few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


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. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. 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.


Your response:
Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Apply trigonometry to general triangles.

Understand congruence in terms of rigid motions.

Experiment with transformations in the plane.

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

Prove theorems involving similarity.

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

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

Apply geometric concepts in modeling situations.

Define trigonometric ratios and solve problems involving right triangles.

Reason with shapes and their attributes.

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

Analyze, compare, create, and compose shapes.

Find arc lengths and areas of sectors of circles.

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

Use coordinates to prove simple geometric theorems algebraically.

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

Understand and apply the Pythagorean Theorem.

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

Make geometric constructions.

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.

Explain volume formulas and use them to solve problems.

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

Prove geometric theorems.

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

Draw, construct, and describe geometrical figures and describe the relationships between them.
problem_activity: The two triangles in the picture below are congruent:
[IMG]
a.   Give a sequence of rotations, translations, and/or reflections that take
$${\triangle PRQ}$$
to
$${\triangle ABC}$$
.
b.   Is it possible to show the congruence in part (a) using only translations and rotations? Explain.


correct_option_index: 6