Counting must seem to be the simplest and most straight forward task. Count the seats. What could be easier? No group in three terms has ever agreed on the number of seats. There is uncertainty even in the most obvious of measurements.
The activity generates student discussion, dialog, and even arguments over mathematics. At present mathematics curricula is often driven by a goal to prepare students for future careers. The complication is that telling a student, "This is important to your future career" does not generate motivation to learn in the present. The parents, teachers, administrators, community, and politicians may all understand the importance of mathematics, but that understanding does nothing to motivate the actual student in the here and now. And without motivation, no living entity actually learns.
Students measured the coordinates of a ball moving through the air amd then used a computer software package called Qalculate! to reproduce the parabolic arc from the ball arc equation.
Site swap mathematics sought to introduce the students to the idea that there are many fields of mathematics beyond the traditional disciplines of algebra, geometry, trigonometry, and calculus that they often meet. This activity introduced a new mathematical notation and sought to expand the students mathematical horizons. The activity was also designed to show that fun and math are not mutually exclusive propositions.
Site swap mathematics is a notation developed by mathematicians to describe sequences of ball throws that can be juggled. As in any mathematical system there are true and false expressions, provable and unprovable theorems, and rules that govern operations. Site swap also permits an opportunity for students to become acquainted with the juggling that site swaps describe. The students worked on the most basic expression: 333... repeated indefinitely.
Angie starts by trying to perform a 303.
Gary went directly to attempting a 333...
Lavanaleen and Patsipa working with two balls.
Corazon was also working on a 303.
Never one not to master a subject, Princeton concentrates on his 303.
Angie flashing a 333 and maintaing control right through to catching all three. In background Joanne has three under control.