few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response, in json format:
{
  "explanation": "This problem applies trigonometric identities, including the angle addition formula for cosine.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Understand ratio concepts and use ratio reasoning to solve problems.

Analyze proportional relationships and use them to solve real-world and mathematical problems.
problem_activity: Optional activity
The purpose of this optional activity is to practice using a proportional relationship in another context. The chosen numbers make the unit rate a useful tool to answer the questions.
Launch
Remind students of the value of a quarter and a dime.
Student Facing
4 quarters are equal in value to 10 dimes.
How many dimes equal the value of 6 quarters?
How many dimes equal the value of 14 quarters?
What value belongs next to the 1 in the table? What does it mean in this context?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "br": [{}], "_values": ["number of", "quarters"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["number of", "dimes"]}]}]}], "tbody": [{"tr": [{"td": [{"_value": "1"}, {}]}, {"td": [{"_value": "4"}, {"_value": "10"}]}, {"td": [{"_value": "6"}, {}]}, {"td": [{"_value": "14"}, {}]}]}]}]}
Student Response
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Student Facing
Are you ready for more?
Pennies made before 1982 are 95% copper and weigh about 3.11 grams each. (Pennies made after that date are primarily made of zinc). Some people claim that the value of the copper in one of these pennies is greater than the face value of the penny. Find out how much copper is worth right now, and decide if this claim is true.
Student Response
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Activity Synthesis
Ask students for the value that belongs next to the 1 in the table. Invite several students to explain the significance of this number.
Speaking: MLR8 Discussion Supports.
To provide a support students in precision of language when describing proportional relationships from a table, provide sentence frames for students to use, such as: “_____ is equal in value to _____, because . . . .”
Design Principle(s): Cultivate conversation


correct_option_index: 1