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Nicknames for Factoring Rules

Lesson Plans > Mathematics > Algebra > Factoring

Nicknames for Factoring Rules

Who would have thought that giving nicknames to algebraic rules and methods could help students become more proficient in their work? It came about entirely by accident, rather than by plan, but my Algebra One class now has a "nickname" for most of the factoring methods we've discussed in class.

It all started when we were factoring by grouping. I did a problem similar to the following on the board:

ax2 + bx - a2yx - aby

We began by splitting it into two groups, and factoring each group:

x(ax + b) - ay(ax + b) 
(ax + b)(x - ay)

At this point, one of the students said, "Well, that was spiffy." I said, "I've never heard anyone refer to a factoring method as 'spiffy' before." She replied, "Well that's what it is. From now on I'm calling it the 'spiffy method.'" Alrighty then.

Next it was the perfect square trinomial method: 9x2 - 30xy + 25y2 = (3x - 5y)2. "That," the same student announced, "is a sweet thing." Okay. From now on I'm calling the perfect square trinomial factoring method "Sweet Thing."

And on it went. The next day while we were working a difference of squares problem, another student muttered under her breath, "This is Sparta!" Uh...okay? So difference of squares is the "sparta" rule.

My contribution to all of this foolishness was that I gave the name "DUH!" to the "factor out the GCF" rule. I named it that because students so often forget it.

As of yesterday, almost entirely by accident, and without planning it, we realized that we'd named all of the factoring rules the students had learned. Spiffy, Cutesy, Sweet Thing, Sparta, and DUH! I told them that from now on, every time we have a difference of squares factoring problem, I was going to declare, "This is SPARTA!"

All of this was ridiculous and entirely unplanned. But it's having a wonderful consequence in class: students are much more eager to spot DUH, or recognize that something they factored can be "spartaed" (yes, we turned Sparta into a verb). It has become almost a game to them, to make sure they find all the ways they can use the different rules. They now take great delight in telling each other, "You forgot about SPIFFY!"

The unplanned nature of this, I think, is what made it work so well. I'm not planning to keep these nicknames for incoming students, but next year you can be sure I'll be listening carefully for any under-the-breath muttered comments that could be turned into nicknames, in hopes of recreating the way this class has turned factoring into a game.

But I'm definitely keeping "DUH!" from one year to the next.

Lesson by Mr. Twitchell

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