# Understand that positive and negative numbers are used together to describe quantities having

### Cluster

Apply and extend previous understandings of numbers to the system of rational numbers.

Evidence of Learning Statements

 Students with a level 1 understanding of this standard will most likely be able to: Students with a level 2 understanding of this standard will most likely be able to: Students with a level 3 understanding of this standard will most likely be able to: Students with a level 4 understanding of this standard will most likely be able to: Define integers as positive or negative in a real-world context where the meaning of 0 is determined in the situation. Identify opposite quantities used in real-world situations. Use integers to represent contextual situations involving quantities that have opposite directions or values. Explain the meaning of zero when used to represent quantities in real-world situations. Generate contextual situations involving rational numbers and their opposites.

Instructional Focus Statements

Level 3:

In elementary grades, students used positive rational numbers to represent contextual situations. Students are very familiar with the number line and the directionality of increasing and decreasing quantities. In grade 6, students will extend that understanding to continue the line beyond zero. In grade 6, they extend their learning to use integers to represent real-world situations and explain the meaning of 0 in these situations. For example, using −20 to represent a $20 debt or 20 to represent a$20 deposit into a bank account. For the first time, students are introduced to the concept of negative values.

Students should initially be exposed to negative numbers in contexts where it is natural to describe the magnitude (such as the vertical distance from sea level in meters) and direction quantity (above or below sea level) of the numbers. Students should have opportunities to engage in discourse around real-world contexts that involve positive and negative values and understand that some quantities can be measured in negative, or opposite values (i.e., temperature). Discussion should also include other quantities where this would not be appropriate, such as the number of football players on a team. Given a real-world context, students should explain the meaning of zero in each situation.

Students are not expected to perform operations with negative numbers in grade 6, nor are they expected to define the complete Real Number System. However, a comprehensive understanding of numbers and their opposites will be beneficial as students learn to perform operations with negative numbers in grade 7.

Level 4:

Students at this level have a strong understanding of how rational numbers are used to represent real-world situations. Students should be challenged to extend their learning to create contextual situations involving both positive and negative rational numbers. Students should continue discussions around the quantities used, and the meaning of zero in contextual situations using precise mathematical language.