The constant

Functions are as reliable as a cookie.
The scene: yesterday at my 4:30 tutee session.
The topic: functions.
The set-up: To CFU (teacher term for "Check For Understanding," I ask a lot of seemingly obvious questions. Well, obvious to you and me, but not necessarily to the student.

Me: So, when y=10, and x is something else, y is still 10. What do you think y is when x is 1?

Student: ::pauses to think (another teacher term! "Wait Time!" and I give A LOT of wait time to this kid:: x is 1?

Me: Yes. If x is 1, what is y. Remember that our function is y=10 now.

Student: Y is....ten?

Me: Yes! Why is y ten?

Student: Because the function rule says y=10.

Me: Correct. Now, if x is 100, what is y?

Student: .....10?

Me: Yes! What about if x is 1000?

Student: Ten!

Me: You got it!

Student: And if x is a million, y is....ten!

Me: That's right.

Student: Oh! Y is ALWAYS ten because y=10! I get it! If x is ten million, y is ten! If x is a gajillzion, y is ten! If x is a hundred thousand light years trillzilion, y is ten!

Me: Um, sure!


Lightbulb moments are great, aren't they? And yes, my student did actually say "trillzilion."