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: Use properties of rational and irrational numbers.

Represent and model with vector quantities.

Represent complex numbers and their operations on the complex plane.

Compute fluently with multi-digit numbers and find common factors and multiples.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Use complex numbers in polynomial identities and equations.

Extend the properties of exponents to rational exponents.

Perform operations on matrices and use matrices in applications.

Perform operations on vectors.

Perform arithmetic operations with complex numbers.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Reason quantitatively and use units to solve problems.

Apply and extend previous understandings of numbers to the system of rational numbers.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
problem_activity: Task
Carbon 14 is a form of carbon which decays exponentially over
time.
The amount
of Carbon 14 contained in a preserved plant is modeled
by the equation
$$
f(t) = 10\left(\frac{1}{2}\right)^{ct}.
$$
Time in this equation is measured in years
from the moment when the plant dies ($t = 0$) and the amount of Carbon 14 remaining in the preserved plant is measured in micrograms
(a microgram is one millionth of a gram).  The number $c$ in the exponential
measures the exponential rate of decay of Carbon $14$.
How many micrograms  of Carbon $14$ are in the plant at the time it died?
The best known estimate for the half-life of Carbon 14, that is the amount of time it takes for half of the
Carbon $14$ to decay, is $5730 \pm 40$ years.   Use this information to
calculate the range of possible values for the constant $c$ in the equation for $f$.
Use your answer from part (b) to find the range of years when there is
one microgram remaining in the preserved plant.


correct_option_index: 11