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: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
problem_activity: Narrative
The purpose of this activity is for students to count their collection in a way that makes sense to them. Students are provided with 10-frames and counting mats to help them organize their collections. Students use appropriate tools strategically as they choose which tools help them count their collections (MP5). The purpose of the activity synthesis is to highlight that collections can be arranged in different ways, which will be useful in a future activity when students rearrange objects and notice that the total number of objects remains the same.
Required Materials
Materials to Gather
10-frames
Collections of objects
Counting mats
Required Preparation
Each student needs a collection of 11–20 objects.
Launch
Groups of 2
Give each student a collection of objects and access to 10-frames and a counting mat.
“How many objects are in your collection?”
Activity
3 minutes: independent work time
“Tell your partner how many objects are in your collection.”
30 seconds: partner discussion
“Switch collections with your partner. Do you agree with your partner about how many objects are in the collection?”
3 minutes: independent work time
Monitor for students who arrange their objects in different ways to count them.
Student Response
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for free access to Student Response.
Activity Synthesis
Invite previously identified students to demonstrate how they arranged and counted their collections.
“What do you notice about how they counted?”
If needed, “Each person arranged their objects in a different way, but they all counted each object one time.”
After each student shares, write or display the number and say “There are _____ objects in their collection.”


aligns: no