Showing thousands of examples that two odds add up to an even may be convincing, but it's not a proof. A proof would explain why two odds must add up to an even for any two odd numbers. Disproving a conjecture is usually an easier process. Finding just one counterexample is enough to disprove a conjecture, because this shows that it does not work for all cases. Whenever possible, try to get students involved in proving conjectures, not just providing evidence.
Proof is what real math is all about.
Some children realize that the number is going to be the same as the number of feet in the classroom, the number of hands in the classroom, etc. Someone points out that you'll get a different number if you figure out how many fingers in our classroom. Showing the underlying similarities of two seemingly different approaches to a problem helps children develop flexibility. Many children will love to create their own number games. This leads into a lot of thinking about what are the characteristics of a good mathematical game.