How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle? I will be teaching some "topology" to high school students. I was wondering how to explain to such a school student that on a sphere the shortest path between 2 points is given by a great circle?
Also, how to explain that if they lived on a sphere they would have no notion of "above" or "below"? I cannot find a nice way to convince them since they see the sphere embedded on 3d? 

Use a ball. Note that the less curvy a line is, the straighter it is (and therefore shorter). 
Then note that cutting a slice through the middle of the ball gets you the straightest line available. Which is a good definition of a great circle.
(And as other answerers have pointed out, if the ball is edible then you will be nourishing bodies as well as minds).
