I'm going to talk about the first day of "actual" class in my classroom. The first day of school we have limited time in normal academics as we do a "student inservice" where the kids learn about the school, discuss our core values, and such.
I start the first class by getting the kids up and moving around by playing "vacation human bingo." We spend a lot of time playing games and doing activities that involve getting up and moving around in my math class so this is a good introduction to that. This is a "get to know you" activity where students go around and ask each other to sign their bingo board under a category that they did over the summer (such as visited three other states, etc.) Each student can only sign another student's bingo board once so interaction with many different people is encouraged. After a short period of playing time, we sit down and go over our boards. This provides even more of a chance for the kids to get to know one another. Next I go over class expectations, unit of study, my grading policy, etc. Since we are a 1 to 1 school, I share this document containing much of that information with the kids (and their parents) before school and ask them on this first day if any of them have questions about what math will look like. Then to wrap up I've begun using an activity I borrowed from Lisa Henry (@LMHenry9) where I give the students a bunch of numbers (32 to be exact) and sixteen things about me (such as number of siblings, number of my house, year I graduated high school, etc) and have them guess which ones go where. As I walk around, I get a little feeling about the kids' ability to estimate and reason when they guess at what year I was born in (no, 1905 isn't correct!) Finally I end the first day by assigning the first homework assignment. I ask students to write about themselves in a million words or less (I borrowed this from Paul Bogush, @paulbogush). We being school on a Wednesday so I make this assignment due the following Tuesday (thereby giving the students some time to think and actually write about themselves not just rush through.)
Overall, I like how the first day runs. It gives the students a good idea of what math class will be like plus they get to play with numbers a bit too. I'm looking forward to seeing some other ideas that I can "borrow" as well.