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

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

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

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

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

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

Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

Apply trigonometry to general triangles.

Understand congruence in terms of rigid motions.

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.

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

Define trigonometric ratios and solve problems involving right triangles.

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

Experiment with transformations in the plane.

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

Understand similarity in terms of similarity transformations.

Make geometric constructions.

Prove theorems involving similarity.

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

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

Translate between the geometric description and the equation for a conic section.
problem_activity: Task
In the two triangles below, angle $A$ is congruent to angle $D$, side $AC$ is congruent to side $DF$ and side $AB$ is congruent to side $DE$:
[IMG]
Sally reasons as follows: "If angle $A$ is congruent to angle $D$ then I can move point $A$ to point $D$ so that side $AB$ lies on top of side $DE$ and side $AC$ lies on top of side $DF$. Since $AB$ and $DE$ are congruent as are $AC$ and $DF$ the two triangles match up exactly and so they are congruent.''
Explain Sally's reasoning for why triangle $ABC$ is congruent to triangle $DEF$ using the language of reflections:
Construct a reflection which maps point $A$ to point $D$. Call $B'$ and $C'$ the images of $B$ and $C$ respectively under this reflection.
Construct a reflection which does not move $D$ but which sends $B'$ to $E$.  Call $C''$ the image of $C'$ under this reflection.
Construct a reflection which does not move $D$ or $E$ but which sends $C''$ to $F$.


correct_option_index: 12