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? 

Set up lines of latitude and longitude on the sphere so that the two points, call them $A$ and $B$, are on the same meridian.
Then any motion from $A$ to $B$ can be "tracked" along the meridian by taking a moving point on the meridian that has the same latitude as the point moving from $A$ to $B$.   The motion along the meridian (an arc of a great circle) is shorter, because at every instant it sweeps out length at a rate less than or equal to that of any other motion at the same latitudes.
In the extreme case, when the points are antipodal, this is all still true but the inequality becomes an equality if the other motion is along a different 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? 

They do live on a sort of sphere.  Do two people on opposite sides of the Earth have a way of deciding which one is upside down?  Assigning directions North/South or East/West relies on extra information such as a magnetic pole or the motion of the sun relative to the Earth.
