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# Rise and Shine

## What time should school start in the morning?

What time should school start in the morning? The circadian rhythm is a 24-hour cycle that regulates how a body feels. As humans get older, the rhythm changes...which often leads to conflicts between parents and their sleep-deprived teens.

Students use periodic functions to compare the alertness levels of adults vs. teenagers over the course of the day and debate the merits of starting school later.

### REAL WORLD TAKEAWAYS

• Humans beings’ alertness changes throughout the day because of their natural circadian rhythm.
• A typical teenager’s circadian rhythm is shifted from an adult’s. Teenagers experience peak alertness later in the day.
• The typical work day matches adults’ peak alertness; the typical high school day does not match teenagers’ alertness.

### MATH OBJECTIVES

• Identify key features of a graphed periodic function including: period, amplitude, and relative maximums and minimums
• Interpret a trigonometric function modeling a real-world phenomena and use it to justify decision-making

This complex task is best as a culminating unit activity after students have developed formal knowledge and conceptual understanding.
Algebra 2
Trig. Functions
Algebra 2
Trig. Functions
Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Mathematical Practices MP.3 Construct viable arguments and critique the reasoning of others.