Monday, March 19, 2012

It's Opposite Day!

Grr, Blogger's post scheduling failed me again ... better late than never?

No, not really. Some of my students think every day is, though, finding it highly amusing to speak in opposites, so I've had enough of that.

Math is all about opposites, though. More specifically, inverses, such as inverse operations. Many of the math problems we did in school related to "undoing" something. Pretty much anything we did could be undone. (I hit some advanced math courses in college with operations that were irreversible. Most of you probably don't want to go there.)

Addition and subtraction. Multiplication and division. Squaring and square-rooting. Even all the way up to trig—sine and arcsine–and calculus—derivatives and integrals.

It's an accepted fact that mathematicians, at their core, are lazy creatures. So it makes me a little crazy when I have students who don't grasp the power of the opposite. These two things add up to 64. You need 100, so how many more do you need? Some kids will guess and check, or count up ... or add 64 to 100. (This particular case kind of goes back to my earlier rant on subtraction.)

It happens in higher math classes, too, though less frequently (fortunately). In algebra, the idea of "undoing" is huge, so when someone gets to Algebra 2 without catching that division undoes multiplication, I get a little headdesk-y. Then I teach them about it until they understand. The squaring/square-rooting dyad is newer to them, so I make sure to drill it into their heads.

And because I'm on the topic, here's a little puzzle you can solve with the power of opposites.

I have a mystery number. I divide it by two, subtract 200, square the result, multiply that by ten, and add 52, getting a result of 412. What was my mystery number?

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