few_shots: 
Example:
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.

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
standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Problem 1
Determine the rate of change in each situation. Then describe the relationship using function language (for example, ____ is a function of ____ because _____.)
a.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width: 100%;"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "Amt of watermelon in pounds,", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}], "td": [{"_attributes": {"style": "text-align: center;"}, "_value": "0"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.25"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.5"}, {"_attributes": {"style": "text-align: center;"}, "_value": "1.5"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2"}, {"_attributes": {"style": "text-align: center;"}, "_value": "3"}, {"_attributes": {"style": "text-align: center;"}, "_value": "5"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "Cost of watermelon in dollars,", "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}], "td": [{"_attributes": {"style": "text-align: center;"}, "_value": "0"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.35"}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.70"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2.10"}, {"_attributes": {"style": "text-align: center;"}, "_value": "2.80"}, {"_attributes": {"style": "text-align: center;"}, "_value": "4.20"}, {"_attributes": {"style": "text-align: center;"}, "_value": "7.00"}]}]}]}]}
b.
$${d=25t}$$
, where
$$d$$
is distance in miles and
$$t$$
is time in hours
c.    Giovanni can decorate
$$2$$
cakes,
$$c$$
, every
$$5$$
hours,
$$h$$
.
Problem 2
Determine the starting or initial output value in each situation.
a.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:80%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Distance traveled in cab in miles,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "3"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}]}, {"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Cost of cab ride in dollars,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "2.50"}, {"_attributes": {"style": "text-align:center"}, "_value": "4.75"}, {"_attributes": {"style": "text-align:center"}, "_value": "9.25"}, {"_attributes": {"style": "text-align:center"}, "_value": "11.50"}]}]}]}]}
b.
{"table": [{"_attributes": {"align": "Center", "class": ["table", "table-bordered"], "style": "width:80%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Distance traveled in cab in miles,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}, {"_attributes": {"style": "text-align:center"}, "_value": "2"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "5"}]}, {"td": [{"_attributes": {"style": "background-color:#eeeeee"}, "strong": [{"_value": "Cost of cab ride in dollars,", "em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$y$$"}]}]}]}, {"_attributes": {"style": "text-align:center"}, "_value": "4.50"}, {"_attributes": {"style": "text-align:center"}, "_value": "7.00"}, {"_attributes": {"style": "text-align:center"}, "_value": "12.00"}, {"_attributes": {"style": "text-align:center"}, "_value": "14.50"}]}]}]}]}
c.
$${p=16d+20}$$
where
$$p$$
is the total number of pages read in a book and
$$d$$
is the number of days
Problem 3
The function formula below shows the relationship between temperature in degrees Fahrenheit and degrees Celsius. °F is a function of °C.
$${F=\frac{9}{5}C+32}$$
a.   Determine what 28°C is in °F.
b.   Determine what 23°F is in °C.


aligns: yes