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: Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

Understand similarity in terms of similarity transformations.

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

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

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

Reason with shapes and their attributes.

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

Make geometric constructions.

Understand and apply theorems about circles.

Understand congruence in terms of rigid motions.

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

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

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

Apply trigonometry to general triangles.

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

Explain volume formulas and use them to solve problems.

Apply geometric concepts in modeling situations.

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply the Pythagorean Theorem.

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

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

Prove geometric theorems.

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

Find arc lengths and areas of sectors of circles.
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: 20