Puzzle: Who am I?
I must have posted this once before, but I forget. And two classes worked this last week. And had fun. So I’ll share:
There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.
1a. I have 2 digits
1b. I am even
2a. I contain a “7”
2b. I am prime
3a. I am the product of two consecutive odd integers
3b. I am one more than a perfect square
4a. I am divisible by 11
4b. I am one more than a perfect cube
5a. I am a perfect square
5b. I have 3 digits
Can you solve this? Can you use it in your classroom?
In mine, I let kids flounder for 10 – 15 minutes (seems like an eternity), quietly dropping little hints… Finally (and finally in one class means after two kids stumbled into the answer, in the other class none had), I said “look, there’s not so many possibilites” and I began listing them (vertically):
Now, I was doing all the work, but saying it out loud, until one, then a few, then half of them were jumping in ahead of me. Every once in a while (and I created four of these, this starts aa, next ab, next ba, next bb) every once in a while I stopped and asked a quiet kid “what next?” — it’s hard to turn off teaching.
And then I asked them to start eliminating impossible variations, and they did. One class got down to 3, the other 4, and then they went back at them, with all this gained knowledge (and technique!)
I tried to keep them (fairly successfully, thank you) from telling each other the answer. And for the next two days I had a trickle of kids finding me in the hall and shouting the answer at me, excited that they’d gotten it.
If I could get the same enthusiasm for adding rational expressions….