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: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Compute fluently with multi-digit numbers and find common factors and multiples.

Use properties of rational and irrational numbers.

Extend the properties of exponents to rational exponents.

Use complex numbers in polynomial identities and equations.

Apply and extend previous understandings of numbers to the system of rational numbers.

Represent and model with vector quantities.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Reason quantitatively and use units to solve problems.

Perform arithmetic operations with complex numbers.

Represent complex numbers and their operations on the complex plane.

Perform operations on vectors.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Perform operations on matrices and use matrices in applications.
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: 4

9