Teachers' Circle Session 2

The High School Tucson Teachers' Circle

April 28, 2011

Cody's Donut Shop and the Mathematics of Choice presented by Cody Patterson

Cody started the evening with a warm-up problem to determine the number of unit squares on the boundary of an 8x8 array of squares. Participants were challenged to explain answers in as many ways as they could. In the follow-up discussion, five different methods were featured. One of the points made was that although one or two methods used may be the fastest for determining the answer to this specific problem, there are ways of approaching the problem that are useful for modeling a general solution.

The next sets of problems led us to the combinations and permutations formulas with good understanding of what components of the formula meant and why they are needed.

Cody saved his Donut Shop problem for after dinner. Most of us weren't "buying" his bacon bits donuts, but the problem was fun to ponder. He cleverly introduced a strategy used to solve a class of combinatorics problems in a way that makes sense and was so entertaining that it is easy to remember.

Click here for a copy of the problems.

From the new Core Standards for Mathematical Practice, all eight were apparent to some degree in the presentation!

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

In the table below, you may click on any image to see a larger version of it. Click the left (return to previous) arrow at the top to return to the page.


Cody introduced his talk.	Solutions were discussed in general terms.	Dan, Kalyani, and Rama Rao discussed ideas to solve a problem.


Cody explained the donut shop problem.	The groups shared ideas with each other.