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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
problem_activity: Task
Materials
Completed monthly weather recording sheet
[IMG]
Crayons
Sentence strips with frames (see below)
Student worksheet
Actions
Every day for a month the students record the weather by shading in an appropriate box on the recording sheet (attached).
At the completion of a month of school, the teacher projects the completed recording sheet using a document projector (if working with the whole class) or shows it to the students (if working in a small group setting).
The teacher asks the students to count how many days in the month each type of weather occurred, writing the number by the type of weather.
The teacher or another student asks questions like these:
How many rainy days did we have this month?
How many more rainy days did we have than sunny days?
How many days did we record the weather?
Students compose answers to the questions using sentence frames like these:
In September there were ___  ______ days
There were ___ more ________ days than ________ days
There were ___ fewer _________ days than _______ days
We recorded ____ days of weather altogether.
Both numbers and types of weather are used to fill in the blanks.  Students pair up and share an idea for each sentence frame; then the teacher chooses a student to fill in one of the frames orally, while it is recorded onto the sentence frame.
The students copy the data from the recording sheet onto their worksheet to create their own graph. The teacher may need to model this for the students the first time they do it.
The students choose a sentence based on the completed frames to match each of the weather pictures given.  So, for the sunny picture a student could write, "There were 5 more sunny days than rainy days," or "There were 12 sunny days in September."  The frame of "We recorded ___ days of weather altogether" could be stated orally, or added at the bottom of the recording sheet to be filled in. The teacher may need to model this for the students the first time they do it.


aligns: yes