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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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: 
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.

Answer: 
Yes. 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.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Recognize and represent proportional relationships between quantities.
problem_activity: Optional activity
In this activity, students make a visual display of their scenarios from the previous activity (after sharing their rough draft with another group and getting some feedback).
When the posters are complete and displayed around the room, students view each others' work and use sentence starters to give feedback and to critique the reasoning of others (MP3).
Launch
Keep students in the same groups. Tell them that they should incorporate the feedback they received when making their posters.
Engagement: Develop Effort and Persistence.
Provide prompts, reminders, guides, rubrics, or checklists that focus on increasing the length of on-task orientation in the face of distractions. For example, provide a task checklist which makes all the required components of the poster explicit.
Supports accessibility for: Attention; Social-emotional skills
Student Facing
Create a visual display of your two situations that includes all the information from the previous activity.
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
When the posters are complete, hang them around the room. Provide students with these sentence starters, and give them an opportunity to view their classmates’ work and write their responses. This provides a structured way for students to critique the reasoning of others (MP3).
The most surprising combination of things was ____________________ because ______________________________________________________________.
The group _______________________________ should check their work where they ___________________________________________________________________.
I really liked when the group ____________________________ did this __________________________________ because _______________________________________.
Representing, Reading, Writing: MLR7 Compare and Connect.
Use this routine when students share their visual displays. Direct attention to the different ways pairs explained quantities and their relationships and justified whether the relationship was proportional (e.g., distance traveled in yards and time elapsed in minutes, for every one minute they traveled 5 yards, the relationship is proportional because the graph of the line passes through the origin). Emphasize the language used to describe the proportional relationships and justify whether the relationship was proportional. These exchanges strengthen students' mathematical language use and reasoning of proportional relationships.
Design Principle(s): Maximize meta-awareness


aligns: yes