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: 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: Problem 1
Given the graph below, over which interval is the average rate of change the greatest? Explain your reasoning.
[IMG]
a. Between
$${f(4)}$$
and
$${f(10)}$$
b.
$${10 \leq x \leq 15}$$
c. Between
$${(0,0)}$$
and
$${(4,11)}$$
d. From
$${x=0}$$
to
$${x=10}$$
Problem 2
The table below defines the relationship
$${y=f(x)}$$
.
Find the average rate of change from
$${f (0)}$$
to
$${f(5)}$$
.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:30%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$x$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "0"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "5"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$f(x)$$"}]}, {"_attributes": {"style": "text-align:center"}, "_value": "26"}, {"_attributes": {"style": "text-align:center"}, "_value": "17"}, {"_attributes": {"style": "text-align:center"}, "_value": "5"}, {"_attributes": {"style": "text-align:center"}, "_value": "1"}]}]}]}]}
Problem 3
You leave from your house at 12:00 p.m. and arrive to your grandmother’s house at 2:30 p.m. Your grandmother lives 100 miles away from your house.
What was your average speed over the entire trip from your house to your grandmother’s house?


aligns: yes