If you"re teaching math to students who are ready to learn about absolute value, typically around Grade 6, here"s an overview of the topic, along with two lessons to introduce and develop the concept with your students.

You are watching: The distance of a number from zero on a number line

## What Does Absolute Value Mean?

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative. Take a look at some examples.

The absolute value of 5 is 5. The distance from 5 to 0 is 5 units.

The absolute value of –5 is 5. The distance from –5 to 0 is 5 units.

The absolute value of 2 + (–7) is 5. When representing the sum on a number line, the resulting point is 5 units from zero.

The absolute value of 0 is 0. (This is why we don"t say that the absolute value of a number is positive. Zero is neither negative nor positive.)

## Absolute Value Examples and Equations

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines.

|6| = 6 means “the absolute value of 6 is 6.”|–6| = 6 means “the absolute value of –6 is 6.|–2 – x| means “the absolute value of the expression –2 minus x.–|x| means “the negative of the absolute value of x.

The number line is not just a way to show distance from zero; it"s also a useful way to graph equalities and inequalities that contain expressions with absolute value.

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Consider the equation |x| = 2. To show x on the number line, you need to show every number whose absolute value is 2. There are exactly two places where that happens: at 2 and at –2:

Now consider |x| > 2. To show x on the number line, you need to show every number whose absolute value is greater than 2. When you graph this on a number line, use open dots at –2 and 2 to indicate that those numbers are not part of the graph:

In general, you get two sets of values for any inequality |x| > k or |x| ≥ k, where k is any number.

Now consider |x| ≤ 2. You are looking for numbers whose absolute values are less than or equal to 2. This is true for any number between 0 and 2, including both 0 and 2. It is also true for all of the opposite numbers between –2 and 0. When you graph this on a number line, the closed dots at –2 and 2 indicate that those numbers are included. This is due to the inequality using ≤ (less than or equal to) instead of

Math Activities and Lessons Grades 6-8