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: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with 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_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
problem_activity: Narrative
The purpose of this activity is for students to estimate the number of shipping containers on a fully loaded cargo ship. Then they make many assumptions about the arrangement of the containers on the boat to come up with a better estimate.
Launch
Groups of 2
Display image.
“How many containers are on the cargo ship?”
“What is an estimate that’s too high?” “Too low?” “About right?”
1 minute: quiet think time
Record responses.
Activity
“A cargo ship can hold many more than 60 containers. The second image is a picture of a cargo ship that is fully loaded.“
5 minutes: independent work time
“Discuss your estimates and assumptions with your partner.”
2 minutes: partner discussion
Monitor for students who are making different assumptions:
The ship is fully loaded.
Some of the space is taken up with structures.
There are more containers below deck that we can’t see.
All containers are the same size.
the specific side lengths of the shipping containers
Student Facing
How many containers are on the cargo ship?
[IMG]
Record an estimate that is:
|                    too low                     |                  about right                   |                    too high                    |
|------------------------------------------------|------------------------------------------------|------------------------------------------------|
| \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) |
How many containers are on the cargo ship?
[IMG]
Record an estimate that is:
|                    too low                     |                  about right                   |                    too high                    |
|------------------------------------------------|------------------------------------------------|------------------------------------------------|
| \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) |
What assumptions were you making when you came up with your estimates?
Student Response
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for free access to Student Response.
Activity Synthesis
Invite students to share their estimates and any assumptions they made.
“How could you improve your estimate?” (Recreate the ship using a model. Check the height, width, and length of the container arrangement. See how many are on one side of the ship and multiply that to get a closer estimate.)


aligns: yes