How are -11 + 9 and 9 + (-11) related?

In this lesson you will learn to demonstrate the commutative property of addition by using a

number line.

Let’s ReviewLet’s Review

What’s an integer?

Integers include positive and negative whole numbers as well as 0.

...-3, -2, -1, 0, 1, 2, 3 ...

Non-Examples:

-5.2 0.28 -9.9 4

Let’s ReviewLet’s Review

Positive NumbersNegative Numbers

Increasing in Value

Decreasing in Value

What’s a number line?

Let’s ReviewLet’s Review

What’s addition?

Addition is the process of joining two groups.

7 + 11 = 18

addend addend sum

Let’s ReviewA Common Mistake

Re-ordering the addends in an addition problem without re-ordering the signs.

+9-11

+9 11

- Commutative Property

Let’s ReviewA Common Mistake

+9-11

+9 11- =-

Re-ordering the addends in an addition problem without re-ordering the signs.

Let’s ReviewA Common Mistake

+9-11

+9-11( )( )

Re-ordering the addends in an addition problem without re-ordering the signs.

Let’s ReviewA Common Mistake

+9-11=

+9 -11( )( )Commutative Property

Re-ordering the addends in an addition problem without re-ordering the signs.

Let’s ReviewCore Lesson

62

8

6 2

8

6 + 2

2 + 6

Commutative Property

Let’s ReviewCore Lesson

-4 -3

-4 + (-3)

-3 + (-4)

-7

-4-3

-7

Commutative Property

Let’s ReviewCore Lesson

9-11

9 + (-11)

-11 + 9

-2

-11

9

-2

Commutative Property

In this lesson you learned to demonstrate the commutative property of addition by using a

number line.

Let’s ReviewGuided Practice

14 + (-9)

-9 + 14

Show that 14 + (-9) is equal to -9 + 14.

Let’s ReviewGuided Practice

-6 + (-8)

-8 + (-6)

Demonstrate that -6 + (-8) has the same value as -8 + (-6).

Let’s ReviewExtension Activities

Use Cuisenaire rods to represent integers 1-10. Model addition problems that show the commutative property by laying the rods on a number line.

These rods represent 8 + (-5) and -5 + 8.Both sums are positive 3!

Let’s ReviewExtension Activities

The commutative property of addition is sometimes called the order property.

Use the commutative property to rearrange these addition expressions so you can add them mentally. (Hint: Try to make sets of ten.)

A) -15 + 28 + (-5)B) -99 + 17 + 3 + (-1)C) 74 + 12 + (-4) + 5

Let’s ReviewExtension Activities

Partner Game:First partner writes an integer addition problem for the second partner.

The first partner solves the original problem on her own paper. The second partner switches addends using the commutative property and solves the equivalent problem on his paper.

Both partners compare their answers.

Let’s ReviewQuick Quiz

Which expression has the same value as -13 + 7?A) 7 + (-13)B) 13 + (-7)C) -13 + (-7)D) -7 + 13

Which expression has the same sum as -9 and -2?A) 2 + 9B) 2 + (-9)C) 9 + 2D) -9 + (-2