Wednesday, October 8, 2014

Commutative and Distributive

In Mrs. Essenburg's class we have been busy learning about multiplication. In addition to learning the facts, we are also learning how to think about multiplication.

One of the things we've been learning is about the different properties of multiplication. Understanding these properties will help us as we move into more complex multiplication problems.

One of these properties is the commutative property.

The commutative property states that when you multiply you can switch the factors around and it doesn't change the product.

For example, 3 x 8 = 8 x 3

When we first learned this property, we made it. We showed it with unifix cubes, like this.

After that, we drew pictures to show the commutative property.

Understanding the commutative property is very helpful, because counting four groups of five is a little easier than counting 5 groups of 4! Knowing that you can switch the factors and still get the same product makes it easier to figure out different problems.

The other property we have been learning about is the distributive property. This one is a little more complicated, so we spent more time on it. 

The distributive property states that for any multiplication equation you can break a factor into two pieces, then add those two pieces together, and it will equal the multiplication equation you started with.

For example, 7 x 4 = (3 x 4) + (4 x 4)

Again, we started out by making the distributive property.

At first, the distributive property looked a little confusing, because we weren't used to solving these types of problems, but it helped a lot to make the problems so we could see what was happening. After that, we started drawing them out.

However, the best way to be sure that we understand something is if we can explain it to someone else. So, to make sure we understand the distributive and commutative properties, we made something called a paper slide video. Check it out below.

We will continue using these and other properties of multiplication this year.

We learned about the distributive and commutative property first by making examples, then by drawing examples, and finally by explaining examples. Did we explain these properties well enough for you to understand them? Can you comment below with an example of either the commutative or distributive properties?

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