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: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Understand the relationship between numbers and quantities; connect counting to cardinality.
problem_activity: Narrative
The purpose of this warm-up is for students to consider concepts of number in a familiar context. Students may use the structure of the chart and the 5-frames to determine how many students made each choice (MP7). Students have an opportunity to hear and practice the count sequence. Adjust the context and choose a different question with 3 possible responses to better reflect students’ interests and experiences as needed.
MLR8 Discussion Supports.
Display an image or drawing of each type of pet above the corresponding 5-frame. Invite students to respond to the question using the sentence frame, “My favorite pet is a . . .”
Advances: Speaking, Representing.
Required Materials
Materials to Copy
Questions About Us Chart 5-Frame Template
Required Preparation
Cut out enough 5-frames to make a chart with a space for each student to answer the survey question.
Launch
Groups of 2
Display Questions About Us chart.
“Which pet is your favorite: dogs, cats, or rabbits?”
30 seconds: quiet think time
Record each student’s choice with a circle in a 5-frame.
Activity
“How can we figure out how many students chose dogs?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students chose dogs?”
“How many students chose cats?”
30 seconds: quiet think time
Share responses.
“How many students chose rabbits?”
30 seconds: quiet think time
Share responses.
Student Response
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Activity Synthesis
“What was different about the question that we answered today?” (There were 3 choices instead of 2.)


correct_option_index: 0