There are a number of 'properties' that you need to know that are very important when you are working with the various number operations. They are things that you probably don't realize you have been using; you just didn't realize they had names! Being able to recognize them by name is important because in many standardized tests, these names are used and without knowing the names, you are stuck between a rock and hard place…so, let's get right to work, shall we?

Do you have a specific table where you sit down to everyday at lunch? Are the people who eat lunch with you the same group of friends each day? Sometimes, do you sit next to one friend and then maybe, the next day, because you were late getting your lunch, you sit next to someone else but since you're all friends, it really doesn't matter, right?

The Commutative Property is kind of like that. It deals with moving around or 'commuting' and if you look at the root word in commutative and you can remember that the Commuter Lane on the freeway is only for those people who have two or more people in a car, then you can remember this property.

With the Commutative Property you are dealing with changing the order of your group members. So, let's take a look at it with some pictures.

Andrea, Jocelyn, Manny, Lupita, and David always eat lunch together. They sit at the same table every single day.

On Monday, they were sitting on the bench in this order.

On Tuesday, David and Andrea wanted to discuss their history test. Manny had stopped at the library before heading to lunch. Their bench order had changed.

This is an example of the Commutative Property where the order changed.

Now, let's go back to your group of friends. You probably hang out with the same group most every day right? But, sometimes, you may need to discuss stuff with certain people in your group for some reason, just like David and Andrea in our example above, who wanted to talk about their history test. This is where the Associative Property comes in. Look at the root word in associative…it's associate or group! So, here's another one that is not too difficult to figure out if you simply read into the word itself. Let's check out an example.

The friends all commute to school and their parents take turns with the carpool duty.

On Mondays, Lupita's mom picks up David and Andrea.

Jocelyn's dad picks up Manny.

For modified days, Lupita's sister picks up David and Lupita. Andrea, Jocelyn, and Manny stay late those days for choir and Jocelyn's dad takes them home.

The groupings for the carpool are different yet everyone gets to and from school with out a problem.

What happens when your favorite teacher (like your math teacher) gets sick? Who comes in to teach the class? Is it, perhaps, a 'substitute?' Yeah, that's right! This is like the Substitution Property, where if two things are the same, then, it doesn't matter which one substitutes for the other (now, I don't know if your math teacher would agree with this but…).

Click Let's Practice Properties! to download a worksheet!

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