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: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
problem_activity: Narrative
In this Info Gap activity, students solve abstract multi-step problems involving an arrangement of angles with several unknown measurements. By now students have the knowledge and skills to find each unknown value, but the complexity of the diagram and the Info Gap structure demand that students carefully make sense of the visual information and look for entry points for solving the problems. They need to determine what information is necessary, ask for it, and persevere if their initial requests do not yield the information they need (MP1). The process also prompts them to refine the language they use and ask increasingly more precise questions until they get useful input (MP6).
Here is an image of the cards for reference:
[IMG]
Required Materials
Materials to Copy
Info Gap: Whole Bunch of Angles
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
MLR4 Information Gap
Display the task statement, which shows a diagram of the Info Gap structure.
1–2 minutes: quiet think time
Read the steps of the routine aloud.
“I will give you either a problem card or a data card. Silently read your card. Do not read or show your card to your partner.”
Distribute the cards.
“The diagram is not drawn accurately, so using a protractor to measure is not recommended.”
1–2 minutes: quiet think time
Remind students that after the person with the problem card asks for a piece of information, the person with the data card should respond with “Why do you need to know (restate the information requested)?”
Activity
5 minutes: partner work time
After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.
Student Facing
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
[IMG]
Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
Some students may be overwhelmed by the visual information. Ask them to try isolating a part of the diagram at a time, covering other parts that are not immediately relevant.
Activity Synthesis
Select students to share how they found each angle measure. Record their reasoning and highlight equations that clearly show the relationships between angles.
“Which angle measurements were easy to find? What made them easy?” (Sample response:
\(p\)
and
\(d\)
, because it was fairly easy to see that each of them and a neighboring angle make a straight angle.)
“Which ones were a bit more involved? Why?” (Sample response:
\(e\)
, because there are 5 angles that meet at that point. We needed to find
\(a\)
or
\(d\)
before finding
\(e\)
.)


aligns: no