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: Relate area to the operations of multiplication and addition.
problem_activity: Task
Part I.
a. How many circles are there in all?  Write down a number sentence that shows how you thought about it.
[IMG]
b. Alonso said he figured out how many shaded circles there were first and then how many unshaded circles there were second.  Once he knew how many of each, he added them together to find the total.  Write a number sentence Alonso could have used that shows his reasoning.
c. Jennifer said, “I just saw 3 rows of 8 circles.”  Write a number sentence that Jennifer could have used that shows her reasoning.
​Part II.
a. The area model below shows the floor plan for a storage closet.  The storage closet will have a tiled floor with grey tiles on the left and white tiles on the right.  How many tiles are needed for the storage closet in all?  Write down a number sentence that shows how you thought about it.
[IMG]
b. Think back to how Alonso figured out how many circles there were in Part I.  Use Alonso’s same strategy here to find out how many tiles are needed.  Write a number sentence with Alonso’s reasoning.
c. Think back to how Jennifer figured out how many circles there were in Part I.  Use Jennifer’s same strategy here to find out how many tiles are needed.  Write a number sentence with Jennifer's reasoning.


aligns: yes