Why can't you flatten a sphere?

Experimentation is fun!

Give him a globe, some string, a ruler, a compass, some paper, and a pencil. Then have him try to map 4 different cities from the globe onto the paper, keeping ALL the distances between them the same as on the globe.

Show him a triangle on the sphere with 3 right angles. He knows that it is impossible in a plane right ?

One simple way is to think of an orange peel. Have the 10-year old peel an orange nicely and tell him to try to flatten the peel pieces completely without breaking or streching any part of the peel.