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:
Thought: 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: Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

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

Represent and solve problems involving addition and subtraction.

Rewrite rational expressions.

Represent and solve problems involving multiplication and division.

Add and subtract within 20.

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

Analyze patterns and relationships.

Use polynomial identities to solve problems.

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

Solve equations and inequalities in one variable.

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

Create equations that describe numbers or relationships

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

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

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

Gain familiarity with factors and multiples.

Interpret the structure of expressions.

Generate and analyze patterns.

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

Work with addition and subtraction equations.

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

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

Write and interpret numerical expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.
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: 33