few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. 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.

Example 2:
Concept/skill: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
problem_activity: Categorize each representation of a function as linear, exponential, or quadratic. Explain your reasoning for each one.
{"table": [{"_attributes": {"align": "center", "class": ["table"], "style": "width:70%"}, "tbody": [{"tr": [{"td": [{"p": [{"_attributes": {"style": "margin-left:40px"}, "_value": "a."}, {}], "table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "-2"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "3"}, {"_attributes": {"style": "text-align:center"}, "_value": "6"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "13"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}, "_value": "22"}]}]}]}]}, {"p": [{"_attributes": {"style": "margin-left:40px"}, "_value": "b."}, {"_attributes": {"style": "text-align:center"}}], "table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "48"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "24"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "3"}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "6"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}, "_value": "3"}]}]}]}]}]}, {"td": [{"p": [{"_attributes": {"style": "margin-left:40px"}, "_value": "c.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$f(x)=x(x-4)$$"}]}]}, {"p": [{"_attributes": {"style": "margin-left:40px"}, "_value": "d.", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$f(x)=4-{x\\over2}$$"}]}]}]}, {"td": [{"p": [{"_attributes": {"style": "margin-left:40px"}, "_value": "e."}, {"_attributes": {"style": "margin-left:40px; text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG", "style": "height:166px; width:250px"}}]}]}, {"p": [{"_attributes": {"style": "margin-left:40px"}, "_value": "f."}, {"_attributes": {"style": "margin-left:40px; text-align:center"}, "img": [{"_attributes": {"alt": "", "src": "https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG", "style": "height:177px; width:250px"}}]}]}]}]}]}]}


aligns: yes