Download Comparing & Ordering Integers

Comparing &
Ordering
Integers
Objective

Content Objective: We will compare and order integers. We
will communicate mathematical ideas using graphical
models.

Why learn this: We use positive and negative numbers to
measure temperature, height (as in above and below sea
level), money, and more. We use absolute value to determine
the distance from a point, without regard to the direction we
are moving from that point.
Vocabulary

integers: all positive whole numbers, their
opposites, and zero.

opposites: two numbers that are the same
distance from zero on the number line, but in
opposite directions. Ex. 2, -2

absolute value: a number’s distance from zero on
the number line (always a positive value).
Finding Absolute Value
Find the l3l and l-3l.
l3l and l-3l = 3
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!
Integers less than zero
are negative integers
Integers greater than zero
are positive integers
-6 -5 -4 -3 -2 -1 0 1 2
negatives are
written with
a (-) sign
zero is neither
negative nor
positive
3 4 5 6
positives CAN
be written
with a (+) sign
5
4
3
2
1
0
-1
-2
-3
-4
-5
positives
are written
with + sign
Integers greater than zero
are positive integers
zero is neither
negative nor
positive
negatives
written with
a - sign
Integers less than zero
are negative integers
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
Quick Practice
Write the opposite of each number.
a)
2
a) -2
b) 4
c) -3
d) -11
b) -4
c) 3
d) 11
Quick Practice
Find each absolute value.
a)
l-21l
a) 21
b)l14l
b)14
c) l-1l
c) 1
d)l21l
d)21
Comparing Integers
Compare -4 and 1 using <, =, or >.
Remember, numbers increase going from left to right.
-4 < 1
Quick Practice
Which number in the pair is farther away from zero.
a) 4, -5 b) 2, 5 c) -1, -3
a) -5
b) 5
d) -12, 11
c) -3
d) -12
Quick Check
Compare using <, =, or >.
a) -6
-3
b) -23
0
a) -6 < -3 b) -23 < 0
e) l-21l
21
e) l-21l = 21
f) -14
c) 17
-18
c) 17 > -18
l14l
c) l-1l
f) -14 < l14l
d) 5
-1
d) 5 > -1
-5
c) l-1l > -5
Ordering Integers
Order the numbers -8, 7, -4, and 3 from least to greatest. Use a
number line to plot the points. Then put them in order from
least to greatest.
Remember, numbers increase going from left to right.
-8, -4, 3, and 7
Extension
The number shows the
amounts of money Erica,
Jerry, Bob, and Ray
have in their wallets or
owe one of their parents.
Ray
Erica
Jerry
Who has the most money?
Who has the least money?
Who owes four dollars?
Bob
10
8
6
4
2
0
-2
-4
-6
-8
-10
Quick Practice
In golf, the person with the lowest score is the winner. Rank
the players below by ordering their scores from lowest to
highest.
Player
B. Hive
L. Emons
T. Ricks
J. Umps
P. Tree
Score
-12
-4
+10
-3
-5
1. B. Hive
2. P. Tree
1. L. Emons
2. J. Umps
3. T. Ricks
l-4l
> l-3l
l12l
= l-12l
l-20l
>
l10l
l-14l
<
l-15l
l-7l >
6
-5
< l-4l
-15
<
5
l-13l
>
l12l
19
= l-19l
l-27l <
28
Integers & Absolute Value
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
Extension
Evaluate 6 + | n | if n = - 16.
6 + | n | = 6 + | - 16 |
= 6 + 16
= 22
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?
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!
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?
107 feet
Sea level (0 feet)
-112 feet