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Canalysis (Updated!)

What are the ideal dimensions of a soda can?

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Canalysis (Updated!)

What are the ideal dimensions of a soda can?

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Check it out! This lesson was just updated in September 2024, and we hope you love the new and improved version. If you've already prepped an earlier version, fear not, you can still find those here through Thursday December 5, 2024.

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Canalysis - Student Handout.pdf
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Canalysis - 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.

What’s the ideal size of a soda can? Soda companies spend billions of dollars each year to manufacture 12-ounce cans. If the companies changed the cans’ dimensions, though, they would save lots of money.

In this lesson, students create rational functions to explore the relationship between volume, surface area, and cost to determine the optimal size of a soda can.

REAL WORLD TAKEAWAYS

  • The typical soda can is 6 cm wide by 12 cm tall. But cans could come in other dimensions and maintain the same volume.
  • The cost of a soda can depends on how much aluminum it uses. The typical can costs more than it could.
  • Even though the current can is not the most cost-effective, there may be reasons soda manufacturers still prefer it.

MATH OBJECTIVES

  • Write and graph functions for volume and surface area
  • Rewrite and graph a function in terms of a given variable
  • Find the minimum value of a function and interpret its meaning in a real-world context
Appropriate most times as students are developing conceptual understanding.
Algebra 2
Rational Functions
Algebra 2
Rational Functions
Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Mathematical Practices MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

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