Integers & Absolute Value
Objectives:
• To be able to identify, compare, and order positive and negative integers.
• To be able to determine the absolute value of numbers and expressions.
Standards:
Vocabulary:
Integer - all positive whole numbers, their opposites, and zero
do not include fractions or decimals
Opposites - two numbers that are the same distance from zero on the number line, but in opposite directions. (example 2, -2)
Number Line - a graph that shows all integers Absolute Value - a number’s distance from zero
on the number line (always a positive value).
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
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
WHERE DO WE
SEE INTEGERS IN
OUR DAILY LIVES
Money!
Temperature!
Elevations (height or depth of places in the world) Years
Time
Recipes/Cooking
Real World Examples
Positive
• Temperature is above zero
• You are above ground (or above sea level)
• You make a deposit into your bank account
• You earn money
• You score points in a game
Negative
• Temperature is below zeo • You are below ground (or
below sea level)
• You make a withdraw from your bank account • You loose money
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
Graphing integers on a Number Line
Graph each integer on the number line by placing a dot in the correct spot.
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
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?
Opposites
Quick Practice
Write the opposite of each number.
a)2 b) 4 c) -3 d) -11
Use a # Line to Compare
• Graph each integer on a number line • The number to the right is bigger, the
number to the left is smaller
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
Ordering Integers
Also use a number line to order integers •Graph each integer on the number line •The number to the right is bigger, the number to the left is smaller
•List the numbers from left to right for least to greatest
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 →
Quick Practice
Which number in the pair is farther away from zero.
a) 4, -5 b) 2, 5 c) -1, -3 d) -12, 11
What is absolute value?
The distance of a number from zero on the # line Absolute Value is ALWAYS positive because the it
tells us the distance (not the direction)
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
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|
= 7the absolute
value of – 7
|
– 7|
= 7Absolute Value is indicated by two vertical lines
Example 1: | 3 | or | -3 | 3
Example 2: | - 68 | or | 68 |
68
Example 3: - | 6 | (this means the opposite of the absolute value. The only time the absolute value is negative is when the negative is outside the absolute value symbols.)
- 6
Example 4: | - 9 | - | - 8 | 9 – 8
= 1
Quick Practice
Find each absolute value.
a) l-21l b) l14l c) - l-1l d) -l21l
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
Comparing/Order Absolute Values
First find the absolute value, then compare/order 1.
2.
12 = 12
3. Order from least to greatest 15, l-7l, l5l, -3, l-3l Values = 15, 7 , 5 , -3, 3 Least to Greatest = -3, l-3l, l5l, l-7l, 15
(notice the answer was written with the original #s)
l-4l > l-3l
4 > 3
Summary
Think, pair, share: •What is an integer?
•When do we use integers in real life? •How do you compare & order integers? •What are opposites?
•What is absolute value?
