Check out this week's Lesson Collaboration Call + other upcoming events with Citizen Math teachers! Everyone is welcome.

Canalysis (Updated!)

What are the ideal dimensions of a soda can?

Login to add lessons to your favorites

Canalysis (Updated!)

What are the ideal dimensions of a soda can?

Login to add lessons to your favorites
Log In or Sign Up to Access Lesson Materials
Canalysis - Student Handout.pdf
Log In or Sign Up to Access Lesson Materials
Canalysis - Teacher Guide.pdf
Log In or Sign Up to Access Lesson Materials

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.

Other Algebra 2 Lessons

Pandemic (Updated!)

How long does it take for a virus to spread through a population?

Algebra 2
Exponential Functions (Adv.)
Appropriate most times as students are developing conceptual understanding.

Win At Any Cost (Updated!)

How should professional sports teams spend their money?

Algebra 2
Bivariate Statistics
Appropriate most times as students are developing conceptual understanding.

False Flags (Updated!)

How accurate should government surveillance be?

Algebra 2
Probability (Adv.)
Appropriate most times as students are developing conceptual understanding.

Second Degree (Updated!)

How dangerous are heat and humidity?

Algebra 2
Polynomial Functions
Appropriate most times as students are developing conceptual understanding.

Pic Me (Updated!)

What’s the best way to be successful on Instagram?

Algebra 2
Bivariate Statistics
Appropriate most times as students are developing conceptual understanding.

Pandemic (Updated!)

How long does it take for a virus to spread through a population?

Algebra 2
Exponential Functions (Adv.)
Appropriate most times as students are developing conceptual understanding.

Win At Any Cost (Updated!)

How should professional sports teams spend their money?

Algebra 2
Bivariate Statistics
Appropriate most times as students are developing conceptual understanding.

False Flags (Updated!)

How accurate should government surveillance be?

Algebra 2
Probability (Adv.)
Appropriate most times as students are developing conceptual understanding.

Second Degree (Updated!)

How dangerous are heat and humidity?

Algebra 2
Polynomial Functions
Appropriate most times as students are developing conceptual understanding.

Pic Me (Updated!)

What’s the best way to be successful on Instagram?

Algebra 2
Bivariate Statistics
Appropriate most times as students are developing conceptual understanding.