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 ExerciseOn your own, write two different rational numbers that are the same distance from

zero. Find as many examples as possible.

VocabularyThe 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 1-4Find the absolute value of each and write what

other number has the same absolute value.

1. |10|

2. |-6|

3. |8|

4. |-1|

VocabularyThe magnitude of a quantity is found by

taking the absolute value of its numerical part.

Examples 5-9Use 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, continuedUse 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 2Order integers from least to greatest:

7, -2, -9, 5, -12, 8, 0, -1, 2, -5

Below each integer, write its absolute value.

Example 10Order 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 112.1, -4, -6, 0.25, -1.5, 0, 3.9, -6.3, -4, 2,

3.99, -9a. Separate the numbers into positive and

negative values and zero on a chart.b. 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 12a. 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.

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 Learning4321

How will you “Sharpen Your Saw”?