A little math magic
“Think of a number” I tell the kids, “and don’t tell me it. Make sure it’s not too big, because you need to do some math with it.”
“Now square your number. You have a result?” I give them a moment, actually after each step. There’s no sense in leaving anyone behind, even the easily distracted. “Take your whole result, and throw it out, except for the rightmost digit, the units digit. Everyone should have a one digit number.”
“Now take that one digit number (everyone has a one digit number?) and square that. Once again, throw it all out, except the rightmost digit. Now, take that last one digit number, and multiply it by your original number.” Fussing with paper, a few calculators… And I ask them one by one what their final result is, and tell them one by one what their original number was.
- “71” “Your number was 71”
- “72” “Your number was 12”
- “75” “Your number was 15”
(more below the fold –>)OK, obviously there is a trick, and they knew that one existed just as well as you do. Still, they played this morning three full rounds (and I got one number wrong, and caught 2 kids who flubbed the arithmetic). And after watching, they hadn’t broken the “code.”
So their assignment (and yours, if you like) : Try this game with a bunch of numbers, starting with 1. I suggested that by 20 or 30 they should know the “rules” to teach someone else to be the mathematician. And I offered a little extra credit. I will report back at the end of the week if anyone did it.
Frankly, I think I could do this with younger kids (these were 9th graders). What do you think?