## Tuesday, October 18, 2011

### Class 14: 10/13/11-"Back of the Envelope" problems

Dr. Petrosino began class today by asking, “What do you know about pi?” and “Who can give me a value?” Student responses were the usual 3.1459 with some students carrying the decimal out farther than others. A few minutes of discussion then occurred centered around those two questions and the idea of estimation. The discussion concluded with Dr. Petrosino stating estimation is closely related to guessing. The class was then challenged to consider if grading estimations is possible, and if so, how it could be done fairly for students in their classrooms. This question remained the central theme throughout the duration of the class.

The majority of class time was activity based. Dr. Petrosino introduced the students to their activity by showing them some ““back of the envelope” problems (also know as Fermi Questions). Some examples shown were those that Bill Gates would ask in his interviews for Microsoft. The class was then divided up into groups of three and had ten minutes to solve one of the three Fermi Questions presented. The three questions presented are the following.
1.  What is the total weight of all the leaves in New England (in Kg)?
2.  How many crossings of the Atlantic Ocean have occurred since 1492?
3.  How many hairs on the average 20 year olds head?

Students were required to use assumptions and estimations to perform the calculations required. Their assumptions came from their own background knowledge, and collaborating with their groups. This element of collaboration was crucial in making their answers more precise. After the ten minutes were over each group presented their findings on the board in front of the class. These presentations allowed other students to see what each group discovered and compare answers. After the students were comfortable with the process of trying to solve one of these problems Dr. Petrosino presented more challenging Fermi Questions.

The activity did a wonderful job of demonstrating some of the elements of a Legacy Cycle. It consisted of a challenge, multiple perspectives and going public (Klein & Harris, 2007). The class ended with Dr. Petrosino explaining the difficulty of putting these questions on standardized test. The students agreed that these “back of the envelope” problems would be extremely frustrating to solve on without collaboration and under the pressure of a test. In response to the challenge question, estimations problems, like the Fermi Questions, allow students to use problem solving and critical thinking skills, but should be solved through collaboration in groups instead of individual. For more information on Fermi problems and the solutions follow this link!

Each day in PBI a different student takes responsibility for blogging about what goes on in class. Today’s blog is brought to you by ­­Casey.