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: 
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
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