few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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 problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
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
Teachers with a valid work email address can
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for free access to Student Response.
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: no