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: Find arc lengths and areas of sectors of circles.

Translate between the geometric description and the equation for a conic section.

Understand similarity in terms of similarity transformations.

Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.

Analyze, compare, create, and compose shapes.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Visualize relationships between two-dimensional and three-dimensional objects.

Solve real-world and mathematical problems involving area, surface area, and volume.

Define trigonometric ratios and solve problems involving right triangles.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Apply geometric concepts in modeling situations.

Prove theorems involving similarity.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Experiment with transformations in the plane.

Reason with shapes and their attributes.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Make geometric constructions.

Understand congruence in terms of rigid motions.

Classify two-dimensional figures into categories based on their properties.

Apply trigonometry to general triangles.

Prove geometric theorems.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Task
On graph paper, sketch a line segment with end points $A=(0,2)$ and $B=(0,6)$. Plot all points $C=(x,y)$ such that the triangle ABC has an area of 6 square units.
What two basic geometric theorems are needed to solve this problem?


correct_option_index: 26