How Did This Happen?
Never thought I'd append "wiki" to a post, but here we are. Here, approaching the dead center of August, I'm getting Google hits along the lines of "first day geometry lesson" and I don't have content to show for it.
So I'm posting some of my first day procedures, which are by no means authoritative1. The comments section of this post seems an inadequate container for all the first-day wisdom you all have, so I'm going to encourage you to add on to The First Day Wiki.
Here's my contribution, both for general ed and for math classes:
If you've gotta do a syllabus, do it different from their other classes. Six classes of the same six-page packet detailing the same rules, expectations, and standards has gotta numb a kid by the end of the day. Hell, it numbs me.
So sketch out what you want to talk about on one page. Omit crucial words or numbers and then let them fill 'em in. Nothing earthshattering, certainly. You're still talking but they get to build a document, which is different enough to count.
and then what I read from:
You can have some good times mid-year by showing student self-portraits to the class and asking them to identify the student by her roughly drawn outlines.
You buy some styrofoam cups. Lots of 'em. After you have the class organized so you and they are comfortable (after seating arrangements but before any syllabus discussion) you get 'em in groups with those around them.
You say, how many stacked cups would it take to reach the top of my head? You hold one up.
You take bets from the groups. Betting is fun. You write down the bets. You make sport of the groups who wager only one above the previous group's wager.
You say, alright, we're gonna figure it out now and if anyone gets close to the answer, we'll cancel homework for the first night. Of course, you weren't planning any homework anyway, but they go nuts.
(Depending on the age, there's also a great discussion to be had here about how "close" is close enough. 5% error? 10% error? What does x% error even mean?)
You pass out a ruler and three cups to each group and you facilitate. You wander around. Ask them how they'll do it.
They'll ask you how tall you are. (Big helper: use centimeters.)
Many will find the height of the cup and then divide it into your height. Have them stack that many cups and watch as it doesn't come close. Have them discuss why.
The question to ask is: if you add one cup to the stack what happens to the height of the stack.
You should hover your group interaction around the idea of slope and y-intercept. The slope here is the lip of the cup: how much the height increases every time you add a cup. The y-intercept is everything that isn't the lip (the base). Your equation is:
You don't need to take them into detail on the equation. This project has been done — first day! — with younger crowds.
At the end, you actually stack the cups high and see who was closest. Maybe pass out candy. Cancel the imaginary homework assignment. Maybe hold up a different brand of cup, one with a thinner lip and ask what would happen.
So you've collaborated, done some project-based learning, tackled a challenging problem together, joked around, become acquainted with some students. The syllabus, the rules, the standards, you can always go over those another day.