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, in json format:
{
  "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: Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

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

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.

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

Add and subtract within 20.

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

Represent and solve equations and inequalities graphically.

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

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

Solve equations and inequalities in one variable.

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

Rewrite rational expressions.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Work with addition and subtraction equations.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and interpret numerical expressions.

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

Represent and solve problems involving multiplication and division.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Analyze patterns and relationships.

Reason about and solve one-variable equations and inequalities.

Use polynomial identities to solve problems.
problem_activity: Bob can paint a fence in 5 hours, and working with Jen, the two of them painted the fence in 2 hours. How long would it have taken Jen to paint the fence alone?


correct_option_index: 15

29