Introducing Unsolved Mathematical Mysteries in Grade School

I came across this excellent (and provocatively titled) article, "Unsolved problems with Common-Core", which suggests interesting exercises to students all the way from kindergarten to high-school.

These exercises then form a gateway to a big, usually unsolved, mathematical conjecture or hypothesis.

Here is an example for kindergarten/1st grade:

Can you color the map of Africa with four colors so that no two countries that touch are filled in with the same color?

This is followed by:

The unsolved problem: without trying all possibilities, can you tell when a map can be colored in with 3 colors so that no two countries that touch are filled in with the same color?

Fascinating stuff!