few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
Thought: This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Build new functions from existing functions.

Analyze functions using different representations.

Construct and compare linear and exponential models and solve problems.

Understand the concept of a function and use function notation.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.

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

Interpret functions that arise in applications in terms of the context.
problem_activity: Task
Katy is told that the cost of producing $x$ DVDs is given by $C(x) = 1.25x + 2500.$ She is then asked to find an equation for $\frac{C(x)}{x}$, the average cost per DVD of producing $x$ DVDs.
She begins her work: $$\frac{C(x)}{x} =\frac {1.25x+2500}{x}$$ and finishes by simplifying both sides to get: $$C = 1.25+\frac{2500}{x}$$  Is Katy's answer correct? Explain.


correct_option_index: 5