In this lesson, students encounter a situation in which a quantity increases and then decreases. They don’t yet have a name for this new pattern of change, but they should recognize that it is neither linear nor exponential, and that the graph is unlike the graph of an exponential function.

Students make sense of this new kind of relationship in a geometric context and describe it in concrete and qualitative ways (MP2). Though some students may choose to represent the relationships with calculations or with expressions, these are not required or emphasized in the lesson. Students will have many opportunities to reason symbolically about quadratic patterns in upcoming lessons.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate tools to solve problems, so consider making technology available.