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: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
problem_activity: Problem 1
Two different students solved the problem
$$1\frac9{10}+5\frac4{10}$$
below. Study their work and determine whether the strategy they used works.
|                          **             Student A            **                          |                          **             Student B            **                          |
|------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at1a.png | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at1b.png |
Problem 2
Two different students solved the problem
$$4\frac38-3\frac68$$
below. Study their work and determine whether the strategy they used works.
|                           **            Student C           **                           |                           **            Student D           **                           |
|------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at2a.png | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/03/24/g4mathu5l14_at2b.png |
Problem 3
Solve.
| $$1+\frac{5}{12}$$                          $$\frac{11}{12} + \frac5{12}$$ | $$8+4\frac36$$                          $$7\frac56+4\frac36$$ | $$1\frac1{10}-\frac1{10}$$                          $$1\frac1{10}-\frac2{10}$$                          $$1\frac1{10}-\frac4{10}$$ | $$6\frac15-5$$                          $$6\frac15-4\frac45$$                          $$6\frac15-4\frac25$$ |
|----------------------------------------------------------------------------|---------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------|


aligns: no