In the days leading up to the activity, ask students to bring in some kind of round treat, such as Oreos, doughnuts, bagel chips, cucumber slices, etc. Make up a few plates of different-sized treats, then print out copies of the secret "pi'ed" poem, shown below.
Throughout the day, students must stealthfully and anonymously place the treats into the classrooms of other teachers. Depending on your school policies, you may want to preempt this with an email or a list of willing participants. After each class finds the circumference of their treats, they are allowed to eat them as long as they promise to pay it forward!