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: 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: Narrative
The purpose of this activity is for students to use their own language and the language generated by the class in the last activity to describe how objects were sorted and tell how many objects are in each category. Students walk around the room and look at how other students sorted their objects. Consider using a signal to let students know when it is time to rotate.
Action and Expression: Internalize Executive Functions
. Check for understanding by inviting students to rephrase directions in their own words. Keep a display of directions visible throughout the activity.
Supports accessibility for: Memory, Attention
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
The math tool sorts from the previous activity are needed for this gallery walk.
Launch
Groups of 2
“Now you’re going to walk around to other tables to look at how other students sorted their tools. For each group’s work, talk to your partner about how they sorted the math tools and how many objects are in each category.”
Students move so they are looking at another group’s work.
“Look at the objects on your own. How did they sort the math tools? How many objects are in each category? When you are ready to share your thinking with your partner, put your thumb up.”
30 seconds: quiet think time
“Take turns sharing your thinking with your partner.”
1 minute: partner discussion
Activity
“Move to the next group’s work. Talk to your partner about how they sorted and how many tools are in each category.”
Repeat as time allows.
8 minutes: partner discussion time
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“What are some different ways you saw the math tools sorted?”


correct_option_index: 0