Summarize: Commutative: the ORDER in which you add or multiply numbers doesn't matter. Associative: how you GROUP the numbers when you add or multiply doesn't matter. Same kid friendly meanings for identity (how the number still sees itself in the mirror), inverse (opposite and upside down), and distributive (break a number apart).
Interesting. Ramblings of a fifth and sixth grade teacher....
This is actually a very smart idea to use in lower elementary to find the greatest common factor as well as the lowest common multiple because when the students get into the higher mathematics when they start learning about the Venn Diagram. However, this could go from being an aid to becoming a crutch for the students.