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 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_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Solve quadratic equations in one variable.
problem_activity: Narrative
The purpose of this warm-up is to allow students to connect language to mathematical representation, which will be useful when students need to compare quantities and numbers in later activities. In the synthesis, students have the opportunity to practice using the language “more” to compare quantities.
This warm-up gives students opportunities to make sense of a problem by acting it out first before thinking about how to solve the problem (MP1).
Launch
Groups of 2
Display and read the story.
“What is the story about?”
30 seconds: quiet think time
Share responses.
Read the story again.
“How can you act out this story?”
30 seconds: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share responses.
Choose a way to represent the story as a class.
Read the story together.
Student Facing
Lin and her brother are setting the table for dinner.
Lin put 8 cups on the table.
Her brother put 6 plates on the table.
Did Lin or her brother put more things on the table?
[IMG]
Student Response
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Activity Synthesis
“Did Lin or her brother put more things on the table? How do you know?” (Lin put more things on the table. When we acted it out, there were 2 plates that did not have any cups, so there were more plates. 8 is more than 6.)
“Tell your partner about 8 and 6 using ‘more.’” (8 is more than 6.)
“8 plates is more than 6 cups. 8 is more than 6.”


aligns: no