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


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

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:
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
problem_activity: Problem 1
Fill in each blank using a
$${<}$$
or
$${>}$$
inequality symbol
a.
$$5$$
_______
$$8$$
b.
$${11.3}$$
_______
$${11.13}$$
c.
$${\frac{2}{3}}$$
_______
$${\frac{3}{4}}$$
d.
$${-0.6}$$
_______
$${0.3}$$
e.
$$\frac{11}{8}$$
_______
$$-\frac{11}{8}$$
Problem 2
Here are the low temperatures (in Celsius) for one week in Juneau, Alaska:
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "table-layout:fixed; width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Monday"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Tuesday"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Wednesday"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Thursday"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Friday"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Saturday"}]}, {"_attributes": {"style": "background-color:#eeeeee; text-align:center"}, "strong": [{"_value": "Sunday"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$5$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$-1$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$-6$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$-2$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$3$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$7$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$0$$"}]}]}]}]}]}
a.   Arrange the temperatures in order from coldest to warmest temperature.
b.   On a winter day, the low temperature in Anchorage was
$$23$$
degrees below
$$0$$
°C, and the low temperature in Minneapolis was
$$14$$
degrees below
$$0$$
°C. Sophia wrote: “Minneapolis was colder because
$$-14 < -23$$
.” Is Sophia's statement correct? Explain your answer.
c.   The lowest temperature ever recorded on Earth was
$$-89$$
°C in Antarctica. The average temperature on Mars is about
$$-55$$
°C. Which is warmer, the coldest temperature on Earth or the average temperature on Mars? Write an inequality to support your answer.
Problem 3
The elevation of New Orleans, Louisiana, is
$$7$$
feet below sea level. The elevation of Coachella, California, is
$$-72$$
feet. Write an inequality to compare the elevations of the two cities.


aligns: no