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

Understand congruence in terms of rigid motions.

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

Understand and apply theorems about circles.

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

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

Prove geometric theorems.

Experiment with transformations in the plane.

Apply trigonometry to general triangles.

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

Understand similarity in terms of similarity transformations.

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

Find arc lengths and areas of sectors of circles.

Make geometric constructions.

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

Explain volume formulas and use them to solve problems.

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

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

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

Analyze, compare, create, and compose shapes.

Reason with shapes and their attributes.

Use coordinates to prove simple geometric theorems algebraically.
problem_activity: Problem 1
Circles
$$A$$
and
$$C$$
are shown below.
[IMG]
Write an equation that describes each of the circles.
Problem 2
Write the equation of a circle whose diameter has endpoints of
$$(-8, 2)$$
and
$$ (2, 2)$$
.
Problem 3
Describe how you could prove that circle
$$A$$
is similar to circle
$$B$$
.
[IMG]


correct_option_index: 0

3

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