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: Perform operations on matrices and use matrices in applications.

Use complex numbers in polynomial identities and equations.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Perform arithmetic operations with complex numbers.

Perform operations on vectors.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Apply and extend previous understandings of numbers to the system of rational numbers.

Extend the properties of exponents to rational exponents.

Represent and model with vector quantities.

Compute fluently with multi-digit numbers and find common factors and multiples.

Represent complex numbers and their operations on the complex plane.

Reason quantitatively and use units to solve problems.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Use properties of rational and irrational numbers.
problem_activity: Activity
The purpose of this activity is for students to practice interpreting the solution of an inequality, especially those involving negative numbers. Students also practice representing inequalities written in natural language with symbols and number lines, and connecting the solution of an inequality with a number line. The work in this activity will be useful when students solve more complex inequalities in the associated Algebra 1 lesson.
Student Facing
Solve each inequality. Then, check your answer using a value that makes your solution true.
\(\text-2x<4\)
Solve the inequality.
Check your answer using a value that makes your solution true.
\(3x+5>6x-4\)
Solve the inequality.
Check your answer using a value that makes your solution true.
\(\text-3(x+1)\geq13\)
Solve the inequality.
Check your answer using a value that makes your solution true.
For each statement:
Use a number line to show which values satisfy the inequality.
Express the statement symbolically with an inequality.
The elevator can lift up to 1,200 pounds. Let
\(x\)
represent the weight being lifted by the elevator.
[IMG]
Over the course of the senator's term, her approval rating was always around 53% ranging 3% above or below that value. Let
\(x\)
represent the senator’s approval rating.
[IMG]
There's a minimum of 3 years of experience required. Let
\(x\)
represent the years of experience a candidate has.
[IMG]
Student Response
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Activity Synthesis
The goal of this discussion is to help students make sense of their solutions. Here are questions for discussion:
"After you checked your answers using a value from your solution, did any of your answers change?" (Yes. Initially I thought the solution was
\(x <\text-2\)
, but I used
\(\text-3\)
to check my answer and realized it was incorrect. When I substituted
\(\text-3\)
for
\(x\)
in the original inequality, I got
\(6<4\)
which is not true. This reminds me to change the inequality symbol when I multiply or divide by a negative number.)
"Could the elevator hold 1,300 pounds?" (No. It holds
up to
1,200, so this is the largest amount the elevator can hold.)
"Could the senator’s approval rating be 54%?" (Yes. The situation says the approval rating can be 3 points above and below 53%, and 54% fits that requirement.)
"How can the number line be useful in writing the solution to an inequality?" (It helps to see which values are included in the solution and which are not. It can also be used to check your answer after you solve an inequality.)
"On the graph of the minimum years of experience for a candidate, does it make sense to have an upper bound? What examples can you think of that would make this situation have an upper bound?" (Yes, because realistically a person cannot have infinity years of experience and that is what the current graph of the inequality reprsents. For example, many people retire after a certain age, so it would be hard for someone to have more than 50 years of experience. Also, the average lifespan is about 110 and people ususally start working as teens or young adults, so this creates another limit on how many years of experience someone can actually have.)


correct_option_index: 6