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: Write expressions in equivalent forms to solve problems.

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

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

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

Add and subtract within 20.

Represent and solve equations and inequalities graphically.

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

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

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

Multiply and divide within 100.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Create equations that describe numbers or relationships

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

Interpret the structure of expressions.

Write and interpret numerical expressions.

Use the four operations with whole numbers to solve problems.

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

Rewrite rational expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Solve systems of equations.

Use properties of operations to generate equivalent expressions.

Analyze patterns and relationships.

Generate and analyze patterns.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

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

Understand the relationship between zeros and factors of polynomials.
problem_activity: Task
Consider the algebraic expressions below:
$$ (n + 2)^2 - 4 \qquad \text{and} \qquad n^2 + 4n. $$
Use the figures below to illustrate why the expressions are equivalent:
[IMG]
Find some ways to algebraically verify the same result.


correct_option_index: 15