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:
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.

Analyze, compare, create, and compose shapes.

Make geometric constructions.

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

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

Explain volume formulas and use them to solve problems.

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

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

Apply geometric concepts in modeling situations.

Prove geometric theorems.

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

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

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

Reason with shapes and their attributes.

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

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

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

Understand and apply the Pythagorean Theorem.

Understand similarity in terms of similarity transformations.

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

Apply trigonometry to general triangles.
problem_activity: Task
On the map below, $\frac14$ inch represents one mile. Candler, Canton, and Oteen are three cities on the map.
[IMG]
If the distance between the real towns of Candler and Canton is 9 miles, how far apart are Candler and Canton on the map?
If Candler and Oteen are $3\frac12$ inches apart on the map, what is the actual distance between Candler and Oteen in miles?


correct_option_index: 5