few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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: 
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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
problem_activity: A bakery sells small cakes for
$${ {{$1}}0}$$
each. At this price, the bakery typically sells
$${100}$$
cakes per week.
The owner of the bakery wants to increase the price of the cake in order to maximize revenue. She determines that for each
$${{$1}}$$
increase in price, she sells
$$5$$
fewer cakes per week.
a.  Which function represents the weekly revenue,
$${R(x)}$$
, the owner of the bakery can expect to earn from the cakes based on
$$x$$
increases in price by
$${{$1}}$$
.
i.
$${R(x)}=(10-x)({100}+5x)$$
ii.
$${R(x)}=(10+x)({100}-5x)$$
iii.
$${R(x)}=(10-5x)({100}+x)$$
iv.
$${R(x)}=(10+5x)({100}-x)$$
b.  At what price will the owner of the bakery earn the maximum weekly revenue from sales of the small cakes?


aligns: no