few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Interpret expressions for functions in terms of the situation they model.

Use functions to model relationships between quantities.

Model periodic phenomena with trigonometric functions.

Build a function that models a relationship between two quantities.

Extend the domain of trigonometric functions using the unit circle.

Define, evaluate, and compare functions.

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

Prove and apply trigonometric identities.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Analyze functions using different representations.

Construct and compare linear and exponential models and solve problems.
problem_activity: Task
Suppose a can of cold soda is left in a warm room on a summer day.  The graph below shows the temperature of the soda as it gradually increased:
[IMG]
The function that describes the temperature, $F$, of the soda (in degrees Fahrenheit) after $t$ minutes can be expressed by
$$F(t)=C - R e^{-kt},$$
for some positive values of $C$, $R$, and $k$.<
Use the graph to estimate $C$.
Use the graph to estimate $R$.
What was the approximate room temperature?  What was the initial temperature of the soda when placed in the room?


correct_option_index: 0

9