few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
{
  "explanation": "This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

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

Create equations that describe numbers or relationships

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

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

Add and subtract within 20.

Gain familiarity with factors and multiples.

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

Rewrite rational expressions.

Solve systems of equations.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

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

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

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

Perform arithmetic operations on polynomials.

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

Analyze patterns and relationships.

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

Use the four operations with whole numbers to solve problems.

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

Multiply and divide within 100.

Write and interpret numerical expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.
problem_activity: Task
A physics professor says: "Of course, it is easy to see that
$$ L_0 \sqrt{1 - \frac{v^2}{c^2}} = 0 $$
when $v = c$."
Give a possible explanation in terms of the structure of the expression on the left why the professor might say that.
Assuming that $L_0$ and $c$ are positive, what is the greatest possible value of the expression on the left?  Explain your answer in terms of the structure of the expression.


correct_option_index: 21