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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

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


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
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.

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: 
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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Problem 1
Bisect the following angle using constructions. Write your steps for construction.
$${\overline{CA}\cong \overline{AB}}$$
[IMG]
Problem 2
You and your partner will be provided with a list of steps (in random order) needed to copy an angle using a compass and straightedge. Your task is to place the steps in the correct order, then follow the steps to copy the angle below.
[IMG]
|                                                Draw circle                     $$B$$                    : center                     $$B$$                    , any radius.                                                 |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Label the intersections of circle                     $$B$$                    with the sides of the angle as                     $$A$$                    and                     $$C$$           *           .          * |
|                                                                  Label the vertex of the original angle as                     $$B$$                    .                                                                   |
|                                                                           Draw                     $${\overrightarrow{ED}}$$                    .                                                                           |
|                                                         Draw                     $${\overrightarrow{EG}}$$                    as one side of the angle to be drawn.                                                         |
|                           Draw circle                     $$F$$                    : center                     $$F$$                    , radius                     $$FA$$                    .                           |
|                           Draw circle                     $$E$$                    : center                     $$E$$                    , radius                     $$EA$$                    .                           |
|           Label intersection of circle          *             $$E$$            *          with                     $${\overrightarrow{EG}}$$                    as                     $$F$$                    .           |
|                 Label either intersection of circle                     $$E$$                    and circle                     $$F$$                    as                     $$D$$                    .                  |


aligns: no