The Mathematics

As is typical of programs in EDC's Center for Mathematics Education, the mathematics of CSSM has a low threshold and a high ceiling.  For example, we plan to begin the institute with this modification of a Balanced Assessment task, asking participants to keep track of questions that arise as they work on the problems.  

Below is a collection of rectangles.

• Which of the rectangles is the “squarest”?
• Arrange the rectangles in order of “square-ness” from most to least square.
• Devise a measure of “square-ness,” expressed algebraically, that allows you to order any collection of rectangles in order of “squareness.”
• Devise at least one more measure of “square-ness” and discuss the advantages and disadvantages of each of your measures.

We anticipate that many possible measures of “squareness” will arise as participants work on this problem.  If it does not arise, we will then present a measure that connects this simple problem with continued fractions, the Euclidean Algorithm, and some of the most fundamental ideas of number theory.