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:
{
  "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 real-life and mathematical problems using numerical and algebraic expressions and equations.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Analyze patterns and relationships.

Solve systems of equations.

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

Write and interpret numerical expressions.

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

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

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

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Use the four operations with whole numbers to solve problems.

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

Interpret the structure of expressions.

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

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Generate and analyze patterns.

Reason about and solve one-variable equations and inequalities.

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

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

Rewrite rational expressions.
problem_activity: Task
In a carefully controlled biology lab, a population of 100 bacteria reproduces via binary fission. That is, every hour, on the hour, each bacteria splits into two bacteria. Assuming no bacteria deaths, find an expression for the number $P(t)$ of bacteria in the population after $t$ hours.
In the next lab over, a population of protists reproduces hourly according to multiple fission. The function which gives the population of protists after $t$ hours is $$P(t)=50\cdot 3^t.$$ Interpret the significance of the numbers 50 and 3 in the context of the biological experiment.


correct_option_index: 24