*Contributor: Erika Wargo. Lesson ID: 12701*

If you pay back to a friend a loan of $1.25, your wallet will be at -$1.25. But you can't have negative dollars and coins. How do you figure out what to give him? Absolute values come to the rescue!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Beaver

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Lucy and Connor are playing a game. For every answer they get correct, they move forward one space. For every answer they get incorrect, they move backwards one space. The players begin on zero (0). During the first game, Lucy took 5 steps forward and 2 steps back. Connor took 2 steps forward and 5 steps back.

- Where did Lucy end up?
- Where did Connor end up?
- What do you notice about the location of each player on the number line?

Number lines can help you add, subtract, compare, and find the distance between numbers.

When you find how far a number is from zero, that is called *absolute value*.

As you watch a video to learn more about absolute value, answer the following in your math journal:

- In your own words, explain the meaning of absolute value.
- What notation is used to indicate absolute value?
- How do you find absolute value using a number line?

Discuss the questions above with a parent or teacher after you watch *Math Shorts Episode 10 - Absolute Value*:

Absolute value is the distance between the number and zero on a number line. Absolute value is the *positive* value of a number because distance is always a positive quantity. Two numbers that are the same distance from zero on a number line, but on opposite sides of zero, are called *opposites*. A number and its opposite have the same absolute value. All numbers will have an opposite except for zero.

**Example** Find the absolute value of -5 and 5.

The number line below shows two integers, -5 and 5. The distance from -5 to 0 is 5 units. The distance from 5 to 0 is 5 units. The absolute value of -5 is 5. The absolute value of 5 is 5.

**Example** If the absolute value of a number is 13, where would the number be located on a number line?

Since absolute value is the distance from zero on a number line, first identify both numbers that give an absolute value of 13.

If you started at 0 on a number line and moved 13 units to the right, you would arrive at 13. The opposite of 13 is -13. If you started at -13 on a number line and moved 13 units to the right, you would arrive at zero. For a number to have an absolute value of 13, it can be -13 or 13.

The notation would look like this:

|−13| = 13 and |13| = 13

In your math journal, write a response to the following:

- What is the absolute value of -17? Explain how to use a number line to find the absolute value.
- Will the absolute value of a number ever be negative? Explain.

In the *Got It?* section, you will practice finding and interpreting the absolute value of integers through interactive practice.

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