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:
Thought: 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: Find arc lengths and areas of sectors of circles.

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

Experiment with transformations in the plane.

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

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

Reason with shapes and their attributes.

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Prove theorems involving similarity.

Understand and apply theorems about circles.

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

Make geometric constructions.

Apply trigonometry to general triangles.

Use coordinates to prove simple geometric theorems algebraically.

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

Apply geometric concepts in modeling situations.

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.

Understand and apply the Pythagorean Theorem.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Explain volume formulas and use them to solve problems.

Prove geometric theorems.

Analyze, compare, create, and compose shapes.

Visualize relationships between two-dimensional and three-dimensional objects.
problem_activity: Task
Suppose $\triangle ABC$ and $\triangle DEF$ share three corresponding congruent sides as pictured below:
[IMG]
Show that $\triangle ABC$ is congruent ot $\triangle DEF$ as follows:
Apply a translation to move $\triangle ABC$ to $\triangle A^\prime B^\prime C^\prime$ with $A^\prime = D$.
Apply a rotation to move $\triangle A^\prime B^\prime C^\prime$ to $A^{\prime \prime}B^{\prime \prime}C^{\prime \prime}$ with $A^{\prime \prime} = D$ and $B^{\prime \prime} = E$.
Explain why $\left|A^{\prime \prime}C^{\prime \prime}\right| = \left|DF\right|$ and conclude that $\overleftrightarrow{DE}$ is the perpendicular bisector of $\overline{C^{\prime \prime}F}$.
Show that reflection over $\overleftrightarrow{DE}$ maps $F$ to $C^{\prime \prime}$ and conclude that $\triangle ABC$ is congruent to $\triangle DEF$.


correct_option_index: 6