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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.