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: Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Create equations that describe numbers or relationships

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

Multiply and divide within 100.

Use polynomial identities to solve problems.

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

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Represent and solve equations and inequalities graphically.

Reason about and solve one-variable equations and inequalities.

Interpret the structure of expressions.

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

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

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

Represent and analyze quantitative relationships between dependent and independent variables.

Rewrite rational expressions.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

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

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

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 connections between proportional relationships, lines, and linear equations.

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

Generate and analyze patterns.

Represent and solve problems involving multiplication and division.
problem_activity: Task
Working with complex numbers allows us to solve equations like $z^2 = -1$
which cannot be solved with real numbers.  Here we will investigate complex numbers which arise as square roots of certain complex numbers.
Find all complex square roots of -1, that is, find all numbers $z = a + bi$ which satisfy $z^2 = -1$.
Find all complex square roots of 1.
Which complex numbers satisfy $z^2 = i$?


correct_option_index: 8