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: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Classify two-dimensional figures in a hierarchy based on properties.
problem_activity: Narrative
The purpose of this activity is for students to use language to describe and distinguish quadrilaterals (MP6). The activity has the same structure as the activity where students tried to identify which rectangle on the coordinate grid their partner was thinking of. Students rely on what they remember about categories of quadrilaterals, such as rectangles and rhombuses. They can also use informal language such as tilted, arrow, or red pattern block. The goal of the synthesis is to share and gather language which was helpful for distinguishing the quadrilaterals.
This activity uses
MLR2 Collect and Display
. Advances: Conversing, Reading, Writing.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Provide a graphic organizer that lists characteristics of different quadrilaterals for students to use as a reference as they ask questions about the shape.
Supports accessibility for: Memory, Attention, Conceptual Processing
Required Materials
Materials to Gather
Dry erase markers
Sheet protectors
Materials to Copy
Guess Which One
Required Preparation
Consider giving each student a sheet protector and a dry-erase marker so that students can easily reuse the blackline master for multiple rounds of the game.
Launch
Groups of 2
Distribute the blackline master with the sheet protectors and dry-erase marker to each group or instruct students to use the image of quadrilaterals in their workbook.
Activity
8 minutes: partner work time
MLR2 Collect and Display
Circulate, listen for and collect the language students use to describe the quadrilaterals as they sort. Listen for:
language and gestures used to describe angles, such as: wide, open, skinny, square, big, small, obtuse, acute, right
language and gestures used to describe sides, such as: straight, cross, intersect, parallel, perpendicular
language used to describe shapes, such as: square, tilted, flat, trapezoid, rhombus, diamond, arrow, parallelogram
Record students’ words and phrases on a visual display and update it throughout the lesson.
Student Facing
Play a round of Guess Which One.
Partner A: Select one of the quadrilaterals. Do not reveal your choice to your partner.
Partner B: Ask “yes” or “no” questions to guess which shape your partner picked. After each question, cross out or remove quadrilaterals based on your partner’s answer.
[IMG]
[IMG]
[IMG]
Use the space to record your questions for this round.
Han and Mai were playing Guess Which One. These are the last two shapes. What question can Mai ask to determine which shape is the one that Han picked?
[IMG]
If there is time: Switch roles and play Guess Which One again.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not ask specific questions during this task,
collect a set of questions during a practice round and ask, “Which questions could you ask to find out which shape your partner chose?”
Activity Synthesis
“Are there any other words or phrases that are important to include on our display?”
As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
Remind students to borrow language from the display as needed.
Invite previously selected students to share.
Display rhombus card that is not a square.
“What are some names we can use to describe this shape?” (quadrilateral, diamond, parallelogram, rhombus)


correct_option_index: 0