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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only 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: 
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.

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, does the following problem or activity 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_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
problem_activity: Problem 1
A clothing manufacturer has to use at least 1,000 yards of cotton to make room for new inventory to make shirts and pajamas. A shirt requires 1 yard of fabric, and a pair of pajamas requires 3 yards of fabric. It takes 2 hours to make a shirt and 3 hours to make a pair of pajamas, and there are 1600 hours available to make all of the clothing. Let
$$x$$
represent the number of shirts and
$$y$$
represent the number of pajamas.
What is the smallest number of pajamas the manufacturer can make and meet all of these conditions?
Problem 2
Phil and Cath make and sell boomerangs for a school event. The money they raise will go to charity. They plan to make them in two sizes: small and large.
Phil will carve them from wood.
The small boomerang takes 2 hours to carve, and the large one takes 3 hours to carve.
Phil has a total of 24 hours available for carving.
Cath will decorate them. She only has time to decorate 10 boomerangs of either size.
Phil and Cath want to make as much money for charity as they can.
The small boomerang will make $8 for charity.
The large boomerang will make $10 for charity.
How many small and large boomerangs should they make?
How much money will they then make?


aligns: yes