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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

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: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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_pos_0

HS_2
standard_description: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
problem_activity: Problem 1
a.   Create as many rectangles as you can with an area of 12 square units. Find the perimeter of each rectangle that you created. Then record the length, width, area, and perimeter of each rectangle in the table below:
| **                Length (units)               ** | **                Width (units)               ** | **                Area (square units)               ** | **                Perimeter (units)               ** |
|---------------------------------------------------|--------------------------------------------------|--------------------------------------------------------|------------------------------------------------------|
|                                                   |                                                  |                                                        |                                                      |
|                                                   |                                                  |                                                        |                                                      |
|                                                   |                                                  |                                                        |                                                      |
|                                                   |                                                  |                                                        |                                                      |
|                                                   |                                                  |                                                        |                                                      |
|                                                   |                                                  |                                                        |                                                      |
|                                                   |                                                  |                                                        |                                                      |
b.   What do you notice about the rectangles you created? What do you wonder?
Problem 2
What is the greatest perimeter you can make with a rectangle that has an area of 24 square units?


aligns: no