My first day bell ringer for Algebra 2 came from Fawn Nyugen's lovely site, http://www.visualpatterns.org/:

(Her's looks WAY more professional):
I gave the students quiet time. Then opened the conversation to the entire class:


I was a bit flummoxed when no table emerged at first. It was both WONDERFUL and odd that NO ONE after the first block class (the next 2 classes) made a table. The part I liked about the conversation was this:

Ss: I notice that the perimeter grows by 6 each time.

T: So you mean after the first term you get + 6 and then the next one you +6 again?

Ss: Yeah

T: How do you say that with your big girl/big boy pants on? I mean, if we want that to happen on every nth term?

Ss: Times Six

T: So if we said 6n, what does the "n" represent

Ss: The nth day, I mean the nth position

T: But does that work?

Ss: No! you have to add two for the ends that don't get shared.

T: So which of the various answers are now reasonable to eliminate? How can we test the answers that left ?

Blah, blah.

MTBoS, please let me know if I could have done a better job with the generalization of this pattern. What parts were good? I was completely unsure of how to end this lovely conversation. Suggestions?