to at least assure the teacher after me that I prepared my students to the best of my ability without using too much rote thinking.

After doing a bit of looking at my lesson plans and digging through the oft-maligned IMPACT textbook, I realized that the best way to multiply these polynomials with a geometric model. Even if the figures aren’t drawn to scale, the way kids can visualize that x * 3 can’t be x³ or the difference between 2x and x² is crucial to their understanding of algebra.

But what are we going to do with (the very specific case of) multiplying binomials with other binomials? Oh right: we use the distributive property and treat it like everything else, meaning we’re going to “pass” each term in the first polynomial to the other terms in the other “-nomial” with operation of multiplication, ya dig? So, no matter how big the polynomial, the distributive property of multiplication works. It’ll take some time to adjust for all of us, but that simple tweak, if done well, can yield a good chunk of understanding for our kids in math.

Anything to clear the mess out and keep the algebra crystal clear.

Mr. Vilson, who officially does not run an edublog …

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{ 5 comments… read them below or add one }

David Wees December 6, 2011 at 12:39 am

I started using the distributive method as my only method for teaching multiplication of polynomials, after having attempted to use analogies related to archers and castle walls, etc… It works, provided your students still remember long multiplication (which by the way, I review briefly before I teach multiplication of polynomials), and it is much more understandable conceptually than FOIL.

Susan Klonsky December 6, 2011 at 7:34 am

Don’t worry… It will be much easier to teach these skills when you have 63 kids in your math class.

Monise December 6, 2011 at 1:36 pm

I am a nerd. FOIL is the first thing I think of when I see binomials. Guess I had some pretty cool Math teachers too:-)

Whit Ford December 6, 2011 at 8:57 pm

Amen. I have been helping students move away from FOIL for years, and came up with FFFT! instead. While it usually gets a laugh, it seeks to drive home the distributive approach: http://mathmaine.wordpress.com/2011/12/06/multiplying-polynomials-and-ffft/

Tyson Spraul December 6, 2011 at 9:31 pm

The geometric model of multiplication + distributive property is the primary way I teach multi-digit multiplication to my 4th graders. We call it the “box method” in class, but I guess the Brits call it the “grid method”. It’s seems to be much less confusing for kids than the U.S. Standard Algorithm, and develops a better conceptual sense of numbers.
http://www.primaryresources.co.uk/maths/powerpoint/Multiplication_gridmethod.swf

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