few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Concept/skill: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
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 $P$.


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

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

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: Recognize and represent proportional relationships between quantities.
problem_activity: Problem 1
Shade in the grids to represent the following fractions:
|                                  a.                     $${30\over 100}$$                                  |                                  b.                     $${3 \over100}$$                                   |                              c.                     $${{1\over3}\over 100}$$                               |
|------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------|
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/12/18/screen-shot-2017-12-18-at-40254-pm.png |
Problem 2
Fill in the chart below to represent equivalent fractions, decimals, and percentages.
| **           Fraction          ** | **           Decimal          ** |   **           Percent          **   |
|-----------------------------------|----------------------------------|--------------------------------------|
|          $$\frac{1}{4}$$          |                                  |                                      |
|                                   |               0.5                |                                      |
|                                   |                                  |                 20%                  |
|          $$\frac{1}{3}$$          |                                  |                                      |
|                                   |               0.05               |                                      |
|          $$\frac{3}{8}$$          |                                  |                                      |
|                                   |               1.3                |                                      |
|                                   |                                  | $$\frac{1}{2}$$                    % |
Problem 3
Use mental math to answer the questions below.
a.
What is 50% of 20?
What is 25% of 48?
What is 10% of 125?
What is 5% of 50?
b.
6 is 50% of what number?
10 is 25% of what number?
9 is 10% of what number?
c.
21 is what percent of 210?
450 is what percent of 900?
20 is what percent of 80?
30 is what percent of 20?


aligns: no