Understand a rational number as a point on the number line. Extend number line diagrams coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates

Understand ordering and absolute value of rational numbers.

1a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

 

1b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

 

1c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p+ (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

1d. Apply properties of operations as strategies to add and subtract rational numbers.