Here's what they saw today:
I told them to break the code. It didn't take long, especially because there was a huge hint up there. But the point was that I wanted to talk about codes, encryption and reversible functions today.
After they broke the code, I asked them to explain the encryption process in terms of functions. We ended up with G(a), which takes letters and spits out numbers, and f(n), which takes a number and gives you three more than that.
Then I gave them another encryption.
This time I told them the key. It was g(n) = absolute value(n - 10).
"Wait, it could be two letters."
"It's 'HELLO' but it could've been 'FILLO'."
It's a lousy code, because it's ambiguous. The information about the starting letter is ambiguous.
The rest of the lesson was sort of lousy, with some good moments. I teachernated that if a function is reversible, then it makes a good code. And another way to say that it's reversible is that it has an inverse function. Most of the rest of class was spent trying to figure out if various functions had inverses. But there were some highlights:
- "It's only a bad code if you use all the alphabet." We talked about restricting the domain artificially.
- "So any code that has two different letters with the same number is lousy." Nailed it, kid.
But I feel like I didn't nail this lesson. The concept seems solid, but I don't think I made it really interesting or especially challenging. Any ideas on how to improve it? I'm giving it another shot next week with 11th graders.