In this lesson, students are introduced to rational functions through the context of calculating the minimum surface area for a can with a specific volume. Rational functions are functions defined by a fraction with polynomials in the numerator and denominator.

Students begin the lesson making sense of a central problem (MP1) by considering which of 4 cylinders with the same volume and different dimensions would take the least amount of materials to build. Next, students consider the inverse relationship between the radius and height for cylinders of a specific volume. They calculate heights for several cylinders given a radius, and this repeated reasoning (MP8) encourages students to rearrange the formula for the volume of a cylinder to suit their needs. In the last activity, students build an equation for the function relating the radius and surface area of a cylinder with a specific volume, and they use the equation and graph to answer the original question: Which cylinder would take the smallest amount of materials to build?