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:
{
  "explanation": "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

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options: Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

Build new functions from existing functions.

Define, evaluate, and compare functions.

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

Build a function that models a relationship between two quantities.

Model periodic phenomena with trigonometric functions.

Use functions to model relationships between quantities.

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

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.
problem_activity: Task
A wheel of radius 0.2 meters begins to move along a flat surface so that the center of the wheel moves forward at a constant speed of 2.4 meters per second.  At the moment the wheel begins to turn, a marked point $P$ on the wheel is touching the flat surface.
[IMG]
Write an algebraic expression for the function $y$ that gives the height (in meters) of the point $P$, measured from the flat surface, as a function of $t$, the number of seconds after the wheel begins moving.
Sketch a graph of the function $y$ for $t>0$.  What do you notice about the graph?  Explain your observations in terms of the real-world context given in this problem.
We define the horizontal position of the point $P$ to be the number of meters the point has traveled forward from its starting position, disregarding any vertical movement the point has made.  Write an algebraic expression for the function $x$ that gives the horizontal position (in meters) of the point $P$ as a function of $t$, the number of seconds after the wheel begins moving.
Sketch a graph of the function $x$ for $t>0.$  Is there a time when the point $P$ is moving backwards?  Use your graph to justify your answer.


correct_option_index: 4

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