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:
Thought: 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: Represent and analyze quantitative relationships between dependent and independent variables.

Use the four operations with whole numbers to solve problems.

Analyze patterns and relationships.

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

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

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving addition and subtraction.

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

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

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

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

Generate and analyze patterns.

Gain familiarity with factors and multiples.

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

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

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

Add and subtract within 20.

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

Multiply and divide within 100.

Work with radicals and integer exponents.

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

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

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Problem 1
Without solving the systems, explain why the following system must have the same solution.
| System 1:                       $${4x-5y=13 }$$                        $${3x+6y=11}$$ | System 2:                       $${8x-10y=26}$$                        $${x-11y=2}$$ |
|---------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------|
Problem 2
Solve the system of equations by writing a new system that eliminates one of the variables.
$${3x+2y=4}$$
$${4x+7y=1}$$


correct_option_index: 32