1. Negative Numbers and Absolute Value
Negative numbers are all numbers to the left of zero on a horizontal number line. On a vertical number line, negative numbers are below zero.
Here are some real-world scenarios where a negative number can represent the situation.
A withdrawal of 15 dollars
A loss of 5 yards
10 degrees below zero
100 feet below sea level

2. A number line can help us see the values of negative numbers and how they compare to each other.
And we can use inequality signs to help us compare the numbers.
-4 < > < > > -5

3. The Absolute Value of a number is that number’s distance from zero
The Absolute Value of a number is that number’s distance from zero. The absolute value of any number is ALWAYS POSITIVE.
The value of the plotted point is (-6), but the ABSOLUTE VALUE of the plotted point is 6. Can you plot another point that has the same absolute value of -6?

4. E W Let’s take a closer look…
Suppose the number line below represents a street, where the blue house is 5 miles east from the school and the red house is 4 miles west from school. E W
So, even though the red house is at -4, its distance from the school is 4. The blue house is just 5 [miles] from the school.

5. E W Which house is closer to the school? By how many miles?
2. How far is the red school from the blue school? Explain. E W
Suppose a yellow house is built the same distance from the school as the blue house. Where could the yellow house be?

6. Absolute Value with Vertical Number Lines

7. Absolute Value with Vertical Number Lines
With Absolute Value, it does not matter whether an object is positioned at a positive or negative number. The distance from zero is always positive. In the picture, we say “above” or “below” 0. For example, the diver is 3 meters below sea level and the cliff top is 7 meters above sea level.

8. The Absolute Value Symbol…
Two vertical lines that are on either side of any integer signifies “absolute value.”

9. = 4 x can be______ or ______
What can the value of x be in the expression shown below?
= x can be______ or ______
= x can be______ or ______
= x can be______ or ______

10. Heights of Places in Relation to Sea Level
Absolute Value in Information Tables
Heights of Places in Relation to Sea Level
Bunny Hill
Hidden Valley
Great Mtn.
Ariel’s Grotto
Millie’s Meadow
50 ft.
-20 ft.
2000 ft.
-1500 ft.
10 ft.
Which location is closest to sea level?
How far is the peak of Bunny Hill to the bottom of Hidden Valley?
How much closer is Ariel’s Grotto to sea level than Great Mountain?
What is the difference in distance between Bunny Hill and Millie’s Meadow?

12. Create your own absolute value picture.

13. Your picture must have…
A vertical number line
Three points above and below zero with:
A “position number” (positive or negative)
AND an absolute value description
(i.e. 7 feet below sea level)
Find one distance measurement from any two points in your picture.
(i.e. The bird and fish are 40 meters apart)