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: Explain volume formulas and use them to solve problems.

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

Experiment with transformations in the plane.

Understand similarity in terms of similarity transformations.

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

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

Analyze, compare, create, and compose shapes.

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

Apply geometric concepts in modeling situations.

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

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

Use coordinates to prove simple geometric theorems algebraically.

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

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

Apply trigonometry to general triangles.

Understand and apply the Pythagorean Theorem.

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.

Understand and apply theorems about circles.

Prove theorems involving similarity.

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

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

Prove geometric theorems.

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

Find arc lengths and areas of sectors of circles.
problem_activity: Task
Imagine you are a ninja that can slice solid objects straight through. You have a solid cube in front of you. You are curious about what 2-dimensional shapes are formed when you slice the cube. For example, if you make a slice through the center of the cube that is parallel to one of the faces, the cross section is a square:
[IMG]
[IMG]
For each of the following slices, (i) describe using precise mathematical language the shape of the cross section. (ii) draw a diagram showing the cross section of the cube.
[IMG]
a. A slice containing edge AC and edge EG b. A slice containing the vertices C, B, and G. C. A slice containing the vertex A, the midpoint of edge EG, and the midpoint of edge FG.


correct_option_index: 1