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:
{
  "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: Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

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

Understand the relationship between zeros and factors of polynomials.

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

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Solve systems of equations.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

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

Rewrite rational expressions.

Write and interpret numerical expressions.

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

Represent and solve equations and inequalities graphically.

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

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

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

Multiply and divide within 100.

Represent and solve problems involving multiplication and division.

Use polynomial identities to solve problems.

Reason about and solve one-variable equations and inequalities.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

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

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

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.
problem_activity: Problem 1
Write the following as an imaginary number.
$${\sqrt{-72}}$$
Why is this not a complex number?
Problem 2
What kind of roots will the following quadratic function have?
$${4x-3x^2=10}$$


correct_option_index: 8