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.

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Topic:
Building Functions (BF), Interpreting Functions (IF)

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI), Similarity, Right Triangles, and Trigonometry (SRT)

How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.

Topic:
Building Functions (BF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.

Topic:
Building Functions (BF), Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE)

Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in Les Misérables, and explore the maximum height from which someone can safely jump.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF)

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Topic:
Building Functions (BF), Interpreting Functions (IF)

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Topic:
Building Functions (BF), Functions (F), Interpreting Functions (IF)

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

Topic:
Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)

How much should Nintendo charge for the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.

Topic:
Creating Equations (CED), Building Functions (BF), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

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Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

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Topic:
Building Functions (BF), Interpreting Functions (IF)

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Topic:
Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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Topic:
Building Functions (BF), Creating Equations (CED)

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Topic:
Building Functions (BF), Linear, Quadratic, and Exponential Models (LE)

How much Halloween candy should you eat? Students interpret graphs to compare the marginal enjoyment and total enjoyment of two siblings feasting on piles of Halloween candy and figure out how much pleasure you get (or don't) from eating more and more.

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Topic:
Building Functions (BF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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Topic:
Building Functions (BF), Interpreting Functions (IF)

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

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Topic:
Number System (NS), Ratios and Proportional Relationships (RP), Reasoning with Equations and Inequalities (REI)