7c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

The Pyramids of Giza. The Great Wall of China. Mount Everest. Some things on this earth are absolute, but nothing is more absolute than absolute value.

Students should know that absolute value represents the distance between a number and 0 on the number line. That is, students can start by physically counting the number of times they have to hop from number to number on the number line to get from 0 to -7. (Spoiler alert: it's 7.) Once they've done that a few times, they'll catch on to the fact that the absolute value of any number just means it's the value of the positive form of that number.

Once they've got a firm grip on the absolute value of numbers and number lines, they can start applying absolute values to real-world situations. To do that, they need to be able interpret what the negative sign means for that particular context. (Does it mean miles traveled south instead of north? Does it mean dollars lost instead of earned?) Knowing what the negative sign means will help them interpret the absolute value of that number.

For instance, when interpreting a distance of -10 miles due north, it's important for students to understand that the negative sign means we're traveling in the opposite of due north—that is, due south. The absolute value of |-10| = 10 miles, however, can tell us the distance away from the starting point.