7d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

This standard is about a three-way collision between absolute value, inequalities, and real-world applications. And your students are the ones rubbernecking.

Primarily, students should understand that a number has two important attributes: its direction (i.e., whether it's positive or negative) and its magnitude (i.e., its absolute value, a.k.a. how far it is away from 0). If they don't understand the difference in these characteristics, they're in for a world of confusion.

When faced with comparisons and inequality statements, students should realize that comparisons of absolute value deal with magnitude, and comparisons of straight up numbers (i.e., numbers with negative signs) deal with direction. For instance, |-30| > |-20| tells us that -30 is further away from 0 than -20, while -30 < -20 tells us that -30 is to the left of -20.

See? Absolute value versus order.

When working with real-world situations, students should be able to differentiate between these two types of comparisons understand the implications of each. Students should keep a watchful eye on how absolute value and ordering work within those specific contexts. Because we'll tell ya, they don't always work together.