Extend previous understanding of numbers to define rational numbers. Plot, order and compare rational numbers.

Given a mathematical or real-world context, represent quantities that have opposite direction using rational numbers. Compare them on a number line and explain the meaning of zero within its context.

Given a mathematical or real-world context, interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of rational numbers.

Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value.

This diagram shows how categories can “nest” within each other. A golden retriever is a dog, a mammal, and an animal.

“Animal” is a much broader category than “mammal,” for example.

You can use this classification diagram to make statements like:

“All golden retrievers are dogs, but not all dogs are golden retrievers.”

Negative numbers represent the opposites of positive numbers.

In different contexts, negative numbers have different meanings.

Elevation below sea level can be thought of as “negative,” because sea level represents zero.

Temperatures below 0 degrees are also represented as negative temperatures.

Money gained can be thought of as “positive,” and money spent can be thought of as “negative.” If you spend more money than you have, you will have a negative bank balance.

Absolute value is the distance a number is from zero.

-3 and 3 have the same absolute value (3) because they are both 3 units away from zero.