So far students have used input-output diagrams, tables, and descriptions of the rules to represent functions. In this lesson, students begin to make connections between these representations of functions and algebraic equations, continuing to build their skills reasoning abstractly and quantitatively about functions (MP2).

This lesson also introduces the use of independent and dependent variables in the context of functions. Students learn that the independent variable represents the input of a function, while the dependent variable represents the output. For an equation that relates two quantities, it is sometimes possible to write either of the variables as a function of the other. For example, in the activity “Dimes and Quarters,” either the number of quarters or the number of dimes could be used as the independent variable for the situation. If we know the number of quarters and have questions about the number of dimes, then this would be a reason to choose the number of quarters as the independent variable.