Lesson 6

Absolute Value of Numbers

In the past several lessons, students have reasoned about the structure of rational numbers by plotting them on a number line and noting their relative positions and distances from zero. They learned that opposite numbers have the same distance from zero. Students now formalize the concept of a number’s magnitude with the term absolute value. They learn that the absolute value of a number is its distance from zero, which means that opposite numbers have the same absolute value. Students reason abstractly about the familiar contexts of temperature and elevation using the concept and notation of absolute value (MP2).

Compare rational numbers and their absolute values, and explain (orally and in writing) the reasoning.
Comprehend the phrase “absolute value” and the symbol $||$ to refer to a number’s distance from zero on the number line.
Interpret rational numbers and their absolute values in the context of elevation or temperature.

Let’s explore distances from zero more closely.

I can explain what the absolute value of a number is.
I can find the absolute values of rational numbers.
I can recognize and use the notation for absolute value.

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absolute value

The absolute value of a number is its distance from 0 on the number line.

The absolute value of -7 is 7, because it is 7 units away from 0. The absolute value of 5 is 5, because it is 5 units away from 0.
negative number

A negative number is a number that is less than zero. On a horizontal number line, negative numbers are usually shown to the left of 0.
opposite

Two numbers are opposites if they are the same distance from 0 and on different sides of the number line.

For example, 4 is the opposite of -4, and -4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.
positive number

A positive number is a number that is greater than zero. On a horizontal number line, positive numbers are usually shown to the right of 0.
rational number

A rational number is a fraction or the opposite of a fraction.

For example, 8 and -8 are rational numbers because they can be written as $\frac81$ and $\text-\frac81$.

Also, 0.75 and -0.75 are rational numbers because they can be written as $\frac{75}{100}$ and $\text-\frac{75}{100}$.
sign

The sign of any number other than 0 is either positive or negative.

For example, the sign of 6 is positive. The sign of -6 is negative. Zero does not have a sign, because it is not positive or negative.