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 problem or activity shown below 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: Tell and write time in hours and half-hours using analog and digital clocks.
problem_activity: Narrative
The purpose of this activity is to connect the time shown on a digital clock with an analog clock with only the hour hand displayed. Students use the cards created in the first activity to write times in the digital format to represent each clock.
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each student needs the clock cards they created in the previous activity.
Launch
Display image in student workbook.
“These clocks both show the same time. What time do they show? How do you know?” (They show 1 o’clock. The arrow is pointing to the 1. There is a 1 on the left of the written time.)
30 seconds: quiet think time
Share responses.
Activity
“On the cards you made in the first activity, write the times under each clock.”
5 minutes: independent work time
Student Facing
These clocks both show the same time.
What time do they show?
How do you know?
[IMG]
[IMG]
Student Response
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Activity Synthesis
Display the card that shows 5 o’clock.
“Find your card that matches this card. What time did you write under this clock? How did you know that it shows 5:00?”
“Find the card that shows 4 o’clock. How did you know that it shows 4:00? How did you write the time?” (The arrow is pointing to the 4. 4:00)
Repeat with other cards as time permits.


aligns: yes