After you go trick-or-treating on Halloween, how much enjoyment do you get from eating each additional piece of candy? Do you get the same amount of satisfaction each time, or do you start to get sick of it (maybe even literally!)?

In this lesson, students will compare the marginal enjoyment (additional enjoyment from each additional piece of candy) and total enjoyment graphs to learn about the candy-eating preferences of two siblings. They’ll discuss how each sibling’s enjoyment changes as they eat candy, and how this affects how much candy they should eat. By the end, students will have learned a bit of calculus without even realizing it. Is that sweet or what?

### Students will

• Plot marginal and total enjoyment data for two siblings as they eat candy
• Interpret graphs of non-linear functions, including discrete ones
• Model non-linear functions graphically

### Before you begin

Students should be able to plot points on a graph. Beyond that, they will be describing features of the graph they create (where graphs are increasing, decreasing, etc.). Some prior experience describing and comparing graphs in this way will be helpful.