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: Calculate expected values and use them to solve problems.

Use probability to evaluate outcomes of decisions.

Understand independence and conditional probability and use them to interpret data.

Summarize, represent, and interpret data on a single count or measurement variable.

Develop understanding of statistical variability.

Investigate chance processes and develop, use, and evaluate probability models.

Use random sampling to draw inferences about a population.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Understand and evaluate random processes underlying statistical experiments.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Investigate patterns of association in bivariate data.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Interpret linear models.
problem_activity: Warm-up
The purpose of this warm-up is to elicit methods students are already using to organize their understanding of different outcomes. In this lesson, students are asked to use different structures to think about the outcomes of experiments that involve multiple steps, so this activity should give you an idea of how students are approaching the problem on their own.
Launch
Arrange students in groups of 2. Tell students they should organize their work so it can be understood by others. Give students 1 minute of quiet think time, 3 minutes for partner discussion, and follow up with a whole-class discussion.
Student Facing
How many different meals are possible if each meal includes one main course, one side dish, and one drink?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "main courses"}, {"_attributes": {"scope": "col"}, "_value": "side dishes"}, {"_attributes": {"scope": "col"}, "_value": "drinks"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "grilled chicken"}, {"_value": "salad"}, {"_value": "milk"}]}, {"td": [{"_value": "turkey sandwich"}, {"_value": "applesauce"}, {"_value": "juice"}]}, {"td": [{"_value": "pasta salad"}, {"_value": "\u2014"}, {"_value": "water"}]}]}]}]}
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
Select several groups to share their methods for organizing their thoughts about the different meals that are possible.
Consider these questions for the discussion:
“How did you know you counted all of the different possible meals?”
“How did you know you didn’t repeat any meals?”


correct_option_index: 5