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: 
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
problem_activity: Narrative
This warm-up prompts students to carefully analyze and compare quadrilaterals and their sides. When students make comparisons, they have a reason to use geometric language precisely (MP6). The activity also enables the teacher to hear the terminology students know and how they talk about characteristics of two-dimensional figures. The knowledge and ideas that students show here may also be insightful to teachers in the next lesson, when students learn about angles.
Launch
Groups of 2
Display the image.
“Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Record responses.
Student Facing
Which one doesn’t belong?
[IMG]
Student Response
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Activity Synthesis
“How might we know if the sides of a figure are parallel?” (We could extend the lines or measure to see if the two sides are always the same distance apart.)
“All four quadrilaterals have at least one pair of parallel sides. Do all quadrilaterals have at least one pair of parallel sides?” (No) “Can you draw one with no pairs of parallel sides?”


aligns: yes