linear combination

At a meeting earlier this week, some of the other math teachers were saying that they didn’t teach their kids about the LCM or how to choose a variable to eliminate when solving systems by linear combination.  I was stunned.  Instead of using the LCM, they said they told the kids to always swap the x coefficients and multiply, being sure to make one equation positive and the other negative.  Let’s leave aside the sloppiness of the language here for a minute.  I can’t really imagine using an approach geared to the lowest level students.  It doesn’t seem fair to everyone else to present material that ignores what ought to be prior knowledge, and after all “Algebra 2” means something. 

But they went on to say that students picked up on the variations on their own.

So, this is a dilemma: should I present a severely dumbed-down approach, hoping that students will make the extensions themselves, or be more comprehensive in my presentation?

If I’m serious about students deciding what and how and how much they will learn, I have to be willing to take the risk of them being lazy.  So I did that today.  The thing is that they’ve seen this before, in Algebra 1.  So, I don’t know how it would have worked with a class that had not seen the technique before.  Luckily (hah) I have an Algebra 1 class too, and can try it there later this year.

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