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

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Reason about and solve one-variable equations and inequalities.

Work with radicals and integer exponents.

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

Generate and analyze patterns.

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

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Rewrite rational expressions.

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

Add and subtract within 20.

Multiply and divide within 100.

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

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

Solve equations and inequalities in one variable.

Solve systems of equations.

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

Write and interpret numerical expressions.

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

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving addition and subtraction.
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: 6