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:
Thought: 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: Work with radicals and integer exponents.

Solve systems of equations.

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving multiplication and division.

Write and interpret numerical expressions.

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

Perform arithmetic operations on polynomials.

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

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Generate and analyze patterns.

Interpret the structure of expressions.

Add and subtract within 20.

Represent and solve equations and inequalities graphically.

Multiply and divide within 100.

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

Use the four operations with whole numbers to solve problems.

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

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

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

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

Rewrite rational expressions.

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

Gain familiarity with factors and multiples.

Understand properties of multiplication and the relationship between multiplication and division.
problem_activity: Activity
In this activity, students get a chance to practice solving equations with a single variable. The equations resemble the types of equations students see in the associated Algebra 1 lesson after they substitute for a variable. Students will work in pairs and each partner is responsible for answering the questions in either column A or column B. Although each row has two different problems, they share the same answer. Ensure that students work their problems out independently and collaborate with one another when they do not arrive to the same answers. Students construct viable arguments and critique the reasoning of others (MP3) when they resolve errors by critiquing their partner's work or explaining their reasoning.
Launch
Arrange students in groups of 2.
Student Facing
Solve each equation.
| row | column A | column B |
|-----|----------|----------|
|  1  |          |          |
|  2  |          |          |
|  3  |          |          |
|  4  |          |          |
|  5  |          |          |
|  6  |          |          |
​​
Student Response
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Activity Synthesis
The purpose of the discussion is to recall strategies for solving equations with one variable. Select students to share their solutions including their reasoning for the steps they take.
Some questions for discussion:
"When there is a variable inside parentheses, how did you approach the problem?" (I distributed the value multiplying the parentheses to remove the parentheses then solved the equation as usual.)
"How could you check that your answer works using the original equation?" (I could substitute the value for
\(x\)
into the original equation and determine if the equation is true.)


correct_option_index: 29