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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only 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_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Relate area to the operations of multiplication and addition.
problem_activity: Problem 1
a.   Your teacher will read you a series of situations. Explain what new information you get with each one.
Version 1: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out the binders to some students.
Version 2: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out the same number of binders to each student.
Version 3: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out 3 binders to each student.
Version 4: Mrs. Powell buys a few boxes with the same number of binders in each box. She plans to give out 3 binders to each student.
Version 5: Mrs. Powell buys a few boxes with 6 binders in each box. She plans to give out 3 binders to each student.
Version 6: Mrs. Powell buys 4 boxes with 6 binders in each box. She plans to give out 3 binders to each student.
b.   What question do you think this problem is going to ask you to solve? Write the question, then find its answer.
Problem 2
Ten children equally share 40 almonds. How many almonds will 3 of those children get?


aligns: no