One of the math concepts that I have seen students struggle with the most, and yet seems so simple at first glance, is absolute value. It often seems that the only thing students ever “get” from an absolute value lesson is this: absolute value = make it positive. That is NOT, however, the definition of absolute value, and therefore, becomes the cause of much confusion as students try to apply and use absolute value in more complicated problems. This **absolute value exploration** teaches absolute value in a way that *makes sense*, and makes it clear to students **why absolute value problems are unique**.

In order for students to accurately use and understand absolute value, it is essential that the definition be made clear right from the beginning: **absolute value = distance from zero**.

Then the discussion can turn to distance and measurement and why *distance* must be positive, and therefore, the *absolute value* of a number (or expression) must be positive.

To demonstrate this for students, I have two students stand next to me and take 5 steps away. One takes 5 steps in one direction, the other 5 steps in the opposite direction. I then ask each student, “How far away are you?” The answer is: “5 steps away.”

**The distance is the same**, even though they are 5 steps away in ** different directions**.

It may seem at first glance that this is mere semantics, and not a distinction worth noting, but trust me, it will prevent many mistakes and misunderstandings down the road if students are taught to think through the use of absolute value with this understanding.

For example, if students’ only understanding of absolute value is that absolute value = positive, they will often get confused or simply ignore the negative in a problem such as: x = -|-4|.

They see those absolute value bars, think “It must be positive,” and therefore solve as x = 4. More complex problems also become confusing when the absolute value of an expression is given, but the final solution for *x* is a negative number.

## FREE Absolute Value Exploration:

The following lesson is intended to help students not only better understand absolute value, but understand WHY absolute value equations and inequalities *must* have two cases to solve.

Included are some **teaching tips**, a **student handout** as well as an **answer key**.

This is not, however, a comprehensive look at absolute value problems. There will still be many problems to consider after this introduction, such as **problems with no solution**, as well as **real world applications** of absolute value.

**But I hope you find this absolute value exploration useful and are able to provide a solid foundation for your students!**

**{Click HERE to go to my shop to download the Absolute Value Exploration!}**

***Psst! Did you know this lesson and SO much more is included in my Algebra Essentials Resource Bundle?** Everything you need to teach in a way that makes sense and set your kids up for success! **Click the graphic below to learn more!**

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Susan says

January 23, 2016 at 6:35 pmThanks.

Even though I have taught and mentored math since 1971, I am always interested in seeing new things.

Bethany says

January 23, 2016 at 10:43 pmMe too, Susan! I hope you found this lesson helpful! 🙂