standard_description: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
problem_activity: Warm-up
This activity encourages students to apply ratio reasoning to solve a problem they might encounter naturally outside a mathematics classroom. The warm up invites open-ended thinking that is validated by mathematical reasoning, which is the type of complex thinking needed to solve Fermi problems in the following activities.
Launch
Arrange students in groups of 2. Display the image for all to see.
Optionally, instead of the abstract image, you could bring in a clear glass, milk, and cocoa powder. Pour 1 cup of milk into the glass, add 5 tablespoons of cocoa powder, and introduce the task that way.
Tell students to give a signal when they have an answer and a strategy. Give students 2 minutes of quiet think time.
Student Facing
Andre likes a hot cocoa recipe with 1 cup of milk and 3 tablespoons of cocoa. He poured 1 cup of milk but accidentally added 5 tablespoons of cocoa.
[IMG]
How can you fix Andre’s mistake and make his hot cocoa taste like the recipe?
Explain how you know your adjustment will make Andre’s hot cocoa taste the same as the one in the recipe.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share their strategies with the class and record them for all to see. After each explanation, ask the class if they agree or disagree and how they know two hot cocoas will taste the same.


aligns: no