BELL RINGERS

Solve the following problems on a loose leaf piece of paper.

1. Draw a model to show the following expression (-5) + (-3) + 6

2. What is the sum of this expression?

3. While playing the additive inverse game you drew the cards

2, -5, 7, and -12. Draw a model to determine the sum. Write an

equation to accompany the model.

4. Write a real world story problem to accompany the equation.

ADDITION OF INTEGERS

TODAY I WILL BE ABLE TO

solve real world

problems using

rational numbers.

LET’S REVIEW

Cards:

Equation:

COUNTING UP AND DOWN

8 + (-3) =

2 + (-4) =

2 + 6 =

THINK AB OUT THESE QUESTIONS

For the equations: 2 + 6 and 2 + (-4) what is the

distance between 2 and the sum on a number line?

Does this sum lie to the right or the left on a

horizontal number line? Above or below on a vertical

number line?

NOW LET’S THINK AB OUT THESE QUESTIONS

Given the expression 54 + 81, determine without

finding the sum, the distance between 54 and the

sum. Explain.

Is the sum to the right or left of 54 on a horizontal

number line? Above or below on a vertical number

line?

YOUR TURN

Given the expression 14 + -3, determine without

finding the sum, the distance between 14 and the

sum.

Is the sum to the right or left of 14 on a horizontal

number line? Is it above or below on a vertical

number line?

COPY THIS QUESTION IN YOUR MATH JOURNAL AND SOLVE

Given the expression (-5) + 3, determine without finding the sum,

the distance between (-5) and the sum.

Is the sum to the right or left of (-5) on a horizontal number line? Is

it above or below on a vertical number line?

Draw a horizontal number line and a vertical number line to justify

your answers.

COPY THIS QUESTION IN YOUR MATH JOURNAL AND SOLVE

Given the expression (-6) + (-2), determine without finding the sum,

the distance between (-6) and the sum.

Is the sum to the right or left of (-6) on a horizontal number line? Is

it above or below on a vertical number line?

Draw a horizontal number line and a vertical number line to justify

your answers.

COPY THIS QUESTION IN YOUR MATH JOURNAL AND SOLVE

Given the expression (7) + (-8), determine without finding the sum,

the distance between 7 and the sum.

Is the sum to the right or left of 7 on a horizontal number line? Is it

above or below on a vertical number line?

Draw a horizontal number line and a vertical number line to justify

your answers.

FORMULA FOR ADDITION OF INTEGERS

We can think of the addition of integers by using this

formula

p + q = sum: p represents the first addend and q

represents the second addend.

Ex: (-9) + 5 = (-4)

p = (-9) q = 5 sum = (-4)

IDENTIFY THE P’S AND Q’S

32 + (-9) = 23

(-15) + 10 = (-5)

62 + 15 = 77

VERBAL DESCRIPTIONS

Write and equation and create a number line model to

answer the following question: the p value is 6 and the

sum lies 15 units to the left of p value. What is the value

of q and the sum of this verbal description?

Equation:

VERBAL DESCRIPTIONS

Write and equation and create a number line model to

answer the following question: the p value is (-4) and

the sum lies 6 units to the right of p value. What is the

value of q and the sum of this verbal description?

Equation:

VERBAL DESCRIPTIONS

Write and equation and create a number line model to

answer the following question: the p value is (-2) and

the sum lies 8 units to the left of p value. What is the

value of q and the sum of this verbal description?

Equation:

ADDITION OF INTEGERS RULES

Add rational numbers with the same sign by adding

the absolute values and using the common sign.

Ex: − +(− ) 𝟒𝟒 𝟐𝟐

Add rational numbers with opposite signs by

subtracting the absolute values and using the sign of

the integer with the greater absolute value.

Ex: 6 + (-18)

(-12) + 65

APPLYING THIS TO THE REAL WORLD

The Schiphol Airport runway in Amsterdam is 13 feet

below sea level. If I climb to the top of the control

tower I increase in elevation by 57 feet. At what

height above sea level am I now standing?

REAL WORLD

A Chinook helicopter flies to 1225 feet above sea

level. The pilot then drops 243 feet in elevation and

hovers. How high above sea level is the Chinook

hovering?

REAL WORLD

New Orleans, Louisiana is 7 feet below sea level. If I

climb in elevation 72 more feet to the city of Baton

Rouge at what elevation would I be?

CHECK FOR UNDERSTANDING REAL WORLD

A Blackhawk helicopter was doing maneuvers on a

routine exercise. On his mission she was rise to 854

feet above sea level. Next she was to drop 61 feet in

elevation and hover. What is her final elevation

above sea level?

CHECK FOR UNDERSTANDING REAL WORLD

Mike bought stock in the Boeing company. He

bought it at $24 a share. One the first day the stock

rose $13 a share. The next day the stock dropped

$16 a share. How much money is each share now

worth?

CHECK FOR UNDERSTANDING REAL WORLD

A scuba diver dives down 323 feet below sea level to

try and tag a hammer head shark. He chases the

shark 40 feet toward the surface. He and the shark

then dive down 15 feet, where he finally tags the

shark. What is the final elevation of the scuba diver?

Copy the questions and answer the following problems on a loose

leaf piece of paper.

1. Refer to the diagram on the right. Write an equation for the

diagram and find the sum. What integers do the arrows

represent.

2. Jenna and Jay are playing the integer game and below are the

two cards that they drew. How to the models for these two

addition problems differ on a number line? How are they the

same?

EXIT TICKET

Copy the questions and answer the following problems on a loose

leaf piece of paper.

3. If the order of the cards change, how the models for these two

addition problems differ on a number line? How are they the

same?

4. Dawn bought a stock when it was down 12 points. The next

day it rose 9 points and on the following day it fell 2 points. At

how many points is the stock?

EXIT TICKET