Mathematical properties are actually quite useful when it comes to making sense of math. For example, the commutative property of addition helps make adding numbers a little easier. If we know that the order the numbers are added does not matter, then in the problem 2 + 9, adding the 2 onto the 9 is easier and more efficient than adding the 9 onto the 2.

The Common Core State Standards in Mathematics requires all third grade students to know their 0 – 9 multiplication facts by the end of the year. We can actually call in another mathematical property to help…the commutative property of multiplication which states that the order the numbers are multiplied does not matter: 3 x 5 is the same as 5 x 3.

But it’s the distributive property that I find the most useful in learning the multiplication facts. I ask my students what the word ‘distribute’ means. Once we agree that it means to share out, I tell them that distributing numbers can help us learn our facts. I then do several problems like the one in the photo where the number ‘9’ is sharing itself out as ‘4’ and ‘5’. Once students get the idea, they work in pairs or small groups to come up with their own examples.

What I like about using tiles to visually show what the distributive property looks like is the tie-in with area. Each tile represents one square unit. In order to find the area of the entire rectangle in square units, we simply multiply the length by the width.

In addition, using tiles can also illustrate congruence. A 3 x 5 rectangle is the same as a 5 x 3 rectangle. And, hey, that’s also the commutative property of multiplication!

When our student can physically manipulate objects to show mathematical concepts, math makes sense. And when that happens, learning increases. That’s a good thing!

CCSSM: 3.OA.B.5; 3.OA.C.7; 3.MD.C.5; 3.MD.C.6; 3.MD.C.7