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: 
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_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
problem_activity: Problem 1
In a 30-minute television show, 12 minutes of the airtime are spent on commercials.
a.   Draw a visual representation of the problem.
b.   Determine what percent of the television show’s airtime is spent on commercials. Choose any strategy.
c.   Find a peer who used a different strategy to solve than you did. Compare and discuss your strategies and solutions.
Problem 2
Cole and Jamie are raising money for the annual Walk for Hunger in their city. They each have a goal to raise $250. So far, Cole has raised $150 and Jamie has raised $180.
a.   What percent of their goal did each boy raise so far?
b.   What is the amount that Cole raised as a percent of the amount Jamie raised?
c.   What is the amount Jamie raised as a percent of the amount Cole raised?
Problem 3
At a middle school, 480 students in sixth through eighth grade responded to a survey that asked them what their favorite season was. The circle graph below shows some of the data from the survey.
Student Survey “Favorite Season”
[IMG]
a.   How many students chose spring as their favorite season?
b.   What percent of students chose summer as their favorite season?
c.   In just the sixth-grade class, 28 students chose winter as their favorite season. This was 20% of the sixth grade. How many students are in the sixth grade at this school?


aligns: no