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

Write expressions in equivalent forms to solve problems.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Represent and solve problems involving addition and subtraction.

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Reason about and solve one-variable equations and inequalities.

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

Interpret the structure of expressions.

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

Represent and solve equations and inequalities graphically.

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

Work with addition and subtraction equations.

Solve systems of equations.

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

Analyze patterns and relationships.

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

Use polynomial identities to solve problems.

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

Generate and analyze patterns.

Rewrite rational expressions.

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

Represent and solve problems involving multiplication and division.

Add and subtract within 20.

Write and interpret numerical expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
problem_activity: Task
The first three steps of two visual patterns are shown below.
[IMG]
[IMG]
The number of tiles in step $n$ of Pattern D is defined by $d(n)=(n+3)^2$. The number of tiles in step $n$ of Pattern E is defined by $e(n)=(n+1)^2-2$.
For each pattern, decide whether there is a step with 167 tiles in it. If so, which step is it? If not, explain how you know.
For each pattern, decide whether there is a step with 169 tiles in it. If so, which step is it? If not, explain how you know.
Describe and justify the steps for solving the following equation for $x$: $$a(x-h)^2=k$$


correct_option_index: 13