What should the first day of school look like?

OR....What should the first day of school NOT look like.

I promise I will not:  read through the syllabus
I promise I will not: lecture on day 1, not even rules!
I promise not to waste any time assigning seats.
I promise I will not:  give a written assessment of any kind, not even an evaluatory/prescriptive one

I promise to:  DO MATH
I promise to:  make the kids think
I promise to :  DO MATH
I promise to:  challenge the students in an engaging fashion with something they can find an entry into which may or may not tie into something they might see again in class.

I have a hint at what I'm teaching, my letter of guarantee of employment for next school year only said that I would be a math teacher at (XXX) High School.  (my certifications potentially allow me to teach math or ELA at middle or high school).  I did speak to an administrator who did say that as things were (at the time of the discussion) that it was likely I was teaching Algebra 2 and Statistics.

In my school, Algebra 2 can be a class Freshmen are placed into, and I know I had a couple classes last year (I also taught Alg2 then as well) that were primarily Freshmen.  I, actually won't know who is in my classes until the weekend before the first day of classes.

I want to start off with an activity like 4-squares, as mentioned on Mary Dooms blog (July 1st, 2013).  I will have my desks set up in pairs (33 kids per class, 15 pairs and 1 triple).   I want the students trying and sharing with their partners and then discussing with the class.  Then I want a meatier challenge.  I'm currently leaning towards Matt Vaudrey's Mullet Lesson (The only lesson they'll remember).  My goal isn't evaluation, its setting a tone of exploration and risk taking with the math (in a fun way).  I've got to speak to a couple of my colleagues about having prepared measurement cards and being willing to have their class interrupted to give them out.

I have 73 minutes, so I'm thinking I can at least get through enough of the mullet lesson to make it interesting.   I'll let the lesson spill into the next day just a little, even if only to get them writing about the thinking process.  (besides, one of the two days we'll be getting books - sad when I barely use them except for homework).

What goals do other teachers have in their lessons for the first day of school?  I remember only 1 such lesson from my high school years (too long ago...).  This particular teacher came in, had us write on the first page of our notebooks 3 pieces of information:  a date, a phone number and Peanut M&M's.  (his birthday, his phone number and his favorite candy.     He got bags and bags of them on that date. Maybe he was onto something...