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: Write and interpret numerical expressions.

Analyze patterns and relationships.

Gain familiarity with factors and multiples.

Use polynomial identities to solve problems.

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

Use the four operations with whole numbers to solve problems.

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

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

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

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

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

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

Create equations that describe numbers or relationships

Represent and solve problems involving addition and subtraction.

Perform arithmetic operations on polynomials.

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

Use properties of operations to generate equivalent expressions.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Interpret the structure of expressions.

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

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

Solve systems of equations.

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

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Represent and analyze quantitative relationships between dependent and independent variables.
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