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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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


Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

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 $P$.


Concept/skill: 
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.

Answer: 
Yes. 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.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
problem_activity: Task
A famous arcade in a seaside resort town consists of many different games of skill and chance.  In order to play a popular “spinning wheel” game at Fred's Fun Factory Arcade, a player is required to pay a small, fixed amount of 25 cents each time he/she wants to make the wheel spin. When the wheel stops, the player is awarded tickets based on where the wheel stops -- and these tickets are then redeemable for prizes at a redemption center within the arcade.
Note: this particular game has no skill component; each spin of the wheel is a random event, and the result from each spin of the wheel is independent of the results of previous spins.
The wheel awards tickets with the following probabilities:
{"table": [{"_attributes": {"class": ["narrow"]}, "tbody": [{"tr": [{"td": [{"_value": "1 ticket"}, {"_value": "35%"}]}, {"td": [{"_value": "2 tickets"}, {"_value": "20%"}]}, {"td": [{"_value": "3 tickets"}, {"_value": "20%"}]}, {"td": [{"_value": "5 tickets"}, {"_value": "10%"}]}, {"td": [{"_value": "10 tickets"}, {"_value": "10%"}]}, {"td": [{"_value": "25 tickets"}, {"_value": "4%"}]}, {"td": [{"_value": "100 tickets"}, {"_value": "1%"}]}]}]}]}
(Note: A picture of a wheel fitting these parameters is included.)
If a player were to play this game many, many times, what is the expected (average) number of tickets that the player would win from each spin?
The arcade often provides quarters to its customers in $5.00 rolls. Every day over the summer, a young boy obtains one of these quarter rolls and uses all of the quarters for the spinning wheel game. In the long run, what is the average number of tickets that this boy can expect to win each day using this strategy?
One of the redemption center prizes that the young boy is playing for is a trendy item that costs 300 tickets.  It is also available at a store down the street for $4.99. Without factoring in any enjoyment gained from playing the game or from visiting the arcade, from a strictly monetary point of view, would you advise the boy to try and obtain this item based on arcade ticket winnings or to just go and buy the item at the store?  Explain.
The histogram below summarizes the results of 90 summer days of the boy playing the game using his "$5 roll per day" strategy. The first bar in the histogram represents those days where 40 to 59 tickets were won.
[IMG]
For approximately what percentage of the 90 days did the boy earn fewer than 100 tickets in a day?
For approximately what percentage of the 90 days did the boy earn 200 or more tickets in a day?
For approximately what percentage of the 90 days did the boy earn 300 or more tickets in a day?
To maintain the spinning wheel game machine, the arcade manager adopts a strategy of emptying the money box (that's where the quarters go after they are inserted in the machine) each time she refills the machine with a new roll of tickets. The ticket refill rolls contain 5000 tickets, and the machine is designed to hold $1300 in quarters in its money box. Assume that the machine was fully loaded with 5000 tickets and had an empty money box when it was first used. Using the manager's maintenance strategy, is there any chance that the money box could become completely full with quarters or overflow with quarters? Explain.
Arcade Wheel
{"table": [{"_attributes": {"class": ["narrow"]}, "tbody": [{"tr": [{"th": [{"_value": "Color"}, {"_value": "Tickets"}]}, {"td": [{"_value": "Orange"}, {"_value": "1"}]}, {"td": [{"_value": "Green"}, {"_value": "2"}]}, {"td": [{"_value": "Blue"}, {"_value": "3"}]}, {"td": [{"_value": "Yellow"}, {"_value": "5"}]}, {"td": [{"_value": "Purple"}, {"_value": "10"}]}, {"td": [{"_value": "Black"}, {"_value": "25"}]}, {"td": [{"_value": "Red"}, {"_value": "100"}]}]}]}]}
Graphics Note: The wheel diagram was developed in Microsoft Excel using its "Pie Chart" graph building feature.  The intent is that each wedge represents 1% of the pie (3.6 degrees).  There are 35 orange wedges (each representing a win of 1 ticket) to correspond to the 35% probability of obtaining 1 ticket in a spin, 20 green wedges (each representing a win of 2 tickets) to correspond to the 20% probability of obtaining 2 tickets in a spin, and so on.
[IMG]


aligns: yes