Teaching Math: Finding the Absolute Value of a Number

As math teachers, we think some concepts are so simple that students should be able to understand them in five minutes. Such is often the case with finding the absolute value of a number. Absolute value is generally taught in 5^th or 6^th grade, yet I found that the majority of my 7^th grade math students didn't really understand it. The idea of absolute value seemed to stay with them, however, when I took the following approach.

Define

At some point, students need to record notes on absolute value into their math notebooks for future reference.
Absolute value is a number's distance from zero on the number line.
It is always positive, never negative.
Absolute value asks "how far?" not "in what direction?"
The symbol for absolute value is | |. It is read as "The absolute value of..."
The absolute values of -10 and 10 are the same: 10 (both are 10 steps from 0.)
The absolute values of 236 and -236 are the same: 236 (both are 236 steps from 0.)
| 8 | = 8 and | -8 | = 8 since 8 and -8 are both 8 "steps" away from 0.

Develop the concept

When you begin this lesson, stand about 3 steps to the right of your desk and ask the students, "How many steps do you think it will take me to reach my desk?" Listen to their estimates and then walk it off: 3 steps. Now position yourself the same distance to the left of your desk. "Now how many steps am I away from my desk?" The response will be the same, 3 steps. Walk that off. Tell the students to think of your desk as 0 on the number line. Emphasize that, when we determine absolute value, it's the same process: we're counting the number of steps a number is from zero, not the direction of travel. It's 3 steps, either way. They see that absolute value is always positive. We don't usually walk backwards, do we?.
So...
|3| = 3
|-3| = 3
The absolute value of both 3 and -3 is 3.

Students act it out

Hang a number line in front of the class that goes from -5 to 5. Ask for two volunteers. Give each student a 9 x 12 sheet of paper, one with |5| written on it and one with |-5|. Tell them to stand by their respective numbers. Ask the class how many steps it will take for |5| to walk to zero (5). Have that student take the 5 steps. Ask how many steps it will take for |-5| to walk to zero (5). Have the second student take the 5 steps. Repeat this with a few more pairs of opposite numbers. Although it may seem redundant to you, the reinforcement will stick in the students' minds, as they'll remember their classmates actually walking toward zero.

Move to the abstract

Place several problems on the overhead for the class to solve. Allow them to quietly work with their partners.
For example:
|19| = 19
|-45| = 45
|640| = 640

Now, get a little trickier:
|-8| + |9| = 8 + 9 = 17
20 x |-5| = 20 x 5 = 100

Vary the problems, depending upon whether or not students know the operations of integers.
Have different students come up to the overhead to verbalize the solutions.

Practice

Distribute practice sheets. You can find free printable practice problems for absolute value at Math Worksheets 4 Kids' website. They begin with basic absolute value and increase in difficulty.

If you're lucky enough to have access to computers, allow students to work through a computer program for absolute value. Click here or here for two programs that provide lots of repetition for recognizing that absolute value is always positive. It would be especially good for special needs' students.

Alert!

Emphasize that the absolute value of 0 is 0. After all, 0 is 0 steps away from 0!

Some students think that parentheses ( ) or brackets [ ] are the same as the absolute value symbol | |. Be sure they understand that those symbols are not interchangeable in this case.

If you follow this method and include absolute value periodically in your daily warm-ups, students will think it's a snap and will be ready to take it to the next step in algebra

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