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How much Halloween candy should you eat? Every Halloween children return home with buckets of delicious candy, eager to tear off the wrappers and dig in. Yet for many people, the more candy they eat, the less they enjoy each additional piece.

In this lesson, students analyze graphs of linear and nonlinear piecewise functions to compare how much enjoyment people get as they eat through their candy and debate the best strategy for maximizing Halloween happiness.

### Students will

• Interpret graphs of non-linear functions, including discrete ones
• Model non-linear functions graphically

### 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.