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.


Topic options: 
A. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
B. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
C. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
D. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
E. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
F. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
G. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
H. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
I. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
J. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
K. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.


Your response:
Thought: In this problem, students learn to recognize equivalent fractions. Each lap around the school is 1/4 mile, while each lap around the playground is 1/12 mile. Three laps around the playground is 3/12 mile, which is equivalent to 1/4.
Answer: D

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: im_task_000212

4
options: Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
problem_activity: Task
A preserved plant is estimated to contain $1$ microgram (a millionth of a gram) of
Carbon $14$.    The amount of Carbon 14 present
in the preserved plant is modeled by the equation
$$
f(t) = A\left(\frac{1}{2}\right)^{\frac{t}{5730}}
$$
where $t$ denotes time since the death of the plant, measured in years,
and $A$ is the amount of Carbon $14$ present in the plant at death, measured
in micrograms.
How much Carbon $14$ was present in the living plant assuming it died  $5000$ years ago?
How much Carbon $14$ was present in the living plant assuming it
died $10000$ years ago?
The half-life of Carbon $14$ is the amount of time it takes for half of the
Carbon $14$ to decay.  What half-life does the expression for  the function $f$
imply for Carbon $14$?


correct_option_index: 2