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: Multiply and divide within 100.

Generate and analyze patterns.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

Rewrite rational expressions.

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

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

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

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

Add and subtract within 20.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

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

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Create equations that describe numbers or relationships

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

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

Use polynomial identities to solve problems.

Solve systems of equations.

Interpret the structure of expressions.

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

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

Reason about and solve one-variable equations and inequalities.

Work with addition and subtraction equations.

Represent and solve problems involving addition and subtraction.

Analyze patterns and relationships.

Apply and extend previous understandings of arithmetic to algebraic expressions.
problem_activity: Narrative
The purpose of this activity is for students to connect story problems to the equations that represent them and to solve different types of story problems. Students identify equations with a symbol for the unknown that match a story problem and justify their decisions by describing how the equations represent the quantities and any actions in the story problem (MP4). When students analyze and connect the quantities and structures in the story problems and equations, they are thinking abstractly and quantitatively (MP2) and making use of structure (MP7).
MLR8 Discussion Supports.
Display sentence frames to support discussion as students explain their reasoning to their partner: “I noticed ___ , so I matched . . .” Encourage students to challenge each other when they disagree.
Advances: Conversing, Representing
Required Materials
Materials to Gather
Base-ten blocks
Materials from a previous lesson
Materials to Copy
Equations for Different Types of Word Problems
Required Preparation
Create a set of cards from the blackline master for each group of 2
–
4.
Each group of 2
–
4 needs a set of cards from the previous lesson.
Launch
Groups of 2
–
4
Give each group the story problems (Cards A–I) from the Story Problem and Diagram Cards.
Give one set of Equation Cards to each group of students.
Give each group access to base-ten blocks.
“Take turns reading the story problems. After one person reads, work together to find an equation that matches. When you think you have found a match, explain to your group why the cards match.”
“If you think that more than one card could match the story, explain the match to your group.”
As needed, demonstrate the activity with a student volunteer.
“When your group finishes, choose 2 story problems from Cards F, G, H, or I and solve them.”
Activity
6 minutes: partner work time
Monitor for students who explain why more than one equation may match a story and how the equations match the quantities in the context of the story problem.
4 minutes: independent work time
Student Facing
Match each story problem with an equation. Explain why the cards match.
Choose 2 story problems and solve them. Show your thinking.
Student Response
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for free access to Student Response.
Advancing Student Thinking
Students may believe that only one equation could match each story. Encourage
students to describe how equations match any actions in the story and whether any other equations show the same actions. If there are no actions in the story, ask students to explain why one or more cards shows the relationship between the parts and the whole. Consider providing the tape diagrams from the previous activity to support students in their explanations.
Activity Synthesis
Invite students to share a match for each story.
Consider asking:
“How does the equation match the story problem?”
“Is there another equation that could match the story problem? Explain why or why not.”


correct_option_index: 31