Here is another opportunity for discovery: one-third. For kids who have learned how to divide and get decimals (or show a child briefly who has learned long division and knows what decimals are). Ask simply, what is one-third in decimal?

The discovery that 1/3 = .33333333... the repeating decimal, is surprising enough on its own for a child who has never seen an infinite series before. What usually will tweak their curiousity, though, is to continue - ok, what is 2/3? Then wait a moment, and see if they think of 3/3 by themselves. The idea that 3/3 = .999999999... may get the child saying, wait a minute - 3/3 = 1!

They have just proved that an infinite series can equal a whole number; if your child doesn't want to accept it, that is ok. Just assure them that if the series stops anywhere, it is less than one, it only equals one if it is really infinite.

The fun thing is, this can be done by a 4th grader.

Down to Grade/Age: 
4th Grade
Up thru Grade/Age: 
5th Grade