In this lesson, students continue to work with proportional relationships represented by tables. They identify the constant of proportionality and use it to answer questions about the context. The contexts are familiar from previous grades: unit conversion and constant speed. When students recognize that the conversion factor or the speed are the constants of proportionality for the relationships, they are reasoning abstractly and quantitatively (MP2). Although students might continue to reason with equivalent ratios to solve problems, the contexts are designed so that it is more efficient to use the constant of proportionality.

This lesson also introduces students to the idea that there are two ways of viewing any proportional relationship. In other words, if is proportional to , then is also proportional to . The two constants of proportionality are reciprocals, and , respectively. This idea will be developed more in future lessons.

Math Community
In today’s activities, students are introduced to the idea of math norms as expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Students then consider what norms would connect and support the math actions the class recorded so far in the Math Community Chart.