few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "This problem involves understanding fractions as numbers by comparing their quantities.",
  "answer": "F"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Prove geometric theorems.

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

Experiment with transformations in the plane.

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

Find arc lengths and areas of sectors of circles.

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

Make geometric constructions.

Understand similarity in terms of similarity transformations.

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

Understand and apply theorems about circles.

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

Explain volume formulas and use them to solve problems.

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

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

Prove theorems involving similarity.

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

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

Apply geometric concepts in modeling situations.

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

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

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.

Define trigonometric ratios and solve problems involving right triangles.

Analyze, compare, create, and compose shapes.

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

Understand and apply the Pythagorean Theorem.
problem_activity: Rotate the following figure
$${90^{\circ}}$$
counterclockwise about the origin, three times.
[IMG]
A shape is formed through these rotations, with center at the origin.
Does this shape have rotational symmetry? If so, by what order/degree?
Doe this shape have reflectional symmetry? If so, what is the line of symmetry? If not, describe why not.


correct_option_index: 2

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