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: Extend the domain of trigonometric functions using the unit circle.

Analyze functions using different representations.

Use functions to model relationships between quantities.

Define, evaluate, and compare functions.

Build a function that models a relationship between two quantities.

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

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

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Model periodic phenomena with trigonometric functions.

Construct and compare linear and exponential models and solve problems.
problem_activity: Problem 1
What is an equation of the line represented in the graph below?
[IMG]
Problem 2
Four lines were used to define the edges of the trapezoid shown below.
[IMG]
Write an equation for each line described below.
a.   Line that passes through points
$$A$$
and
$$B$$
b.   Line that passes through points
$$B$$
and
$$C$$
c.   Line that passes through points
$$C$$
and
$$D$$
d.   Line that passes through points
$$D$$
and
$$A$$
Problem 3
Optional: Play the memory
Matching Game
with linear equations and graphs. Note that this requires some advance preparation.
Directions for students:
Find a partner and clear off your desks.
Separate the cards into a pile with equations and a pile with graphs.
Turn the equation cards over and organize them into rows/columns on one desk.
Turn the graph cards over and organize them into rows/columns on another desk.
On the first person’s turn, turn over an equation card and a graph card. If the cards match, then the player gets to keep the cards. If they do not match, turn the cards over in the same spot. The turn is over.
NOTE: If the player believes she or he has a match, then the player must prove that there is a match. The other player has the option to disagree and explain why. If the other player is right (and the first player was mistaken), then the other player gets to keep the card and then take a turn.
Repeat step 5 for the second player’s turn.
The game is over when all cards have been matched. The person with the most number of pairs wins the round. Another round may be played.


correct_option_index: 2