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

Multiply and divide within 100.

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

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

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.

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

Rewrite rational expressions.

Solve systems of equations.

Add and subtract within 20.

Use polynomial identities to solve problems.

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

Write expressions in equivalent forms to solve problems.

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

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Interpret the structure of expressions.

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

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand the relationship between zeros and factors of polynomials.

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

Generate and analyze patterns.

Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.
problem_activity: Narrative
The purpose of this activity is for students to make sense of the structure of a Take From, Result Unknown story problem. Students have access to connecting cubes or two-color counters and 10-frames, which they may choose to use strategically to represent and solve the problem (MP5). Some students may apply the ideas from the previous unit where they related subtraction to counting back. As students share their methods, the teacher records their thinking. It is important for the teacher to focus attention on the expression during the activity synthesis. Although some students may attempt to write equations and do so accurately, this representation will be the focus in a later lesson.
Students keep their books closed for the launch of the activity, as the teacher displays and reads the problem.
MLR8 Discussion Supports.
Synthesis: Display sentence frames to support whole-class discussion: “_____ and _____ are the same/alike because . . .” and “_____ and _____ are different because . . .” Encourage students to use these sentence frames to compare and contrast representations.
Advances: Speaking, Conversing
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
Display the image from the warm-up.
“This is a picture of a library. Talk to your partner about what you know and what you wonder about libraries.”
3 minutes: partner discussion
Share and record what students know and wonder about libraries.
"We are going to solve a lot of story problems about libraries."
Display and read the numberless story.
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
If not already mentioned, ask, “Are there more or fewer kids at the library after some go home?”
Activity
Ask students to open their books.
Read the problem with numbers.
2 minutes: independent work time
“Share your thinking with your partner.”
2 minutes: partner discussion
Monitor for students who solve or represent the problem in the following ways:
objects
drawings
count back
an expression (
\(9 - 2\)
)
Student Facing
Some kids were at the library.
Then some of the kids went home.
What do you notice?
What do you wonder?
[IMG]
There were 9 kids at the library.
Then 2 of the kids went home.
How many kids are at the library now?
Show your thinking using drawings, numbers, or words.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students use more or fewer than nine objects to represent the kids at the library, consider asking:
“How did you choose how many connecting cubes to take out?”
“There are nine kids at the library. Which connecting cubes show the nine kids? Which connecting cubes show the two kids that went home?”
Activity Synthesis
Invite previously identified students to share in the order listed above.
“How are these representations the same? How are they different?”
If needed, display
\(9 - 2\)
.
“How does this expression match the story problem?”


correct_option_index: 8