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

Represent and solve equations and inequalities graphically.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

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

Solve systems of equations.

Generate and analyze patterns.

Rewrite rational expressions.

Multiply and divide within 100.

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.

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Work with radicals and integer exponents.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

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

Use polynomial identities to solve problems.

Work with addition and subtraction equations.

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

Perform arithmetic operations on polynomials.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
problem_activity: Anton writes a model that describes the number of tacos his friends eat as a function of the cost of the total tacos. Below is a graph of the model.
[IMG]
Anton writes a second model that describes the total cost of the tacos as a function of the number of tacos his friends eat. Below is a graph of the model.
[IMG]
Label the axes appropriately. Which one makes more sense?
How are these two graphs similar? Different?
How are these two equations similar? Different?


correct_option_index: 9