few_shots: 
Example 1:
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.

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


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:
Concept/skill: 
Solve quadratic equations in one variable.

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
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.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

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: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
problem_activity: Narrative
The purpose of this warm-up is for students to consider concepts of number in a familiar context. Students compare groups of images in the synthesis. Adjust the context to better reflect students’ interests and experiences as needed. For example, the question can be adjusted to ask students to choose between two types of playground equipment that are available at school or in the community where students live. A question can also be chosen from the list that students generated in a previous lesson.
Required Materials
Materials to Copy
Questions About Us Chart
Launch
Groups of 2
Display the Questions About Us Chart.
“Would you rather play on the slide or on the swings?”
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 would rather play on the slide?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students would rather play on the slide?”
If needed, ask, “How can we figure out how many students would rather play on the swings?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students would rather play on the swings?”
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
“Did fewer people choose the swings or the slide? How do you know?”


aligns: no