Saturday, September 27, 2008

How to Improve the Combining Like Terms Card Game

I recently received this comment on my original post Sample 5e Lesson Plan: a Card Game for Combining Like Terms:
Please help me understand how do I make the scores MEANINGFUL to the students at the end (other than saying that we just learned how to combine like terms). cchou1@lausd.net
This is a completely valid concern, one that I haven't addressed well enough. One possibility is to make the game a short one, playing one round only and stripping down the structure to the bare minimum. Then you immediately start doing straight practice of combining like terms during the very same class period, telling students only to follow the grouping rules used in the game, and that their answers will look like their "scores" for the game.

Of course, I don't see the world through rose-colored glasses, and I realize that idea may not be the most meaningful way to wrap up this activity. The other most obvious answer is to assign numerical values to a, b, and c and have students plug in those values after simplifying their respective expressions. I think most Algebra I teachers cover evaluating expressions for a given variable just before they move on to combining like terms, so it could be a good way to tie those two topics together. Students get a tangible numerical score, and it could help them understand the concept of variables as well.

I worry though that the evaluating approach would confuse or distract students from what they can combine and how they do so because they would be wrapped up in calculating a numerical result. Perhaps the solution is to keep the original "scores" intact and follow the game with a simple graphic organizer that reviews what they learned and connects it to the big picture. For example [with prospective student answers in brackets and italics like this]:
In this game, we learned that:

An "a" could only be combined with... [ a].
A "b" could only be combined with... [ b ].
A "c" could only be combined with... [ c ].
An "a2" could only be combined with... [ a2 ].
A "b2" could only be combined with... [ b2 ].
A "c2" could only be combined with... [ c2 ].
Numbers without a variable could only be combined with... [other numbers without a variable].
When I had a group of 3 or 4 cards, combining them meant that I had to... [add up the coefficients].
Like terms are terms that have the same [variable] and the same [exponent].
if I have like terms in a problem, I have to... [combine them]!
Finally, one last perspective on the original question. I think there's a lot of inherent meaning in this activity as is. I created the game because I wanted my students to remember what combining like terms looks like, and what a simplified expression might look like. This is why I've never assigned values to the variables. To a typical student, it is a weird, cryptic thing, all these letters and numbers arranged in this way. Our job is to demystify and decode these expressions so that our kids are not confused or intimidated by them, especially considering that they get more complex as we progress through the subject. The fact that they combine their terms mostly independently, and could complete all the statements in my sample graphic organizer above, is infinitely more meaningful and memorable than it would have been if I had done a traditional, straightforward lesson on the topic. The game, and the resulting "scores" they get are very meaningful for everything that comes afterward.

If you think you might want to use some form of this card game, please be sure to read two other follow-up posts I wrote about the game designed to make it work better in your classes:

Follow-Up: Combining Like Terms card game
Combining Like Terms Card Game Revisited

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