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:
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 polynomial identities to solve problems.

Analyze patterns and relationships.

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

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

Gain familiarity with factors and multiples.

Solve systems of equations.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Understand the relationship between zeros and factors of polynomials.

Represent and solve problems involving multiplication and division.

Multiply and divide within 100.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Perform arithmetic operations on polynomials.

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

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

Work with addition and subtraction equations.

Create equations that describe numbers or relationships

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Write and interpret numerical expressions.

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

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

Work with radicals and integer exponents.
problem_activity: Problem 1
Consider the statement: A negative number raised to any whole number power will be negative.
Is this statement always, sometimes, or never true? Justify your response.
Problem 2
Consider the statement: An odd number raised to an odd power will be odd.
Is this statement always, sometimes, or never true? Justify your response.
Problem 3
What is the last digit of
$${7^{2023}}$$
? Explain.


correct_option_index: 33