The purpose of this lesson is to help students make sense of expressions involving variables and rational numbers and reason about their position on the number line. As students start to gain fluency with rational number arithmetic and they encounter complicated numerical expressions and algebraic expressions with variables, it is important to keep the connection between those expressions and numbers on the number line. This includes whether the numbers are positive or negative, which of two numbers is greater, and whether two expressions represent the same number.

Students work through common misconceptions that can arise about expressions involving variables, such as the misconception that must always be a negative number. They also reason about the structure of expressions involving inverse operations as they compare them (MP7).

Then students reason about expressions in and given the positions of and on a number line without a given scale. As they consider the structure of the algebraic expressions on the number line, they connect the letters in an algebraic expression to numbers and compare the expressions' relative values and distance from 0 (MP7). For example, they see that is a quarter of the way from 0 to on the number line, even if the value of  is unknown.