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: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
problem_activity: Problem 1
Rudy is waiting patiently for his new hens to lay some eggs.
a.   On Monday he went to the henhouse to check their nests. He has 12 hens in the house, and each hen had laid 0 eggs. How many eggs did Rudy have in total? Write an equation to represent the situation.
b.   On Tuesday when he went to the henhouse, he discovered that each of his 12 hens had laid 1 egg! How many eggs does he have now? Write an equation to represent the situation.
Problem 2
Solve.
a.
$$4\times 1 = $$
_____
b.   _____
$$= 1\times 7$$
c.
$$5\ \times$$
_____
$$=5$$
d.
$$6\div 6 = $$
_____
e.   _____
$$=9\div1$$
Problem 3
Solve.
a.
$$2\times 0 = a$$
b.
$$b = 0\times 3$$
c.
$$7\times c = 0$$
d.
$$0\div 8 = d$$


aligns: yes