few_shots: Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Your response, in json format:
{
  "explanation": "This task shows one quadratic equation with one variable, x.",
  "answer": "B"
}

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Standard options: 
A. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Your response, in json format:
{
  "explanation": "This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.",
  "answer": "A"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
problem_activity: Task
Materials
Coins and dollar bills
Problem with table of costs displayed
{"table": [{"tbody": [{"tr": [{"th": [{"_value": "Stuffed Animals at the Pet Shop"}, {"_value": "Cost for each animal"}]}, {"td": [{"_value": "Dog"}, {"_value": "2 pennies, 3 nickels, and 1 quarter"}]}, {"td": [{"_value": "Snake"}, {"_value": "6 pennies, 2 nickels, and 2 dimes"}]}, {"td": [{"_value": "Bird"}, {"_value": "5 nickels, 3 dimes, and 1 quarter"}]}, {"td": [{"_value": "Cat"}, {"_value": "5 pennies, 5 nickels, 5 dimes, and 1 quarter"}]}, {"td": [{"_value": "Rabbit"}, {"_value": "7 pennies, 3 nickels, 2 dimes, and 3 quarters"}]}, {"td": [{"_value": "Frog"}, {"_value": "5 pennies, 5 dimes, 5 quarters"}]}, {"td": [{"_value": "Monkey"}, {"_value": "3 pennies, 3 nickels, 3 quarters"}]}]}]}]}
How much money would you spend if you purchased one of each animal at the pet shop?
If you have \$3 to spend at the pet shop, what animals would you buy?
What two animals could you buy if you have \$2 to spend? How much change will you get back?
How much money would you spend if you purchased the dog, snake, and the bird?
Make up a problem for your partner to solve.


correct_option_index: 0