Connecting Slope to Rate of Change

This Instructional Activity is a part of the Lesson 5, Unit 3, Grade 8. The previous task asks students to estimate how many cups it will take to create a 50 cm stack. Students observe that the height of the stack grows regularly with the number of cups, but it is not a proportional relationship. In this task, they examine the relationship more closely, graph the relationship, and then interpret the graph. Each successive cup, after the first, adds the same amount of height to the stack. This amount of height added per cup is the rate of change for the relationship between number of cups in a stack and height of the stack.