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: Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Work with equal groups of objects to gain foundations for multiplication.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving multiplication and division.

Understand the connections between proportional relationships, lines, and linear equations.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand properties of multiplication and the relationship between multiplication and division.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Understand and apply properties of operations and the relationship between addition and subtraction.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Rewrite rational expressions.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Multiply and divide within 100.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Solve systems of equations.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Create equations that describe numbers or relationships

Perform arithmetic operations on polynomials.
problem_activity: Problem 1
At the candy store, M&Ms and Skittles are sold for $0.50 per ounce. Kevita puts some M&Ms in a bag and then adds 8 ounces of Skittles. The total cost for her bag of candy is $6.50.
Kevita and Mary write the equation
$${0.5(x+8)=6.50}$$
to represent the situation, where
$$x$$
represents the number of ounces of M&Ms.
Kevita says that to solve this equation, you first distribute the
$$0.5$$
through the parentheses to get
$${0.5x+4=6.50}$$
.
Mary says that to solve this equation, you first divide by
$$0.5$$
on both sides to get
$${x+8=13}$$
.
Do you agree with either Kevita or Mary? Why? Finish solving the problem to find out how many ounces of M&Ms Kevita put in her bag of candy.
Problem 2
The taxi fare in Gotham City is $2.40 for the first
$${1 \over 2}$$
mile and additional mileage is charged at the rate of $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
What are two different ways you can solve this problem?
Problem 3
The ages of three cousins are consecutive integers. The sum of their ages is 45. Calculate their ages.
a.   Draw a tape diagram to represent the ages of the cousins.
b.   Let the youngest cousin's age be represented as
$$x$$
years old. Write and solve an equation to find the ages of the cousins.


correct_option_index: 14