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: Analyze patterns and relationships.

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

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

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

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

Use the four operations with whole numbers to solve problems.

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

Use properties of operations to generate equivalent expressions.

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

Generate and analyze patterns.

Represent and solve problems involving addition and subtraction.

Understand the relationship between zeros and factors of polynomials.

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

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

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Gain familiarity with factors and multiples.

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

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

Work with addition and subtraction equations.

Multiply and divide within 100.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Solve equations and inequalities in one variable.

Represent and analyze quantitative relationships between dependent and independent variables.

Add and subtract within 20.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and interpret numerical expressions.

Solve systems of equations.
problem_activity: Problem 1
Quiana measures the width of her doorway entrance using a measuring tape. She measures the width as 33 inches. She later finds a better tape measure that measures to the nearest half of an inch. After re-measuring, she determines that the actual measure of the doorway is 32 ½ inches.
a.   What is the amount of error from using the first measuring tape?
b.   What is the error as a percentage of the actual width?
Problem 2
Paul and Kimberly both estimate the weight of their dogs before bringing them to the vet. The table below shows each of their estimates along with the actual weights of the dogs from the vet’s office.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width:60%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Estimate (lbs.)"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Actual (lbs.)"}]}]}, {"td": [{"_value": "Paul's dog"}, {"_attributes": {"style": "text-align:center"}, "_value": "10"}, {"_attributes": {"style": "text-align:center"}, "_value": "11.5"}]}, {"td": [{"_value": "Kimberly's dog"}, {"_attributes": {"style": "text-align:center"}, "_value": "84"}, {"_attributes": {"style": "text-align:center"}, "_value": "82.5"}]}]}]}]}
Paul notices that both his and Kimberly’s estimates were only 1.5 pounds off from the actual weights. Paul says that means his estimate was as good as Kimberly’s estimate.
Do you agree with Paul? Find the percent error for each person’s guess of their dog’s weight, and use it in your answer.
Problem 3
In science class, Justine measured a rock sample and found it to be 15 grams. Her teacher told her that the scale is off and the actual weight is 0.3 grams more than her measurement.
What is the percent error? Give your answer to the nearest percent.


correct_option_index: 21