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: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with 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: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ³ 1.
problem_activity: Task
Many counties in the United States are governed by a county council. At public county council meetings, county residents are usually allowed to bring up issues of concern. At a recent public County Council meeting, one resident expressed concern that 3 new coffee shops from a popular coffee shop chain were planning to open in the county, and the resident believed that this would create an increase in property crimes in the county. (Property crimes include burglary, larceny-theft, motor vehicle theft, and arson -- From http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2010/crime-in-the-u.s.-2010/property-crime accessed on December 5, 2012.)
To support this claim, the resident presented the following data and scatterplot (with the least-squares line shown) for 8 counties in the state:
{"table": [{"_attributes": {"class": ["centered", "narrow"]}, "tbody": [{"tr": [{"th": [{"_value": "County"}, {"_value": "Shops"}, {"_value": "Crimes"}]}, {"td": [{"_value": "A"}, {"_value": "9"}, {"_value": "4000"}]}, {"td": [{"_value": "B"}, {"_value": "1"}, {"_value": "2700"}]}, {"td": [{"_value": "C"}, {"_value": "0"}, {"_value": "500"}]}, {"td": [{"_value": "D"}, {"_value": "6"}, {"_value": "4200"}]}, {"td": [{"_value": "E"}, {"_value": "15"}, {"_value": "6800"}]}, {"td": [{"_value": "F"}, {"_value": "50"}, {"_value": "20800"}]}, {"td": [{"_value": "G"}, {"_value": "5"}, {"_value": "2800"}]}, {"td": [{"_value": "H"}, {"_value": "24"}, {"_value": "15400"}]}]}]}]}
[IMG]
The scatterplot shows a positive linear relationship between "Shops" (the number of coffee shops of this coffee shop chain in the county) and "Crimes" (the number of annual property crimes for the county). In other words, counties with more of these coffee shops tend to have more property crimes annually.
Does the relationship between Shops and Crimes appear to be linear? Would you consider the relationship between Shops and Crimes to be strong, moderate, or weak?
Compute the correlation coefficient.  Does the value of the correlation coefficient support your choice in part (a)? Explain.
The equation of the least-squares line for these data is:
$$ \text{Predicted Crimes} = 1434 + 415.7 \text{(Shops)} $$
Based on this line, what is the estimated number of additional annual property crimes for a given county that has 3 more coffee shops than another county?
Do these data support the claim that building 3 additional coffee shops will necessarily cause an increase in property crimes?  What other variables might explain the positive relationship between the number of coffee shops for this coffee shop chain and the number of annual property crimes for these counties?
If the following two counties were added to the data set, would you still consider using a line to model the relationship? If not, what other types (forms) of model would you consider?
{"table": [{"_attributes": {"class": ["centered", "narrow"]}, "tbody": [{"tr": [{"th": [{"_value": "County"}, {"_value": "Shops"}, {"_value": "Crimes"}]}, {"td": [{"_value": "I"}, {"_value": "25"}, {"_value": "36900"}]}, {"td": [{"_value": "J"}, {"_value": "27"}, {"_value": "24100"}]}]}]}]}


aligns: no