For them, its a game-show-style guess-the-number game.
I want a fun prize for the winner, but all I can come up with is a couple of quarters. That will have to do.
Before class, I write a bunch of numbers on this board and cover them with index cards. I'll even give a hint about the first two.
The students are totally into it . . . 2! . . . 3! . . . 6! . . . 1! . . .
Someone decides to try negatives . . . -1! . . . -2!
Finally, someone else tries 0.5. . . Fancy. But wrong.
I let this go on for a bit.
Then I break the bad news. Sorry guys. It was 6000 and 1/1000. Better luck in round 2.
And there are more guesses . . . 1! . . . -1! . . . 12!
Someone is on to me . . . "Guys, this could be ANYTHING!"
So you give up? It was 58 and 1/58. Okay, on to round 3.
At this point I am expecting all hands to go up. In a perfect world, everyone would want to guess zero! Right? Wrong.
That's where I am surprised. One lonely hand goes up . . . Zero? He asks hesitantly. My first two examples raised enough skepticism that students are sure there must be a catch.
This isn't how it worked in my head but that is okay. I can adjust.
Is Tyler right? Can we know for sure that one of the numbers is zero? Discuss at your tables.
I walk around and listen and most seem to be figuring it out. Someone suggests 5 and -5 but quickly realizes that won't work. For those who aren't convinced, I challenge them to come up with a number other than zero that will work.
We conclude that Tyler is right and move on to the final round.
Not exactly. I tricked you this time by using variables. But tell me what you know . . .
"x minus 3 or x plus 2 equals zero".
Yep. That is all.
P.S. Next time I am giving everyone a white board to write down their guesses for each round. I had a lot of participation, but definitely regret that I didn't get a response from every single student.