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:
Thought: 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: Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

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

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.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Write expressions in equivalent forms to solve problems.

Generate and analyze patterns.

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

Perform arithmetic operations on polynomials.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

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

Gain familiarity with factors and multiples.

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

Interpret the structure of expressions.

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

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

Solve systems of equations.

Rewrite rational expressions.

Add and subtract within 20.

Use polynomial identities to solve problems.

Understand properties of multiplication and the relationship between multiplication and division.
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: 26