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Because we use it every day, we tend to forget that our calendar is pretty strange. The year is broken up into months of different lengths, seemingly without much of a pattern. The same date can occur on different days of the week in different years. Is this really the best way to carve up a year?

In this lesson, students examine some other ways to keep track of dates, and use number sense and function concepts to convert among different calendars. What might a more reasonable calendar look like?

Students will

  • Convert dates among different proposed calendars using multiples and factors
  • Describe conversion rules in terms of functions, domain, and range
  • Use function composition and notation to describe two-step conversion rules
  • Reason about multiples and remainders to develop rules for converting dates into days of the week
  • Explain why functions can have inverses that fail to be functions themselves
  • Make recommendations for improvements to both the current and proposed calendars

Before you begin

Students should be able to reason about factors and multiples, and they should know how to obtain the remainder from a whole number division. Most of the questions revolve around function topics such as domain, range, inverses, and composition, so this lesson can serve as a way to discuss those topics in the context of calendars.

Common Core Standards

Content Standards
Mathematical Practices