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: 
Construct a tangent line from a point outside a given circle to the circle.

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: 
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, 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_neg_0

HS_2
standard_description: Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
problem_activity: Problem 1
In the diagram below,
$$\angle CAB$$
is a central angle,
$$\angle CDB$$
is an inscribed angle, and
$$\widehat{CB}$$
is an intercepted arc.
[IMG]
What do you notice about the inscribed angle and the central angle in relation to the intercepted arc?
The two diagrams below also show that
$$\angle CAB$$
is a central angle,
$$\angle CDB$$
is an inscribed angle, and
$$\widehat{CB}$$
is an intercepted arc.
[IMG]
What is the definition of an inscribed angle and an intercepted arc?
Problem 2
What is the angle measure that represents
$$\widehat{EB}$$
?
[IMG]
Problem 3
Given that
$$\triangle BCD$$
is inscribed in circle
$$A$$
, determine the relationship between
$$\angle t$$
and
$$\angle y$$
.
[IMG]


aligns: no