We used one of the problems for our project this morning:

We stared the project today by having the boys read the problem and talking about some potential strategies for how to approach it:

They started by looking at some simple examples. These examples helped them get a feel for how the problem worked, but didn’t quite point them toward the solution.

From the last discussion they began to believe that they game would always end the same way no matter how you played it. So they decided to see what would happen if they ran through the version of the game presented in the problem.

Their way of running through the game was fascinating to me

Now we talked about why there was only one way to end. They found their way to the idea that the even and odd numbers of white beans was the key to the problem.

Finally I showed them one way of thinking about how the odds and even number of white and black beans changes each turn.

I really like this problem. It is a super fun problem for kids to explore.