options: Model periodic phenomena with trigonometric functions.

Construct and compare linear and exponential models and solve problems.

Understand the concept of a function and use function notation.

Use functions to model relationships between quantities.

Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Extend the domain of trigonometric functions using the unit circle.

Prove and apply trigonometric identities.

Interpret functions that arise in applications in terms of the context.

Define, evaluate, and compare functions.

Interpret expressions for functions in terms of the situation they model.

Build new functions from existing functions.
problem_activity: Warm-up
The purpose of this warm-up is to familiarize students with one of the central graphical representations they will be working with in the lesson. As students notice and wonder, they have the opportunity to reason abstractly and quantitatively if they consider the situation the graph represents (MP2).
Launch
Tell students they will look at a graph, and their job is to think of at least one thing they notice and at least one thing they wonder about the picture. Display the graph for all to see and give 1 minute of quiet think time. Ask students to give a signal when they have noticed or wondered about something.
Student Facing
What do you notice? What do you wonder?
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Student Response
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Activity Synthesis
Ask students to share things they noticed and wondered about the graph. Record and display these ideas for all to see. For each of the things students notice and wonder, ask them to reference the graph in their explanation. If no one notices that at every distance from the starting line, there are two associated times (except at 200 meters), bring that to their attention.
If there is time, ask students to make some estimations or guesses for the wonders that refer to the information in the graph. For example, if someone wonders what the title of the graph may be, ask them to create a title that would make sense for this context.


correct_option_index: 9