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 problem or activity shown below 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: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Problem 1
a.   Solve.
10
$$\times$$
23 = ___________
10
$$\times$$
450 = ___________
10
$$\times$$
10,870  = ___________
b.   What do you notice about Part (a)? What do you wonder?
c.   Use your conclusions from Part (b) to find the solutions below.
___________
$$\times$$
10 = 5,090
60,200
$$\div$$
10 = ___________
___________
$$\div$$
10 = 3,050
20,008
$$\times$$
___________ = 200,080
Problem 2
There are about 39,000 fourth graders in Mississippi and about 390,000 fourth graders in Texas. There are about 3,900,000 fourth graders in the United States.
a.   How many times more fourth graders are there in Texas than in Mississippi? How many times more fourth graders are there in the United States than in Texas?
b.   There are about 3,900 fourth graders in Boston, MA. How many times more fourth graders are there in the United States than in Boston?


aligns: yes