I, apparently, need a new schtick. Today I was doing the old, "What's the diagonal of a 1x1 square?" Students diligently think about pythagoras for 10 seconds, with a few misguided shouts of "1! 1 and a half! 2!" and settle on the square root of 2. This is right after we talk about what square root means, how it's the opposite of square, how "radical something" is "what times itself is the something".
So I say, "ok so what's the square root of 2? what times itself is 2?" Blank stares. Lunges for calculators. "I SAID NO CALCULATORS," I say.
A few speak before they think and say, "one", "one half", "four halves", but realize those aren't going to work before they get all the words out.
"One and a half?"
"OK", I say, and I diligently write on the board 3/2 times 3/2, which gives us 9/4, which we all see is more than 2.
"Hmmm. Must be less than one and a half."
"One and a quarter!" We figure out that one and a quarter is 5/4, and I write 5/4 times 5/4, which gives us 25/16, which is obviously much less than 2.
"one point four?"
"OK", I say, and start writing, to which the kid says,
"Well obviously that's not right because you wouldn't write it down so quick. When I'm right you always say 'Are you sure?'"
That little snot.