The goal of this lesson is for students to focus on qualitative aspects of graphs. The axes in this lesson have no units or scales, allowing students to reason more generally about graphs that represent situations.

In the Warm-up, students analyze two different graphs that represent the same situation given as a series of photos. Depending on which quantities are chosen as the dependent and independent variables, both graphs describe different aspects of the same story. The two functions represented by the graphs have the same independent variable (time) but different dependent variables (distance from edge of lawn versus distance from the camera).

In the following activity, students identify independent and dependent variables from contexts and select an appropriate graph to match their choices. Different choices are possible, so students must be precise about which choice they are making and explain how the choice relates to the graph based on the situation (MP6).

In the final activity, students create a graph from a story. In doing so, students have to make many choices about the aspects of a situation they want to represent with a mathematical object—this is an important part of modeling with mathematics (MP4). Depending on the variables chosen, graphs of the same situation can appear to be different but still tell the same story.