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, in json format:
{
  "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: Understand properties of multiplication and the relationship between multiplication and division.

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

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Interpret the structure of expressions.

Perform arithmetic operations on polynomials.

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

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

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

Add and subtract within 20.

Solve systems of equations.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Represent and solve equations and inequalities graphically.

Use polynomial identities to solve problems.

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

Work with radicals and integer exponents.

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Analyze and solve linear equations and pairs of simultaneous linear equations.
problem_activity: Problem 1
Set A and Set B each include a quadratic function represented as an equation, a graph, and a table.
Determine if all three representations in each set match. If not, explain how you would change one or more of the representations to make them match.
[IMG]
[IMG]
Problem 2
Which quadratic function below has the greatest positive value of
$$x$$
as a solution?
[IMG]


correct_option_index: 3