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:
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 problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

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

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

Write and interpret numerical expressions.

Add and subtract within 20.

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

Multiply and divide within 100.

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

Work with radicals and integer exponents.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Understand the relationship between zeros and factors of polynomials.

Use polynomial identities to solve problems.

Perform arithmetic operations on polynomials.

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

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Analyze patterns and relationships.

Solve systems of equations.

Solve equations and inequalities in one variable.

Use properties of operations to generate equivalent expressions.

Interpret the structure of expressions.

Work with addition and subtraction equations.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

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

Rewrite rational expressions.

Create equations that describe numbers or relationships
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: 27