In this lesson, students investigate the volumes of open-top boxes made from single sheets of paper. Students cut squares from each corner of a sheet of paper and fold the remaining paper to create an open-top box, which can serve as a visual reference while exploring polynomial functions further in this unit. 

Students graph input-output pairs and interpret the points to estimate the side length that results in the box with the largest volume (MP2). The volume of the box is a function of the side length of the square cut from each corner, which affects all three dimensions of the box. This leads students to write a cubic expression for the volume in the form of , providing students with a path into polynomial functions. Students also determine a reasonable domain for the function. 

The focus of this lesson is to interpret features of a polynomial graph, even though students will not be introduced to the term polynomial until a future lesson. Students will learn more precise language to describe graphs and equations of polynomials later in this section.