and Associative Properties of Addition.

You will notice that there is a reason I have wheels on the Commutative Property and a little

face sitting there waiting at the Associative - a friendly face you might even imagine...

Now you'll notice that I colored the 3 and 4 in this case, and the 4 and the 3. When

the 3 "leaves home it drives" to a new location, but it is still a value of 3, even if it's

not in the first position anymore. Same for the 4; it also drives to a new position in

its little car... and drives over to this new position. Now it's first!

But, that doesn't change the answer; 3 +4 = 7, and 4 + 3 = 7. The difference, this is

Commutative. You'll notice, it's because the values commute, just like you might do in

the morning, from home to school.

Now, on the bottom, we have no changing colors, no changing numbers, because it's not the

numbers that move or change! What changes is "with whom the friends choose to hang out".

In this first value, we'll say that 1 + 2, 1 and 2 are friends, and so they associate

with each other, like friends do.

In the second case, we'll say that 2 + 3 happen to be buddies, so that 2 will hang out with

3 first when they go to play. And, so they are associating with each other.

In this first case, we see that 1 + 2 = 3, plus the 3 we already had. 3 + 3 = 6.

In the second case, we see that 2 + 3 = 5, bringing down the 1 we have not yet accompanied,

we have 1 + 5; again 6.

So we have proven that no matter with which value the 2 associates first, the [sum] value

will be coming to 6 either way. This [is] the Associative Property, because of with

whom the 2 associates.

This is the Commutative Property because the values commute.

Thank you very much for today's lesson on Properties of Addition - Commutative versus

Associative.

Now I imagine the decorations make a little bit more sense!

Thank you.