Potty humor is always a big hit with the school-age crowd, and potty algebra takes this topic to a whole new level. Here the class develops a model that connects the dimensions (radii, paper thickness, and length of paper) of a common roll of toilet paper. This short, but high-level, exercise makes a great warm-up application, or an open-ended practice problem.

Concepts

math modeling, algebraic expressions, cylinders

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Additional Tags

math

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Instructional Ideas

• Extend the modeling to other three-dimensional shapes or ways of arranging the toilet paper (folding instead of rolling, for instance)
• Test the formula developed against the measurements of an actual roll of toilet paper
• Link with a science lesson on waste management, or a history lesson on different civilizations' solutions to waste removal throughout history

Classroom Considerations

• Last page of lesson is blank
• Weaknesses in calculating volume and surface area of cylinders will quickly appear in the modeling process, having remediation handy would speed up this process

Pros

• Abstract reasoning made approachable by easy language and common materials
• Strong links developed between geometry and algebraic modeling methods

Cons

• Student activity not separated from teaching notes and answer key
• Only one solution method provided, though reference is made in teaching notes to several possible attacks

Common Core

HSG-MG.A.1