If you"re to teach math to students who are all set to learn about absolute value, typically approximately Grade 6, here"s review of the topic, in addition to two lessons come introduce and also develop the concept with your students.

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What does Absolute value Mean?

Absolute value describes the distance native zero the a number is ~ above the number line, without considering direction. The absolute value of a number is never negative. Take it a watch at some examples.

The absolute worth of 5 is 5. The street from 5 to 0 is 5 units.

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The absolute worth of –5 is 5. The street from –5 to 0 is 5 units.
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The absolute value of 2 + (–7) is 5. When representing the amount on a number line, the resulting suggest is 5 units from zero.
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The absolute value of 0 is 0. (This is why us don"t say the the absolute value of a number is positive. Zero is neither negative nor positive.)

Absolute worth Examples and Equations

The many common way to represent the absolute worth of a number or expression is to surround it through the absolute worth symbol: 2 vertical straight lines.

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

The number line is not simply a way to display distance native zero; it"s additionally a useful way to graph equalities and inequalities the contain expressions with absolute value.

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Consider the equation |x| = 2. To display x top top the number line, you require to display every number who absolute worth is 2. Over there are precisely two areas where that happens: at 2 and at –2:


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Now consider |x| > 2. To present x top top the number line, you require to display every number whose absolute value is higher than 2. Once you graph this top top a number line, use open up dots at –2 and also 2 to indicate that those numbers space not component of the graph:


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In general, you gain two set of worths for any type of inequality |x| > k or |x| ≥ k, where k is any type of number.

Now consider |x| ≤ 2. You are searching for numbers whose absolute worths are less than or same to 2. This is true for any number in between 0 and 2, including both 0 and 2. That is likewise true for all of the the contrary numbers between –2 and also 0. When you graph this top top a number line, the close up door dots in ~ –2 and 2 show that those numbers space included. This is due to the inequality using ≤ (less 보다 or equal to) rather of

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Math tasks and Lessons grades 6-8