## 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 http://bit.ly/dealnodealgame.  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).

#### 2 comments:

1. This looks like some fun. I really like your idea of having the students trade off halfway through the project. This creates some fun accountability.

2. Your title "Without geometry life is pointless" is clever, concise and very true. Before reading your title, I thought that without geometry science is pointless, but you captured the greater truth.

Science started as geometry, which is the truths regarding the features of figures, images, designs. It continued with mechanics, the contrivances made with figures, drawings, moving or static.

You put your finger on the phenomenon of design in nature, which "happens" everywhere, and which captivates us because understanding it and predicting it is good for our movement, life span and reach on the landscape. This phenomenon is governed by the constructal law,

see : http://en.wikipedia.org/wiki/Constructal_law

Adrian Bejan
Duke University