XVII + XII = XLV
Pretend these are all toothpicks. Or matches, or pencils, or whatever. Pencils worked for me, because I had 20 of them a lot of counter space.
I also wrote it on the board. I told the students they could think about it for 2 minutes at the beginning of class, and 3 minutes at the end. If nobody gets it, I’ll tell you the answer. I said “Move 4 pencils to make it a true equation.”
First 2 minutes went by, and they legit wanted to know the answer. No deal. “You’ll have a few minutes at the end. If nobody figures a way, I’ll show you what I came up with. But only if it’s a good class.” It should not be surprising to me at all by this point in my young career, but hook ’em and they’re yours for the class. It was
probably the most productive day I’ve had in a while.
But anyway, the end of class came, and they were watching the clock like normal, but they didn’t try to get up and line up at the door like they normally do. They got their papers back out, or arranged pencils, or started talking to each other, or got up and started drawing Roman Numeral equations on the board. Some creative ones (but I had to deflate the ego a little bit…I said equation, not inequality) moved the = to a > or < symbol…so it was true, but not an equation. Or, moved one of them to have one pencil become an equal-sign transversal. So the two sides are not equal to each other. Good thinking guys, but still not an equation. So I showed them mine…
X II + X V I I = X L V ===> X X + X X V = X L V
12 + 27 = 45 becomes 20 + 25 = 45. Hooray, a true equation.
‘Twas a good day. I’m starting my resolution early.