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 the relationship between zeros and factors of polynomials.

Represent and solve equations and inequalities graphically.

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.

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

Gain familiarity with factors and multiples.

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

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Analyze patterns and relationships.

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

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Solve equations and inequalities in one variable.

Generate and analyze patterns.

Multiply and divide within 100.

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

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

Add and subtract within 20.

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

Work with radicals and integer exponents.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

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

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

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

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Interpret the structure of expressions.
problem_activity: Problem 1
Write the following as an imaginary number.
$${\sqrt{-72}}$$
Why is this not a complex number?
Problem 2
What kind of roots will the following quadratic function have?
$${4x-3x^2=10}$$


correct_option_index: 14