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: Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Gain familiarity with factors and multiples.

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

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

Interpret the structure of expressions.

Rewrite rational expressions.

Understand the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

Use the four operations with whole numbers to solve problems.

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

Reason about and solve one-variable equations and inequalities.

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

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

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

Solve equations and inequalities in one variable.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Perform arithmetic operations on polynomials.

Analyze patterns and relationships.

Write and interpret numerical expressions.

Multiply and divide within 100.

Work with addition and subtraction equations.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Use properties of operations to generate equivalent expressions.

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

Represent and solve problems involving multiplication and division.

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

Generate and analyze patterns.

Work with radicals and integer exponents.
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: 27