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: Understand the relationship between numbers and quantities; connect counting to cardinality.
problem_activity: Narrative
The purpose of this warm-up is for students to consider concepts of number in a familiar context. Students may use the structure of the chart and the 5-frames to determine how many students made each choice (MP7). Students have an opportunity to hear and practice the count sequence. Adjust the context and choose a different question with 3 possible responses to better reflect students’ interests and experiences as needed.
MLR8 Discussion Supports.
Display an image or drawing of each type of pet above the corresponding 5-frame. Invite students to respond to the question using the sentence frame, “My favorite pet is a . . .”
Advances: Speaking, Representing.
Required Materials
Materials to Copy
Questions About Us Chart 5-Frame Template
Required Preparation
Cut out enough 5-frames to make a chart with a space for each student to answer the survey question.
Launch
Groups of 2
Display Questions About Us chart.
“Which pet is your favorite: dogs, cats, or rabbits?”
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 chose dogs?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students chose dogs?”
“How many students chose cats?”
30 seconds: quiet think time
Share responses.
“How many students chose rabbits?”
30 seconds: quiet think time
Share responses.
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
“What was different about the question that we answered today?” (There were 3 choices instead of 2.)


aligns: no