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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

  • Interpret and create graphs of non-linear functions modeling the enjoyment one gets from Halloween candy
  • Relate marginal value to total value
  • Discuss how diminishing marginal returns might affect one's consumption and other choices

Before you begin

Use this lesson for 10 year olds or calculus students. There are no prerequisites other than sense of curiosity...and even that can be built along the way. You may, however, want to pick up some fun size candy bars.

Common Core Standards

Content Standards
Mathematical Practices