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OUR LESSON: Adding Positive and

Negative Integers

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WARM-UPWARM-UP

1) Order from least to greatest 7, -3, 0, -1, 3

2) Insert

a) -15 -16

b) 1 2

3) Find the sum:748 + 93 =

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Let's review what we learned in the last lesson

A variable is a letter that stands for a number

We use variables when we don’t know the number

A variable can be any letter

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A VARIABLE EXPRESSION contains a variable and an operation such as addition, subtraction, multiplication, division.

We can also write VARIABLE EXPRESSIONS such as

s + 9

8 n

16 x h

Review

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Word phrases can be translated into VARIABLE EXPRESSIONS

Word Phrase Variable Expression

2 more than n 2 + n

k times 8 k x 8

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The absolute value of a number is its distance from zero on the number line

The absolute value of 4 is written as

4The absolute value is always positive!

Absolute Value

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OppositesOpposites

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When we add an integer and its opposite, the sum is zero

EXAMPLES: (-5) + 5 = 0

98 + (-98) = 0

Opposites are also called ADDITIVE INVERSES.

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Today we are going to learn how to add integers.

We will explore 3 different METHODS

METHOD 1 - ZERO PAIRS

++

The red chips are NEGATIVE.

The grey chips are POSITIVE

-

-

-

-

+

+

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- +

1 red chip 1 grey chip+ = 0

We call 1 red chip and 1 grey chip a

ZERO PAIR

Zero Pair

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We begin with 3 grey chips

And we add 2 more grey chips

FOR A TOTAL OF 5 GREY CHIPS

If we want to add 3 + 2 ++ ++

++ ++

++

3 + 2 = 53 + 2 = 5

Lets take an ExampleLets take an Example

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We begin with 2 red chips

And we add 4 more red chips

- -

-

--

-

FOR A TOTAL OF 6 RED CHIPS.

-2 + (-4) = -6

Do you have any questions so far????

If we want to add -2 + (-4)

Remember Remember red chipsred chips

are negativeare negative

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++

BUT if we want to add integers with different signs,

we must use

ZERO PAIRS

-

These 2 chips form a ZERO PAIR.These 2 chips equal zero.

Adding integers with different signs

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--

Let's add (-5) + 3

We begin with 5 red chips

And we add 3 grey chips

+ ++

--

-

--

--

Lets see with an ExampleLets see with an Example

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Adding (-5) + 3

We begin with 5 red chips

And we add 3 grey chips

We circle the Zero Pairs and remove them!

(Remember a ZERO PAIR equals zero.)

-

-

-

- -

+ + +

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We begin with 5 red chips

And we add 3 grey chips

We are now left with 2 red chips OR -2

Therefore, (-5) + 3 = -2

- -

ResultResult

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You try a few. Use your red and black pens to make your chips.

(-3) + 1 = 4 + (-5) =

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METHOD 2 - Number Line

We can use a number line to find the sum of 2 integers.

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

WE ALWAYS START AT ZERO!

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1. Start at zero and move to the right (in a positive direction) 3 spaces.

2. Next, move further to the right 4 spaces.

3. Your answer is 7.

Lets add 3 + 4 by number lineLets add 3 + 4 by number line

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

3 + 4 = 73 + 4 = 7

1.1.2.2.

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Now, let's add (-2) + (-8)

1. Start at zero and move to the left (in a negative direction) 2 spaces.

2. Next, move further to the left 8 spaces.

3. Your answer is -10. (-2) + (-8) = -10

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

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Let's see what happens when we add a positive AND a negative number. (-6) + 8

=

1. Start at zero and move to the left (in a negative direction)

6 spaces.2. Next, move to the RIGHT 8 spaces.

3. Your answer is 2. as (-6) + 8 = 2

DO YOU HAVE ANY QUESTIONS??

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

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You try a couple.....

4 + (-7) =

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

(-2) + (-5) =

Start at zero and draw your arrows!

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Method 3 - Rules for adding integers

Adding the The sum of 2 positive numbers is POSITIVE.

Same sign The sum of 2 negative numbers is NEGATIVE.

Example: 4 + 7 = 11

(-3) + (-6) = (-9)

11 + 8 =

(-9) + (-1) =

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Adding Different Signs -

1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.

Example: (-2) + 9 =

1.) 2 9 Absolute Values

2.) 9 - 2

Step

Step Subtract

Step 3.) +7 Sign of the larger number

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Adding Different Signs -

1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.

Step 1.)

Step 2.)

Step 3.)

Try (-11) + 5 =

Absolute Values

Subtract

Sign of the larger number

11 , 5 11 , 5

11 – 5 = 6 11 – 5 = 6

- 6- 6

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GAME TIME !

Click here to play a game

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1.) The temperature in Minneapolis was 7 degrees F at

noon. By 8 pm, the temperature had dropped15 degrees F. What was the temperature at 8

pm?

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2.) You have $60 in your bank account. You withdraw (or take out) $45 to buy new tires for your bike. You then deposit(or add in) your babysitting money of $18.What is the new balance in your bank account?

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Let's see how well we understood the lesson today.

Use a number line to find each sum.

1.) (-7) + 12 =

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

2.) 4 + (-10) =

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Find each sum. Remember your Addition Rules!

3.) (-7) + (-11) =

4.) 12 + (-5) =

5.) 22 + 7 =

6.) (-9) + 5 =

7.) 3 + (-10) =

8.) (-8) + 20 =

9.) 1 + (-30) =

10.) (-15) + (-5) =

11.) Opposites are also called

A_________ I__________.

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Let's Review...

We can add integers using ZERO PAIRS.

There are 3 METHODS we can use to Add Integers.

METHOD 1

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To add (-5) + 3 =

Then we are left with 2 red chips. Therefore, (-5) + 3 = -2

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We can also use a number line to find the sum of 2 integers.

METHOD 2

.

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METHOD 3

Adding the Same Sign –

The sum of 2 positive numbers is POSITIVE. The sum of 2 negative numbers is NEGATIVE.

Rules

Adding Different Signs -

1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.

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You had a great lesson today!

Be sure to practice what you learned!