Wednesday, December 19, 2012

My Gambling Skills

As a wrap-up to our Games of Probability group project, my 6th graders and I were talking about the probability of getting a "Yahtzee" if you were playing with 2 dice instead of five (if there is one mathematical habit of mind that may be burned into the soul of each of my students this year, let it be the idea to try a simpler case). We were discussing the case where you get your Yahtzee on the third roll. We went over the probability of not getting a Yahtzee on the first roll. I rolled 2 dice and didn't get a Yahtzee. We then went over the probability of not getting a Yahtzee on the second roll. I rolled again and didn't get a Yahtzee. We went over the probability of getting a Yahtzee on the third roll. I rolled two dice and, what do you know, rolled a Yahtzee. 
In the words of @cheesemonkeysf, "I love it whenever the Universe tosses a teacher a freebie."

Sunday, December 9, 2012

A Truly Group Project

My fellow 6th grade math teacher and I are trying something crazy this week. We were two weeks into our counting/probability unit and wanted a project that would:
  • Help students practice the foundational skills and concepts
  • Push students to explore more challenging, unfamiliar, open-ended problems
  • Reiterate the importance of group work
  • Reiterate the importance of writing down solutions, reasoning, and explanations in an organized fashion. 
So our crazy new idea? We've put together four open ended, challenging probability games. Eight groups of 3 or 4 will spend tomorrow working on one of these games (2 groups for each game in each class). On Tuesday, groups will rotate and work on a different game, starting where the previous group left off

The hope is that, as an entire group, we make significant progress on each of the four problems. I'm super excited to see how this works (and I'm sure we'll all learn a lot even if it completely bombs). Below are the games we're introducing, and the investigation questions.


Investigate the probabilities associated with this game.  Think about the possible ways to make the required combinations, and then think about the points that you win for each part of the game. Are the points that Milton Bradley assigned to each combination in the game “fair?”  If you feel that they are “unfair” how you would you recommend to the makers of this game that they change the scoring to make it “fair?”

Pig (we're calling this "On a Roll"):
When you think that you understand the game, begin to investigate different strategies that you might use or recommend to others to help players decide when to stop rolling and when to take a chance and roll just one more time.  

Deal or No Deal
Play a version of the game at  Keep track of the revealed suitcases and the banker offers and determine whether or not (with an explanation) you should take each offer. What other questions do you have about this game?

 Drunken Walk (we're calling this "Dizzy Walk"):
1 dimensional version:

Where should you put your house? Would your placement of your house change if you initially rolled a die to determine how many times to flip the coin? Explore other questions you have about this game.

 2 dimensional version:

Let’s call the address of where Larry starts (0,0) and the address he would end up at after flipping HHTTT (2,3). How many different ways are there for Larry to get to (3,5)?

Imagine instead that Larry starts at (5,5). This time, instead of flipping a coin, you spin a spinner split into 4 equal areas marked North, East, South, & West. Now where would you put your house? What if you can create the spinner and determine the size of the 4 areas.
Here are the nitty gritty details of how to play the games if you're interested (ie our handouts).

Saturday, December 8, 2012

Asilomar Conference Recap(s) 2012

Spent last weekend at the California Math Council North conference (#cmcmath) in Pacific Grove, CA. 'Tis a beautiful spot, even though it was raining the whole weekend this year. The one upside to rain, though, is that it made for an excuse to splurge on the quite pricy entrance fee to the Monterey Bay Aquarium.

At the CMC-South (the Palm Springs equivalent) conference in November, Dan Meyer and I lamented the fact that it was impossible to see every good workshop and talked about creating a site to recap sessions (it was actually all Dan's idea but I take credit for my supportive listening). No surprise, Dan had a site up within a week:

The number of session recaps are growing, and I especially recommend Dan's recap of the Friday keynote speaker, Kyndall Brown.

So far, I've written one recap of my own.

[Amy Ellis] Laying a Foundation for Learning to Prove

It’s hard not to enjoy sessions when you’re already drinking the kool-aid. That said, Amy Ellis did a fantastic job of balancing research and practice around laying a foundation for proof well before Geometry class (on a side note, I still hope to lead a session called “Proof Doesn’t Start in Geometry” at some point in the future). She gave a convincing argument for the importance of introducing the idea of proof in early elementary school, and more importantly discussed structures and cultures that promote proof at any age. [Read the entire recap here]

My big take away: don’t fall into the trap that proof must require algebra, two columns, and/or a less eloquent rehash of Euclid.

Henri Picciotto was also kind enough to write not just one, but two recaps of my session on student posed problems. Part one is more of a recap, while part two addresses (or at least states) some of the challenges of implementation.