Math Resources ~ Math Properties

Math Property Activities

Last summer I organized the math materials I had created in preparation for teaching a 5th-grade math class this school year. The result of this organization is several math blog posts.  You can find the updated math section of my website here. I also created four math products that I am selling on Teachers pay Teachers. 

This post contains two free resources for teaching math properties. The first is a foldable organizer. The second is a Smart Notebook practice.

Free Math Properties Foldable Graphic Organizer

Math Properties Organizer

The organizer come in three versions:

  • The first has lines where students write definitions. Students must also create samples for each math property.

  • The second copy of the organizer contains the definitions with keywords missing for students to add. Students must also create samples for each property.

  • The third copy is completed. It may be used as an answer key. The organizer may be displayed on a SmartBoard for students to copy. A great use for the completed organizer is for differentiated instruction. The completed organizer may also be used for students who were absent.

Free Math Properties Foldable Organizer

Common Core State Standards

CCSS.Math.Content.3.OA.B.5 Understand properties of multiplication and the relationship between multiplication and division.

CCSS.Math.Content.6.NS.B.4 Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

The Properties

Commutative Property

You can swap numbers around and still get the same answer when you add or multiply.

[interchangeable in order]


4 x 2 = 2 x 4

Associative Property

In addition and multiplication, you can group a series of numbers in any order and get the same answer.

[grouping doesn’t matter]


(2 x 3) x 4 = 2 x (3 x 4)

Distributive Property

A characteristic of numbers that allows you to multiply a group of numbers and get the same answer you would get if you multiplied each member of the group and then combined the answers.

4 x (3 + 5)

(4 x 3) + (4 x 5)

Identity Property

Numbers that keep their expressions the same.

Multiplicative/Division Identity Property:

You can multiply one [or divide by one] to any number and your number will stay the same.


5 x 1 = 5

Additive/Subtractive Identity Property:

You can add zero [or subtract zero] to any number and your number will stay the same.


5 -0 = 0

Free Resources

Links to printable worksheets for teaching math properties:

Here are the math products I am selling on Teachers pay Teachers:




Gay Miller

Permanent link to this article: