My 7th-graders have been doing some lovely exploration and estimation activities on circles. It took a few days, but I think it was well worth our while, as it helped the abstract formulas make sense to them.
My students today were boggled by the fact that if pi has different digits that go on forever, that means that either the diameter or the circumference is a quantity with also digits that go on forever. That means that we have a "measurable" (ie. finite) quantity that is, in fact, not truly measurable. Trippy, eh? For a moment there, I felt the beauty of abstract math peek its head into our Grade 7 class. The kids now think the circle is a mythical, awe-inspiring form.