For example, I make a really big deal in my classroom about the fact that we cannot divide by zero. We talk about how if I had 10 pieces of candy, there is no way that I can divide them between 0 people. It's just not possible. I guess I tend toward the dramatic side. "Guys, if we divide by zero, the world will explode!" Now, we don't want the world to explode, so we will never divide by zero, right?
At this point, one student usually raises their hand to ask if the world will *really* explode. This is usually the point in the conversation where I ask them to type 10/0 in their calculators. Half the class is usually convinced that 10/0 is actually 0. They type it in, press enter, and stare at a lovely error message.
Wait! My calculator says error. Mine, too! Guys, remember what I told you? If we divide by zero, the world will explode. Our calculators are smart. They know this. They don't want the world to explode, so they give us an error message instead of performing the calculation that we asked them to.
I remind them of what Slope Dude says when he skis off the cliff: UNDEFIIIIIIIINNNNNNED! The cliff has rise but no run. Therefore, the run is zero. He tries to divide by zero, and he dies in the process.
After again acting out Slope Dude's demise, a student raises their hand and kindly asks me to watch my language. "Ms. Hagan, is that language really necessary?" Oh, wait. I guess "undefined" is the worst curse word ever in math and in algebra.
Of course, I still have tons of students who rewrite anything divided by zero as zero. But, some students do listen. I was reminded of this fact when grading papers recently.
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| "Don't want world to explode." - Undefined Slope |