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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only 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 problem or activity shown below 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_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Activity
In this activity, students work in groups and make a poster in their groups using one of their news items. Next, students go on a gallery walk and use sticky notes to ask questions about the information presented on each poster. They practice critiquing the reasoning of others as they study information they have not themselves worked on. They then go back and study the feedback they received from their classmates and revise their own work.
Launch
Keep students in the same groups of 3–4. Give students supplies to make posters. Tell them that they will choose one of their news clippings and make a visual display for the information they worked on in the previous activity. The posters should include all necessary information so that somebody who has not extensively worked with the same information should be able to understand the work.
Allow students 10 minutes to work on creating their display. Review group work as they finish.
After all groups have finished, display each group's work around the room for students to do a gallery walk. Tell students that they should leave feedback for each display on a sticky note attached to each group's work. Feedback can include questions about the display or information as well as compliments or critiques. Comments and questions should be constructive with the goal to help the groups who made the poster improve their work.
Tell each group which poster to start with and in which direction they should move.
As groups finish viewing the displays, allow them time to view the feedback left on their own display and, if necessary, time to improve their display based on the feedback.
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
Writing: MLR8 Discussion Supports.
Provide sentence frames for students to use when asking questions about features of the visuals displays they do not understand. For example, “Why did you ____?” or “How did you ____?”
Design Principle(s): Support sense-making
Student Facing
Choose the example that you find the most interesting. Create a visual display that includes:
a title that describes the situation
the news clipping
your diagram of the situation
the two questions you asked about the situation
the answers to each of your questions
an explanation of how you calculated each answer
Pause here so your teacher can review your work.
Examine each display. Write one comment and one question for the group.
Next, read the comments and questions your classmates wrote for your group. Revise your display using the feedback from your classmates.
Student Response
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aligns: no