few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
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).

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
problem_activity: Narrative
The purpose of this activity is for students to have another chance to practice skip-counting by 2, 5, and 10 and addition and subtraction within 1,000.
Required Materials
Materials to Gather
Materials from previous centers
Required Preparation
Gather materials from:
Write Numbers, Stage 4
Target Numbers, Stages 6 and 7
Five in a Row, Stages 7 and 8
How Close, Stage 4
Launch
“Now you will choose from centers we have already learned.”
Display the center choices in the student book.
“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.
15
–
20 minutes: center work time
“Choose what you would like to do next.”
15
–
20 minutes: center work time
If time allows, have students choose a third center to work on.
Student Facing
Choose a center.
Write Numbers
[IMG]
Target Numbers
[IMG]
Five in a Row
[IMG]
How Close
[IMG]
Activity Synthesis
Invite 2-3 students to share their favorite method for adding and subtracting within 1,000.


aligns: no