Download Absolute Value

Lesson Topic: Absolute Value – Magnitude
and Distance & The Relationship Between
Absolute Value and Order
Lesson Objective: I can…
 Understand the absolute value of a number as its
distance from zero on a number line.
 Use absolute value to find the magnitude of a positive
or negative quantity in a real-world situation.
 Understand that the order of positive and negative
numbers is the same as the order of their absolute
values.
 Understand that the order of negative numbers is the
opposite order of their absolute values.
 Understand that negative numbers are always less than
their positives.
Opening Exercise
On your own, write two different rational
numbers that are the same distance from
zero. Find as many examples as possible.
Vocabulary
The absolute value of a number is the
distance between the number and zero on a
number line.
We represent absolute value as |n|, but the
absolute value of a number is how many
units it is away from 0, so just n.
What is the absolute value of 0?
Example 1-4
Find the absolute value of each and write what
other number has the same absolute value.
1. |10|
2. |-6|
3. |8|
4. |-1|
Vocabulary
The magnitude of a quantity is found by
taking the absolute value of its numerical
part.
Examples 5-9
Use absolute value to determine the
magnitude of each quantity.
5. Maria was sick with the flu and her weight
change as a result of it is represented by -4
pounds. How much weight did Maria lose?
6. Jeffrey owes his friend $5. How much is
Jeffrey’s debt.
7. The elevation of Niagara Falls is 326 feet.
How far is this above sea level?
8. How far below zero is -16 degrees Celsius?
Examples 5-9, continued
Use absolute value to determine the
magnitude of each quantity.
9. Frank received a monthly statement for his
college savings account. It listed a deposit of
$100 as +100.00. It listed a withdraw of $25 as
-25.00. The statement showed an overall
ending balance of $835.50. How much
money did Frank add to his account that
month? How much did he take out? What is
the total amount Frank has saved for
college?
Exercise 2
Order integers from least to greatest:
7, -2, -9, 5, -12, 8, 0, -1, 2, -5
Below each integer, write its absolute value.
Example 10
Order integers from least to greatest:
7, -2, -9, 5, -12, 8, 0, -1, 2, -5
Below each integer, write its absolute value.
Next, order the absolute values from least to
greatest.
Example 11
2.1,
a.
b.
1
-4 ,
2
-6, 0.25, -1.5, 0, 3.9, -6.3, -4,
3
2 ,
4
3.99,
1
-9
4
Separate the numbers into positive and
negative values and zero on a chart.
Write the absolute values of the rational
numbers on another row in your chart.
c. Order all of the absolute values.
d. Order all of the numbers.
Example 12
Find a set of four integers such that their order of
their absolute values is the same.
b. Find a set of four integers such that their order
and the order of their absolute values are
opposite.
c. Find a set of four non-integer rational numbers
such that their order and the order of their
absolute values is the same.
d. Find a set of four non-integer rational numbers
such that their order and the order of their
absolute values are opposite.
e. Order all of your numbers from parts (a)-(d) in the
space below from least to greatest.
a.
Lesson Summary…



The absolute value of positive numbers will
always have the same order as the positive
numbers themselves. Negative numbers,
however, have exactly the opposite order as
their absolute values. The absolute values of
numbers on the number line increase as you
move away from zero in either direction.
The order of negative integers is opposite the
order of their absolute values because as you
approach zero from the left on the number
line the integers increase, but the absolute
values of those integers decrease.
The absolute value of a number is never
negative.
Evaluate Your Learning
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3
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How will you “Sharpen Your Saw”?