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:
{
  "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.

Apply geometric concepts in modeling situations.

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

Define trigonometric ratios and solve problems involving right triangles.

Reason with shapes and their attributes.

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

Analyze, compare, create, and compose shapes.

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

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

Understand congruence in terms of rigid motions.

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

Understand similarity in terms of similarity transformations.

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

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

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

Make geometric constructions.

Understand and apply theorems about circles.

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

Apply trigonometry to general triangles.

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

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

Find arc lengths and areas of sectors of circles.

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

Understand and apply the Pythagorean Theorem.

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Problem 1
A new park is being built in the city. In the park, there will be a cemented walkway that will wind through the park. The walkway will be completely enclosed by a short, gated fence that will line the path on all sides of the path. The blueprint for the pathway is shown in the coordinate plane below. Each square unit in the coordinate grid represents 1 square yard.
[IMG]
a.   The city budget includes enough funds to include 50 square yards of cement and 60 yards of fencing. Will the budget cover the necessary expenses for cement and fencing? Defend your answer.
b.   Two statues will be placed at points
$${(-1, 2)}$$
and
$${(-1, -4).}$$
How far apart, in yards, are the two statues?
Problem 2
You are responsible for a small plot of land in the community garden that measures
$$9$$
ft.
$$\times $$
$$9$$
ft. You want to include
$${48}$$
square feet of gardening space, and you want your garden to have at least one rectangle shape and at least one triangle shape.
Draw a possible plan for your garden on the grid below. Make sure you do not go outside of the
$$9$$
ft.
$$\times $$
$$9$$
ft. space.
[IMG]


correct_option_index: 2