If you"re teaching math to students who are prepared to learn around absolute worth, frequently roughly Grade 6, here"s an overview of the topic, along with two lessons to present and also construct the idea with your students.

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## What Does Absolute Value Mean?

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

The absolute worth of 5 is 5. The distance from 5 to 0 is 5 devices.

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

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

The absolute worth 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 also Equations

The many common way to recurrent the absolute value of a number or expression is to surround it via the absolute value symbol: 2 vertical right lines.

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

The number line is not just a method to show distance from zero; it"s additionally a valuable method to graph eattributes and inefeatures that contain expressions through absolute value.

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

Now think about |x| > 2. To present 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, usage open up dots at –2 and also 2 to suggest that those numbers are not part of the graph:

In general, you get two sets of worths for any type of inehigh quality |x| > k or |x| ≥ k, wright here k is any number.

Now take into consideration |x| ≤ 2. You are looking for numbers whose absolute values are much less than or equal to 2. This is true for any type of number between 0 and also 2, including both 0 and also 2. It is likewise true for all of the oppowebsite numbers in between –2 and 0. When you graph this on a number line, the closed dots at –2 and also 2 suggest that those numbers are had. This is as a result of the inequality using ≤ (less than or equal to) instead of

Math Activities and Lessons Grades 6-8