few_shots: 
Example 1:
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.

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


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:
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: 
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.

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: 
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, 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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
problem_activity: Problem 1
The functions below are parent functions. Graph each one. Use either technology or a table of values where needed.
$${y=x}$$
$${y=x}^2$$
$${y=x}^3$$
$${y=|x|}$$
$${y=\sqrt{x}}$$
$${y=\sqrt[3]{x}}$$
Problem 2
Consider the two functions below.
$${{f(x)}=|x|}$$
$${{g(x)}=|x|+2}$$
Create a table of values for each function and use it to graph each function in the coordinate plane.
Looking at the tables and the graphs, what changed from the parent function,
$${f(x)}$$
, to the new function,
$${g(x)}$$
? What is the same?
Look at the corresponding work in the Desmos activity,
Introduction to Transformations of Functions
, slides 3–6.
Problem 3
Predict what the tables and graph would look like for each function below. Then refer to slide 7 in the Desmos activity,
Introduction to Transformations of Functions
, to try out other values for
$$k$$
.
$${y=|x|+5}$$
$${y=|x|-1}$$
$$y=|x|+k$$
A different parent function and transformations are shown below. Predict what each graph would look like. Then refer to slides 8–14 in the Desmos activity.
$${y=x^2}$$
$${y=x^2}+5$$
$${y=x^2}-1$$
$${y=x^2}+k$$


aligns: yes