- "Add four then add six" and "Add six then add four"
- "Double then triple" and "Triple then double"

- "Add four then subtract six" and "Subtract six then add four"
- "Multiply by two then divide by four" and "Divide by four then multiply by two"

ME: if 4 goes in, what comes out?

Student: 8

ME: Give me a more interesting number to put in the box.

Student: 98

ME: That is not really more interesting…

Student: 98.94

ME: OK, so if we put 98.94 in the box, what comes out?

Student: (with calculator) 197.88

ME: Give me a more interesting number.

Student: 147.324

ME: Is that more interesting?

Student: -3.24

ME: That is definitely more interesting. If we put -3.24 in our box, what do we get out?

Student: -6.48

ME: Excellent. A more interesting number?

Student: Square root of 2

ME: Now we are getting somewhere! What do I get out?

Student: Two root two (others also said things like 2 and root 8, which we discussed)

ME: Give me a more interesting number

Student: pi!

ME: Excellent. And we get…?

Student: 2 pi

Me: Is there another type of interesting number we haven't seen yet?

Student: One half

Another student: Gives one

ME: Can we make that more interesting?

Student: 17 over four

ME: Great, and what do we get?