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 following problem or activity 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 in hours and half-hours using analog and digital clocks.
problem_activity: Narrative
The purpose of this activity is for students to choose from activities that offer practice working with two-digit numbers. Students choose from previously introduced centers.
Mystery Number
Get Your Numbers in Order
Greatest of Them All
Required Materials
Materials to Gather
Materials from previous centers
Required Preparation
Gather materials from previous centers:
Mystery Number, Stage 1
Get Your Numbers in Order, Stage 1
Greatest of Them All, Stage 1
Launch
Groups of 2
“We are going to choose from centers we have already learned.”
Display the student page.
“Think about what you would like to do first.”
30 seconds: quiet think time
Activity
Invite students to work at the center of their choice.
10 minutes: center work time
“Choose what you would like to do next.”
10 minutes: center work time
Student Facing
Choose a center.
Mystery Number
[IMG]
Get Your Numbers in Order
[IMG]
Greatest of Them All
[IMG]
Activity Synthesis
“How were the two centers you worked on the same? How were they different?”


aligns: no