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:
Thought: 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:
Thought: 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:
Thought: 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: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
problem_activity: Problem 1
Part A: Predict the shape of the graph at 2,000 trials.
|                                       10 trials                                        |                                       100 trials                                        |                                       533 trials                                        |
|----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/06/05/algiiu8_l7_at1.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/06/05/algiiu8_l7_at1a.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/06/05/algiiu8_l7_at1b.png |
Part B: At 1,799 trials, the graph looks like this:
[IMG]
The mean of the data is approximately 6, and the standard deviation is 1.7. The blue lines around the graph are what should be the "ideal" normal distribution.
Describe what the mean and the standard deviation mean in terms of this situation.
Problem 2
Match the following distributions with the histograms. Explain your reasoning.
| **           Distribution          ** |                 **           Shape          **                 | **           Mean          ** | **           Standard Deviation          ** |
|---------------------------------------|----------------------------------------------------------------|-------------------------------|---------------------------------------------|
|      **           A          **       |          **           Skewed to the right          **          | **           100          **  |         **           10          **         |
|      **           B          **       | **           Approximately symmetric, mound shaped          ** | **           100          **  |         **           10          **         |
|      **           C          **       | **           Approximately symmetric, mound shaped          ** | **           100          **  |         **           40          **         |
|      **           D          **       |          **           Skewed to the right          **          | **           100          **  |         **           40          **         |
[IMG]


correct_option_index: 1