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: Add up to four two-digit numbers using strategies based on place value and properties of operations.
problem_activity: Narrative
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see.
When students notice that dots are being added on with each image, they look for and make use of structure (MP7).
Launch
Groups of 2
“How many do you see? How do you see them?”
Flash image.
30 seconds: quiet think time
Activity
Display image.
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Repeat for each image.
Student Facing
How many do you see?
How do you see them?
[IMG]
[IMG]
[IMG]
[IMG]
Student Response
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Activity Synthesis
Display the first and third images.
“What changed from the first group of dots to the third group of dots.” (2 more dots were added.)
“The third group has 4 dots and 2 more dots. We can write that as ‘4 and 2’ or ‘
\(4 + 2\)
’.”


aligns: no