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# Sweet Tooth

## How much Halloween candy should you eat?

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.

### REAL WORLD TAKEAWAYS

• Many people’s enjoyment of something pleasurable – like Halloween candy – is not positively linear. More of a good thing is not always better.
• Research suggests that income demonstrates diminishing marginal returns: As Americans earn up to \$60,000/year, additional income tends to make people happier; after \$60,000 additional income does not increase happiness.

### MATH OBJECTIVES

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

Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.