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.
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 key words 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.
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 1100 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]
Examples
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]
Examples
(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.
Example
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.
Example
5 0 = 0
Free Resources
 Math Properties ~ Foldable Graphic Organizer Four Door Flip
 Smart Notebook ~ Property Recognition Practice
Links to printable worksheets for teaching math properties:
 Addition and Subtraction Properties
 Addition and Subtraction Properties
 Multiplication and Division Properties
 Multiplication and Division Properties
 Using the Distributive Property
Here are the math products I am selling on Teachers pay Teachers: