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: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with 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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = �� – 3, 6 + 6 = ��.
problem_activity: Narrative
This Number Talk encourages students to think about equivalent forms of whole numbers and decomposing fractions in order to subtract. When students consider equivalent fractions, look for ways to decompose fractions, or use the structure of mixed numbers to find the value of each difference, they look for and make use of structure (MP7).
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
Activity
1 minute: quiet think time
Record answers and strategy.
Keep expressions and work displayed.
Repeat with each expression.
Student Facing
Find the value of each expression mentally.
\(1 - \frac{8}{10}\)
\(1\frac{4}{10} - \frac{8}{10}\)
\(2\frac{4}{10} - \frac{8}{10}\)
\(10\frac{5}{10} - \frac{8}{10}\)
Student Response
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Activity Synthesis
“How are these expressions alike?” (They all involve subtracting
\(\frac{8}{10}\)
from a number that is at least 1. To subtract, it’s helpful or necessary to decompose a 1 or to write an equivalent fraction.)
“How did you use earlier expressions to help you find the value of later expressions?”


aligns: no