**Associative Property of Addition**

When three or more numbers are added,

the sum is the same regardless of the

grouping of the addends.

Which of the addends go together?

**Commutative Property of Addition**

**Identity Property**

This means that you can add

0 to any number...

and it keeps its identity!

The number stays the same!

**Multiplicative Identity**

**Additive Inverse**

Work with your shoulder buddy to create a thinking map showing all the ways to make 12 using addition.

0 + 12 = 12 + 0

1 + 11 = 11 + 1

2 + 10 = 10 + 2

Peer

Buddy

Pal

Associate

12

0 + 12

12 + 0

1 + 11

11 + 1

2 + 10

10 + 2

3 + 9

9 + 3

4 + 8

8 + 4

5 + 7

What are the different ways of finding the sum of 12?

7 + 5

6 + 6

6 + 6

3 + 9 = 9 + 3

4 + 8 = 8 + 4

5 + 7 = 7 + 5

6 + 6 = 6 + 6

PROPERTIES OF ADDITION

Commutative Property

When two numbers are added, the sum

is the same regardless of the order

of the addends

**Associative Property**

How can we group these numbers?

Let's look at the following equation:

Begin by placing the numbers 3 and 4 in parentheses.

Associative Property of Addition

In math, we always perform the operation that's in the parentheses first!

If we add parentheses, will we get the same sum ?

**Associative Property**

Now, what if we group the numbers differently...

Will we get the same answer again?

Yes...

Remember that, if both

number

sentences equal 9,

then those

number sentences have to

equal each other!

How about trying

the same thing with

another set of numbers:

Do we get

the same thing

when we add them...

even if we group

the numbers differently?

Yes...It sure looks

like it.

It's your turn to try it now...

Go ahead...

Pick any three numbers

you want...

Group them one way and add

them together...

Then, change the

parentheses and add

them again! I'll wait...

Remember that you

always do what's in

the parentheses first!

This rule just says that,

when you are doing addition,

it doesn't matter which

numbers you add first.

You can add the a and b first

OR you can add the b and c first

and you'll get the same answer.

NOTE: This does not work

with subtraction!

What's the answer

to this?

That was easy enough!

How about

switching

the order.

What happens

to the answer

then?

Same answer, right?

Well if both number

sentences equal 5,

then both sides have

to equal each other.

How about trying

the same thing

with some other

numbers:

Do we get the

same answer

when we add

them, eventhough

we switch the order?

**Properties of Addition**

In arithmetic, the identity is

Let's look at the number 5.

Anyway we try to add 0 to it, the 5 just keeps coming back as the answer.

Go ahead and try it with

any number you can thing of... It always works!