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# Sweet Tooth

## How much Halloween candy should you eat?

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# Sweet Tooth

## How much Halloween candy should you eat?

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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.

### 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.
Grade 8
Functions
Grade 8
Functions
Content Standards 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Mathematical Practices MP.4 Model with mathematics. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others.