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 It listed a withdraw of $25 as The statement showed an overall ending balance of $ 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

Example 12 a. 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 Learning How will you “Sharpen Your Saw”?