Teaching Properties of Multiplication and Addition

Properties of multiplication and addition – how well do your middle school math students understand these?

My students often confused the Commutative and Associative properties…..do your math students confuse them too?

I’ve taught these properties in different ways over the years, and today I’m sharing the methods that worked best for me in 6th grade math.

How to Teach Properties of Multiplication and Addition

One of the best strategies for myself and my students was to spend time talking about the root words of the property names.

1) Commutative: commute: one meaning is to travel back and forth. Many students are familiar with commuting as driving back and forth to work. With that definition in mind, commuting can be thought of as moving from one place to another.

So we relate this meaning to moving places in an expression, like 6 + 4 = 4 + 6. In their notes, students might draw a car or something to like that to help keep that connection in mind.

2) Associative: associate means to join or connect; or a companion. So when we talk about this property we think about numbers connecting or joining with each other (associating with each other). Or, they’re companions.

In the associative property, numbers join with, or associate with different numbers, like 6 + (4 + 5) = (6 + 4) + 5.

3) Distributive: distribute means to give to or deliver to members of a group. For this property, we talk about a number being ‘given’ to other numbers (or members) inside a group (the parentheses), like 6(4 + 5) = 6 x 4 + 6 x 5

4) Identity: your identity is who you are, so we talk about Identity properties as properties that leave the numbers as ‘who they are’:

• 5 + 0 = 5
• 6 x 1 = 6

Students often enter middle school having heard of Commutative and Associative Properties, but don’t always remember which is which. Talking about the word meanings seems to help, so as we review the properties, we focus on these meanings. And then we revisit the meanings as the properties come up during the year.

Resources to Teach Multiplication and Addition Properties

To help students keep these properties straight, I’ve created a few different resources for them to keep on hand to refer to throughout the year. The resources include the following properties:

• Associative Property
• Commutative Property
• Distributive Property
• Identity Properties of Addition and of Multiplication

Each of the resources includes  property definitions and examples.

Properties of Multiplication and Addition Math Wheel

The Properties Math Wheel is an excellent, colorful way for students to take notes about the properties.

The sections of the properties wheel include:

• Commutative
• Associative
• Distributive
• Identity of Multiplication
• Identity of Addition

• Each section of the wheel has notes and examples and there are practice problems around the wheel.

Students can add their own memory triggers to the wheel sections. For example, they many want to draw:

• A car to represent commuting or moving
• People in a group to represent associating
• Someone handing out papers for distributing

…whatever will help them associate the property name with its meaning. Even using specific colors with different properties can help students remember the properties by associating them with those colors.

There are 20 problems in the pattern around the circle. Students identify each property and then color the section according to the color code on the wheel.

• The color-coding provides a quick way for you to determine whether students are identifying the properties correctly.
• Then students can color the rest of background pattern however they’d like. They can also color the headings and doodle arrows.

Once the wheels are complete, I have students keep them in their notebooks for reference all year.

See the Properties Wheel on TPT

Free Properties Fold It Up

• This free fold it up is another easy way to take notes about the properties.
• The inside is divided into 5 sections, and the instructions are pretty simple:
  • Fold on the middle line
  • Cut on each of the dotted lines
  • Fold each flap up
  • Add the property names to each flap
  • Add the notes!

When students are labeling, be sure they write the properties on the correct flaps.

• When my first class completed this, a few had stapled the fold it up into their notebooks before labeling, and because of the way they stapled, they started labeling incorrectly.

Select the button below to download this one from TPT.

Download the Fold It up

Do you have some favorite strategies for teaching properties of multiplication and addition? Let us know in the comments!

If you need some additional practice for the properties, you can try the Properties Footloose Task Cards or Properties Truth or Dare Game.

Not sure how Truth or Dare games work? Check out the Truth or Dare games blog post to learn about it!