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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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

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im_task_000870_neg_0

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im_task_001160_neg_0

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standard_description: Derive the equation of a parabola given a focus and directrix.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the Picture Books center. Students look through picture books and notice and describe shapes they see in the pictures.
Required Materials
Materials to Gather
Picture books
Materials to Copy
Picture Books Stage 3 Recording Sheet
Required Preparation
Each group of 2
–
4 needs at least one picture book that shows a variety of shapes throughout the book.
Launch
Groups of 2
Give each student a recording sheet and each group 2
–
4 picture books.
“We are going to learn a new way to do the Picture Books center.”
“Your group will look through picture books and notice and describe shapes you see in the pictures. On your recording sheet, you will each sketch the shape you see, describe it, and name it.”
Activity
10 minutes: partner work time
Monitor for different shapes students notice.
Activity Synthesis
“What shapes did you find most often?”


aligns: no