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: Analyze functions using different representations.

Use functions to model relationships between quantities.

Interpret expressions for functions in terms of the situation they model.

Construct and compare linear and exponential models and solve problems.

Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Model periodic phenomena with trigonometric functions.

Prove and apply trigonometric identities.

Build new functions from existing functions.

Interpret functions that arise in applications in terms of the context.

Build a function that models a relationship between two quantities.

Define, evaluate, and compare functions.
problem_activity: The estimated size for a population of rabbits and a population of coyotes in a desert habitat are shown in the table. The estimated population sizes were recorded as a part of a long-term study related to the effect of commercial development on native animal species.
|  Years since initial count (       *        n       *       )  |   0    |   3    |   6   |   9    |   12   |   15   |  18   |   21   |   24   |
|----------------------------------------------------------------|--------|--------|-------|--------|--------|--------|-------|--------|--------|
| Estimated number of rabbits (       *        r       *       ) | 14,989 | 10,055 | 5,002 | 10,033 | 15,002 | 10,204 | 4,999 | 10,002 | 14,985 |
| Estimated number of coyotes (       *        c       *       ) | 1,995  | 2,201  | 2,003 | 1,795  | 1,999  | 2,208  | 2,010 | 1,804  | 2,001  |
Below are sketches of each graph, with a curve fitted to the data.
[IMG]
[IMG]
Write the function for each situation and then calculate the two different numbers of years where the population estimate is about 13,000 for rabbits and 2,100 for coyotes.


correct_option_index: 6