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: 
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
problem_activity: Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for making 10 when adding. These understandings help students develop fluency with operations within 20.
When students look for ways to rearrange and decompose numbers to make 10, they notice and make use of structure of expressions and whole numbers (MP7).
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
1 minute: think time
Activity
Record answers and strategies.
Keep expressions and work displayed.
Repeat for each expression.
Student Facing
Find the value of each sum mentally.
\(4 + 8 + 2\)
\(4 + 5 + 3 + 2\)
\(9 + 3 + 1\)
\(9 + 5\)
Student Response
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Activity Synthesis
“How did making a ten help when finding the sums?”


aligns: no