The document introduces integers and absolute value. It defines integers as positive or negative whole numbers, and provides examples of where integers are used in daily life. It explains how to identify, compare, order, write and graph integers on a number line. The document also defines absolute value as the distance of a number from zero on the number line, and provides examples of evaluating and using absolute value in expressions. Real-life examples are given to illustrate integers and absolute value.

1. Integers & the
Number Line

2. Integers & Absolute Value
Objectives:
I will be able to identify, compare, and order positive
and negative integers!
I will be able to determine the absolute value of
numbers and expressions!

3. Vocabulary:
 Integer
 Opposites
 Number Line
 Absolute Value
Integers & Absolute Value

4. What is an integer?
Integer: Any positive or negative whole
number
• No decimals!
• No fractions!
Examples:
900
2
-3
-3,000,000

5. WHERE DO WE
SEE INTEGERS IN
OUR DAILY LIVES
Money!
Temperature!
Elevations (height or depth of places in the world)
Years
Time
Recipes/Cooking
Integers are EVERYWHERE!

7. Integers less than zero Integers greater than zero
are negative integers are positive integers
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
negatives are zero is neither positives CAN
written with negative nor be written
a (-) sign positive with a (+) sign

9. 5 positives Integers greater than zero
4 are written are positive integers
3 with + sign
2
1 zero is neither
0 negative nor
-1 positive
-2
-3 negatives
-4 written with Integers less than zero
-5 a - sign are negative integers

10. Writing Integers in Real-Life Situations
Write an integer to describe each situation
Example 1: an increase of 6 inches
+ 6
Example 2: owe your parents $15
- 15
Example 3: a loss of 7 pounds
- 7
Example 4: earned 5 dollars interest
+ 5
Example 5: a temperature of 9 degrees below zero
- 9

12. Graphing integers on a Number Line
Graph each integer on the number line
Example 1: Graph - 4 on the number line
Example 2: Graph - 8 on the number line
Example 3: Graph + 10 on the number line
Example 4: Graph + 2 on the number line
-10 -8 -6 -4 -2 0 2 4 6 8 10

13. Graphing integers on a Number Line
Graph each integer on the number line
Example 1: Graph - 4 on the number line
Example 2: Graph - 8 on the number line
Example 3: Graph + 10 on the number line
Example 4: Graph + 2 on the number line
-10 -8 -6 -4 -2 0 2 4 6 8 10

14. Extension
The number shows the
amounts of money Erica,
Jerry, Bob, and Ray
have in their wallets or
owe one of their parents.
Who has the most money?
Who has the least money?
Who owes four dollars?
10
8
0
6
4
2
-10
- 2
- 4
- 6
- 8
Erica
Ray
Bob
Jerry

15. When graphing integers on a number line, make sure to:
•Use at least 3 numbers
•Use one number that is less then the number (to the left)
and one number that is greater (to the right)
•Put a dot to indicate which integer you are graphing
Example: Graph -3 on a number line:
-4 -3 -2
Graphing integers on a Number Line

16. Comparing Integers

17. Comparing Integers
Replace the □ with <, >, or = to make the sentence true.
Example 1: - 9 □ 8
- 9 < 8
Example 2: 83 □ 84
83 < 84
Example 3: 5 □ - 5
5 > - 5
Example 4: - 6 □ - 4
- 6 < - 4
Example 5: - 7 □ - 7
- 7 = - 7

18. Ordering Integers
Order each set of integers from least to greatest.
Example 1: - 162, - 10, - 81, 59 →
- 162, - 81, - 10, 59
Example 2: 9, - 8, 4, - 9 →
- 9, - 8, 4, 9
Example 3: 2, 6, - 2, 0 →
- 2, 0, 2, 6
Example 4: 7, 5, - 1, - 5 →
- 5, - 1, 5, 7

19. What is absolute value?
The distance of some number from zero on the
number line
Absolute Value is ALWAYS positive!
What does absolute value look like?
7 units 7 units
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Integers & Absolute Value

20. What is absolute value?
The distance of some number from zero on the
number line (ALWAYS Positive)
What does absolute value look like?
the absolute
value of 7 | 7 | = 7
the absolute
value of – 7 | – 7 | = 7
Integers & Absolute Value

21. Absolute Value
Evaluate the expression.
Example 1: | 3 |
3
Example 2: | - 68 |
68
Example 3: | 6 | + | - 9 |
6 + 9
= 15
Example 4: | - 8 | - | - 9 |
8 – 9
= -1
Integers & Absolute Value

22. Extension
Evaluate 6 + | n | if n = - 16.
6 + | n | = 6 + | - 16 |
= 6 + 16
= 22
Integers & Absolute Value

23. Integers & Absolute Value
Absolute Value in real life!
An eyeglass prescription is given as a positive or
negative number. A prescription for a person who is
farsighted is positive. A prescription for a person
who is nearsighted is negative. The greater absolute
value, the stronger the prescription. Which
prescription is stronger, -3 or 2?
Step 1: Think about the problem. What information
was given and what am I trying to figure out?

24. Integers & Absolute Value
Absolute Value in real life!
An eyeglass prescription is given as a positive or negative
number. A prescription for a person who is farsighted
(can’t see near) is positive. A prescription for a person
who is nearsighted is negative. The greater absolute
value, the stronger the prescription. Which prescription
is stronger, -3 or 2?
Step 2: Determine the answer
What is the absolute value of each prescription?
| -3 | | 2 |
3 2
Which prescription is greater?
-3!

25. Absolute Value in real life!
A seagull is flying at an altitude of 107 feet and a
shark is swimming at a depth of 112 feet relative to
sea level. Which animal is farther from sea level?
Sea level (0 feet)
107 feet
-112 feet