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: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with 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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Compare two numbers between 1 and 10 presented as written numerals.
problem_activity: Task
Materials
10-15 quart plastic bags of various counters (different numbers of counters in each bag)
A recording sheet for the activity with pictures of counters and lines for recording the total number of objects
A teacher completed recording sheet with the correct numbers written for each item
[IMG]
Action
The students choose a bag they have not counted. They are given the directions to count the items in the bag and record the number on the line next to the picture of the item in the bag.  The students will then check their answers against the teacher-prepared recording sheet.  If the activity is done in committee, the teacher should ask each student, “How many  (triangles) were in the bag?”  If the activity is done daily, the teacher should ask four or five different students, “How many  (triangles) were in the bag?”  The process is repeated until time runs out or all bags of stuff have been counted.


aligns: no