In this Warm-up students convert units from inches to feet and from feet to inches. This will be helpful when students examine inverse functions and reverse roles of inputs and outputs. As students follow specific processes when converting between units, they look for and express regularity in repeated reasoning (MP8).

The purpose of this discussion is to clarify that relationships can be solved in two directions. Here are some questions for discussion:

• “What is an equation that would represent the relationship between inches and feet?” (Let represent a length in inches and let represent a length in feet. .)
• “If you know the length in inches, how do you calculate the length in feet?” (Multiply the length in inches by 12.)
• “If you know the length in feet, how do you calculate the length in inches?” (Divide the length in feet by 12.)

In this activity students use the situation of creating a square planter to find the area within the planter based on the side lengths and the side lengths based on the area. In the associated Algebra 1 lesson students begin looking at inverse functions. This activity supports students by getting them to find the area of a square based on the side length or find the side lengths of a square based on the area. As students alter their approaches based on the given information, they look for and express regularity in repeated reasoning (MP8).

In this activity, students use a linear graph to find an output for a given input and an input for a given output. In the associated Algebra 1 lesson, students examine some ways to use the inverse of a function. This activity supports students in thinking about solving for the input or output based on the information that is known. Students look for and express regularity in repeated reasoning as they use the graph to find requested inputs and outputs (MP8).