## Thursday, September 2, 2010

### My first day

It's taken me a little while to find the time to post this, but I wanted to post my first day experience.  Why?  Because it's great to be back!

The context
* 6-12 all girls independent school
* 1:1 laptop school (starting this year)
* 16 students in each class
* 4 desks of 4 students each
* 4 classes of 6th grade
* 50 minute period 3 days a week, one 75 minute period per week (staggered by class)
* most all students have (so far as I can tell at this point) relatively strong, but varying math background
* most students have very strong reading/writing skills
* every student has a (so far) positive feelings towards school

Cushy, I know.  I very much understand and appreciate the challenges that I don't have to face (large transient classes, different home languages, severe learning differences, unstable families, etc).  That being said, I am confident that this lesson would work in any classroom because 2 years ago I did a similar first day lesson in a very very different school; it was probably the best lesson of that year.

The lesson
We were on a special first day schedule so I saw each class for 60 minutes.

Introductions: names and something you enjoy outside of school (5 minutes)

The Desk Problem: Look at the people you are now sitting with.  In a short while, I am going to give you 5 minutes to get up, talk, strategize, and rearrange yourselves so that everyone is sitting with as many new people as possible.  I'll then ask each person individually how many new people they are sitting with.  If you're sitting with 2 new people, you get 2 points.  3 new people, 3 points.  I'll then add up all the points and that's your class score.  Let's see if you can beat my other classes.

This was inspired by a boat problem that I don't remember the details of involving fisherman sharing boats with different people every day of the week.

I tend to assume kids are going to figure things out faster than they actually do, but every one of my groups surprised me on this one and within 30 seconds figured out that one person from each table needed to go to 1 of the 4 tables.  After congratulating everyone on their success and talking a little about different methods of getting the 48 points, we brainstormed ways to "tweak" the problem in order to make it more challenging.  Some of the ideas:
1. Winning class is the class to get 48 points as quickly as possible.
2. Changing the number of people, tables and/or chairs at each table.
3. Conducting multiple rounds where you only score points for people you've never sat with.
4. Forcing every person to change tables
I haven't worked on it at all, but I think the problem of finding a maximum score as a function of # of people, # of tables, and # of chairs at each table would be an interesting problem to work on.

Breaking the code: I then gave a few short directions for quality group work (everyone's contributing, everyone's voice being heard, and not making any decisions without everyone understanding and being on board, no questions for me unless it was a question everyone had) and handed this out with no further directions.  They worked on this for the remainder of the period.

Some notable observations:
• no table asked "What are we supposed to do?"
• no table complained "We haven't learned how to do this."
• every table eventually asked "Do we have to decode the whole thing?" which led to some variation of the following conversation:
Me: When do you think it would be fair to say you're done?
Them: When we figure out the code for every letter?
Me: Sounds good to me.
• Every student was engaged until the end of class
• Not every table did a great job of following the rules of group work
At the end of class, I handed out the homework, which kids quickly figured out was the decrypted version of what they'd been working on.

Great first day!  See you tomorrow.

1. Sounds like a fun first day problem.

Your links to the google docs are gated. By the way, we're practically neighbors. Next math circle in our area, let me know!

2. Links should be fixed. Didn't realize that even with sharing on, my docs in my school account aren't accessible outside of school.

And Jason, I'm planning on attending the math circle at AIM next Thursday. Hopefully you can make it.

3. I'm doing a math circle online tomorrow. Will you two be able to come? (See my post for more.)

4. @ Sue: Saw your post...that would definitely be fun, but I'm going to be out of town this weekend and (hopefully) not plugged in. Hope it goes well!

5. I wish I had had math classes like that. You sound like a great teacher. Your class setup and first day problem sound close to the Kirkman Fifteen Schoolgirls Problem. To quote Kirkman[1850]: "Fifteen young ladies in a school walk out three abreast for seven days in succession. It is required to arrange them daily such that no two shall walk twice abreast." Cayley among others took an interest in this problem and it ties in with the combinatorical problem of factorizing complete hypergraphs. Sylvester added an extension to the problem: "to make the school walk out every day in the quarter so that each three may walk together". More precisely, fifteen schoolgirls go for walks three abreast each day of thirteen weeks. You must arrange for any three of the girls to be in the same row in exactly one of the ninety-one walks. I got this from Combinatorics Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability by Bela Bollobas Cambridge Press 1986.

6. For those of you arriving here via The Google Bus, I have a much more detailed description of using a code for the first day here: http://www.withoutgeometry.com/2013/08/on-first-day-of-christmas-school.html

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