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: Define trigonometric ratios and solve problems involving right triangles.

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

Apply geometric concepts in modeling situations.

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

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

Reason with shapes and their attributes.

Find arc lengths and areas of sectors of circles.

Analyze, compare, create, and compose shapes.

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

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

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

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

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

Experiment with transformations in the plane.

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

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

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

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

Understand similarity in terms of similarity transformations.

Understand congruence in terms of rigid motions.

Make geometric constructions.

Prove geometric theorems.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

Understand and apply theorems about circles.
problem_activity: Task
Below are pictures of an equilateral triangle, a square, a regular hexagon, and a circle each having
the same perimeter:
[IMG]
Find the area of the equilateral triangle whose perimeter is $1$ unit.
Find the area of the square whose perimeter is $1$ unit.
Find the area of the regular hexagon whose perimeter is one unit.
Find the area of the circle whose perimeter is $1$ unit.
List the answers to (a), (b), (c) and (d) in increasing size.  How do you think the area of a regular octagon with perimeter $1$ unit would compare to the
triangle, square, hexagon, and circle?


correct_option_index: 17