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: Represent and solve problems involving addition and subtraction.

Represent and solve equations and inequalities graphically.

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

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

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

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving multiplication and division.

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

Analyze patterns and relationships.

Create equations that describe numbers or relationships

Work with addition and subtraction equations.

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

Write and interpret numerical expressions.

Rewrite rational expressions.

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

Add and subtract within 20.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

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

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

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

Work with radicals and integer exponents.

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

Interpret the structure of expressions.

Use polynomial identities to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Activity
The purpose of this activity is to give students practice writing and graphing equations from situations. In the next activity and in the supported Algebra 1 lesson, students will write and graph inequalities  Students then assess the meaning of points off of the line in the situation provided and interpret whether those points might be valid in the situation.
Student Facing
Write an equation that helps to answer the question about the situation. Then draw a graph that represents the equation.
Jada goes to an orchard to pick plums and apricots to make jam. She picks 20 pounds of fruit altogether. If she picks
\(a\)
pounds of apricots, how many pounds of plums does she pick?
[IMG]
Consider the point
\((5,16)\)
. Is it possible for the weight of the fruit to be represented by that point in this situation? Explain your reasoning.
In a video game, a character can run at a top speed of 30 miles per hour, but each additional pound that the character carries lowers the maximum running speed by 1 mile per hour. What is the maximum running speed of the character when they are carrying
\(w\)
pounds?
[IMG]
Consider the point
\((10,15)\)
. Is it possible for a character in this game to be represented by that point in this situation? Explain your reasoning.
Student Response
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Activity Synthesis
The purpose of the discussion is to examine points on and off the lines and determine what they might mean in the situations.
Ask students:
"What are the coordinates for a point on the line that represents the scooter situation? What do the coordinates mean in that situation?" (The point
\((1,22)\)
is on the line. This means that renting the scooter for 2 hours should cost
$
22.)
"What are the coordinates for a point above the line that represents the scooter situation? What do the coordinates mean in that situation? Is it realistic?" (The point
\((2,30)\)
is above the line. This means paying
$
30 for 2 hours with a scooter. It only makes sense if the person is overpaying for some reason like if they broke part of the scooter and have to pay extra.)
"The point
\((5,30)\)
is above the line that represents the maximum run speed for the videogame character. Describe a situation where this might be possible." (If the character has an item that ignores the carry weight or something that boosts their run speed, then maybe this is possible.)


correct_option_index: 1