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Sweet Tooth (Updated!)

How much Halloween candy should you eat?

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Sweet Tooth (Updated!)

How much Halloween candy should you eat?

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Sweet Tooth - Student Handout.pdf
Sweet Tooth - Teacher Guide.pdf
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2023-2024 Versions

In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

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 enjoy eating candy. However, the more candy people eat, the less enjoyment they often get from each additional piece.
  • Enjoyment of something pleasurable is often not linear; each additional item can provide less enjoyment than the one before it. This phenomenon is called “diminishing returns.”
  • Many things in our lives exhibit diminishing returns. These might include how much a test grade improves from additional hours of studying or how much satisfaction we get from buying new things. However, there are some experiences and pursuits that defy diminishing returns or even exhibit positive returns. These are rare and special.

MATH OBJECTIVES

  • Interpret graphs of non-linear functions, including discrete ones
  • Create and graph piecewise functions to reflect a real-world scenario.
  • Use graphs to inform real-life decisions
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.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

Other Grade 8 Lessons

Domino Effect (Updated!)

How much does Domino’s charge for pizza?

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

You're So Fined (Updated!)

How do municipal fines affect people with different incomes?

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

Square Dancing (Updated!)

What secrets are hidden in squares?

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

Timber (Updated!)

What size tree should we use for lumber?

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Cones, Cylinders, Spheres
Appropriate most times as students are developing conceptual understanding.

Fuel Economy (Updated!)

Are hybrid vehicles worth the extra cost?

Grade 8
Solving Linear Equations
Appropriate most times as students are developing conceptual understanding.

Domino Effect (Updated!)

How much does Domino’s charge for pizza?

Grade 8
Writing Linear Equations
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

You're So Fined (Updated!)

How do municipal fines affect people with different incomes?

Grade 8
Solving Linear Systems
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Square Dancing (Updated!)

What secrets are hidden in squares?

Grade 8
Squares, Roots, Irrationals
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Timber (Updated!)

What size tree should we use for lumber?

Grade 8
Cones, Cylinders, Spheres
Appropriate most times as students are developing conceptual understanding.

Fuel Economy (Updated!)

Are hybrid vehicles worth the extra cost?

Grade 8
Solving Linear Equations
Appropriate most times as students are developing conceptual understanding.