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: Solve quadratic equations in one variable.
problem_activity: Narrative
The purpose of this activity is for students to write a
\(10 + n\)
expression that is equal to a given expression. Each expression given has three addends, two of which make a ten.
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Double 10-frames
Launch
Groups of 2
Give students access to double 10-frames and connecting cubes or two-color counters.
“Now you will write a
\(10 + n\)
expression with the same value as each of the given expressions.”
Activity
5 minutes: independent work time
3 minutes: partner discussion
Student Facing
Write a
\(10 + \boxed{\phantom{3}}\)
expression that has the same value as each expression.
\(5 + 7 + 5\)
\(3 + 7 + 6\)
\(1 + 9 + 9\)
\(4 + 8 + 6\)
\(8 + 10 + 2\)
If you have time, write as many expressions as you can with 3 numbers that are equal to
\(10 + 5\)
.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display each
\(10 + n\)
expression.
“In order to make adding three numbers easier, we can rewrite each expression as a
\(10 + \boxed{\phantom{3}}\)
expression.”
Invite students to say the value of each
\(10 + n\)
expression together.


aligns: no