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: Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Rewrite rational expressions.

Write and interpret numerical expressions.

Multiply and divide within 100.

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

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

Use the four operations with whole numbers to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

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

Work with radicals and integer exponents.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

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

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

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

Work with addition and subtraction equations.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Create equations that describe numbers or relationships

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

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

Understand the relationship between zeros and factors of polynomials.

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

Solve systems of equations.

Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.
problem_activity: Narrative
The purpose of this activity is for students to relate drawings of equal groups to arrays. Specifically, students look for arrays that have the same number of objects in each row or column as each drawing has in each group. In some arrays, the equal groups in the drawing are represented as rows, and in some, they are represented in columns. Students have the opportunity to explain the connections they see between the drawings and arrays, receive feedback from their peers, and revise their explanation for precision and clarity (MP3, MP6). This will be useful in future lessons when students record multiplication expressions and equations to represent arrays.
This activity uses
MLR1 Stronger and Clearer Each Time
. Advances: reading, writing.
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Attention, Organization
Required Materials
Materials to Copy
Card Sort Arrays
Required Preparation
Create a set of cards from the blackline master for each group of 2 or 4 students.
Launch
Groups of 2 or 4
Distribute one set of pre-cut cards to each group of students.
Activity
“This set of cards includes drawings of equal groups and arrays. Match each drawing to an array. Work with your partner to justify your choices.”
8 minutes: partner work time
“Independently choose a match you and your partner made. Write down how you know that the drawing matches the array.”
2 minutes: independent work time
MLR1 Stronger and Clearer Each Time
“Share your response to why your cards match with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: structured partner discussion
Repeat with 2–3 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2–3 minutes: independent work time
Student Facing
Match the drawings of equal groups and arrays that are alike. Be prepared to explain your reasoning.
[IMG]
Choose a match you and your partner made. Write down how you know the drawing matches the array.
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
Have 2-3 students share the matches they made and describe how they know those cards go together.
“Did your group agree on the matches? What did you look for to decide two cards were matches?” (Yes, we looked for equal groups that had the same number of dots in a group as one of the rows in the array.)
Listen for language students use to describe their matches and the structure of the arrays. As needed, ask:
“What do you mean by _____?”
“What else could we call _____?”
“How could you use ‘equal groups’ to explain your match?”
Highlight the use of terms like row, column, and equal groups.


correct_option_index: 33