Properties of Whole Number Addition

Let a,b, and c be any three whole numbers

Closure Property:

a+b is a unique whole number

What this means is that sum of two numbers is always a whole number.

Commutative Property:

a+b=b+a

This means that the sum of two numbers is not effected by the order in which they are added together.

Associative Property:

a+(b+c)=(a+b)+c

Grouping and/or associating numbers in different orders will yield the same answer.

Additive Identity Property:

a+0=a+a=a

The sum of any number and zero will always be the original number.

There are many great songs to help students in remembering the properties, the Properties of Addition song I have discovered goes along to a very popular song by a group called One Direction entitled What Makes You Beautiful that a lot of children have heard, and is extremely catchy.

The two properties I have found to be most difficult for students are the Commutative and Associative Properties.I found the Turn Around Addition Song (a teacher at my job showed me this) to help students better understand how the Commutative Property works:

I also found another great song for the Associative Property to help students out:

A lot of teachers have told me that they use songs for teaching their students the properties for addition, subtraction, multiplication, and division. The songs stick in their students heads, and they are constantly singing them when they go to solve their problems, and the students are getting it and getting their homework and tests correct.