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: Represent and solve problems involving addition and subtraction.

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

Multiply and divide within 100.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Reason about and solve one-variable equations and inequalities.

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

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

Use polynomial identities to solve problems.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Add and subtract within 20.

Create equations that describe numbers or relationships

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Gain familiarity with factors and multiples.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Work with radicals and integer exponents.

Solve equations and inequalities in one variable.

Understand the relationship between zeros and factors of polynomials.

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

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

Represent and solve equations and inequalities graphically.

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

Solve systems of equations.

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.
problem_activity: Task
Here are some different ways to write the value $16$:
| $$2^4$$ | $$12-(2^1+2^2)+\frac{500}{50}$$ | $$2^3+2^3$$ | $$\frac23\times48^1-(1+3)^2$$ |
|---------|---------------------------------|-------------|-------------------------------|
Find at least three different ways to write each value below. Include at least one exponent in all of the expressions you write.
81
$2^5$
$\frac{64}{9}$


correct_option_index: 13