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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Thought: This task shows one quadratic equation with one variable, x.
Answer: B

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 $P$.


Standard options: 
A. 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.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Thought: 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.
Answer: A

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
problem_activity: Narrative
In this warm-up, students practice identifying obtuse angles in an image. They may, for instance, rely on the symmetry of the figure or on a grouping strategy, or otherwise scan the figure in a methodical way.
Launch
Groups of 2
“How many angles do you see? How do you see them?”
Display the image.
1 minute: quiet think time
Activity
Display the image.
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Facing
How many angles do you see in the folded paper heart?
[IMG]
Student Response
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Activity Synthesis
“How did you make sure all the angles are accounted for?”(I put a mark through them or numbered them.)
“How many obtuse angles are in this image?” (10)
Label each obtuse angle with reasoning from students.
Consider asking:
“Who can restate in different words the way _____ saw the angles?”
“Did anyone see the angles the same way but would explain it differently?”
“Does anyone want to add an observation to the way _____ saw the angles?”


correct_option_index: 1