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 connections between proportional relationships, lines, and linear equations.

Represent and solve problems involving multiplication and division.

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

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

Analyze patterns and relationships.

Generate and analyze patterns.

Work with radicals and integer exponents.

Add and subtract within 20.

Solve systems of equations.

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

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Represent and solve equations and inequalities graphically.

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

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

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

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Rewrite rational expressions.

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

Perform arithmetic operations on polynomials.

Use polynomial identities to solve problems.

Multiply and divide within 100.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Represent and solve problems involving addition and subtraction.
problem_activity: Simplify the following expressions:
a.
$$(2^5)^7$$
b.
$$(91^3\times 19\times 103^8)^4$$
c.
$$(p^4q^5r)^9$$
d.
$$2^7\over 3^7$$


correct_option_index: 6