A "A' peeling" Problem

A detailed plan for the age-old activity where the class derives the formula for sphere surface area from the skin of an orange, this lesson is a must for any middle school math toolbox. Common teaching pitfalls are identified and suggested formative assessments offered to sidestep them (such as mis-identifying radius measurements or not completely filling drawn circles). The class worksheet provided leads learners not only through the physical steps of the activity, but also the thought process required to get to the sphere formula at the end. All in all, a great treatment of a classic hands-on geometry experience.

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CCSS: Designed
Instructional Ideas

  • Have students do a variety of fruit of different sizes, to emphasize general application of formula
  • Extend by having students model a cube of the same surface area, calculate the volume of the two shapes
  • You might also try using the wrapper for an ice cream cone to derive the formula for surface area of a cone
Classroom Considerations

  • Plan for materials ahead of time (oranges, string, cardstock)
  • Learners might need to shape their orange with (gentle) pressure so that the circumference measured is that of a sphere
Pros

  • Clear step-by-step directions for teacher and class
  • Great hands-on activity to make the abstract formula for surface area concrete
  • Leading questions throughout worksheet keeps the learners focused on the goal of deriving the volume formula without giving too much away
Cons

  • Multiple references to related activities and assessments on the LTF website, but a specific address is not available. The general website address given requires school or teacher registration for material access