few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
{
  "explanation": "This problem involves understanding fractions, multiplication, and division.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Perform arithmetic operations on polynomials.

Interpret the structure of expressions.

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

Use properties of operations to generate equivalent expressions.

Write and interpret numerical expressions.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

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

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

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

Use polynomial identities to solve problems.

Analyze patterns and relationships.

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

Use the four operations with whole numbers to solve problems.

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

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

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

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

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Rewrite rational expressions.

Multiply and divide within 100.

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.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Solve equations and inequalities in one variable.

Solve systems of equations.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.
problem_activity: Task
The population of a country is initially 2 million people and is increasing at 4% per year. The country's annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.5 million people per year.
Based on these assumptions, in approximately what year will this country ﬁrst experience shortages of food?
If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?  In approximately which year?
If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?


correct_option_index: 31