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: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
problem_activity: Narrative
The purpose of this activity is to introduce students to the structure of the MLR4 Information Gap routine. This routine facilitates meaningful interactions by positioning some students as holders of information that is needed by other students.
Tell students that first, a demonstration will be conducted with the whole class, in which they are playing the role of the person with the problem card. Explain to students that it is the job of the person with the problem card (in this case, the whole class) to think about what information they need to answer the question.
For each question that is asked, students are expected to explain what they will do with the information, by responding to the question, “Why do you need to know (that piece of information)?” If the problem card person asks for information that is not on the data card (including the answer!), then the data card person must respond with, “I don’t have that information.” In explaining their answers, students need to be precise in their word choice and use of language (MP6).
Once the students have enough information to solve the problem, they solve the problem independently.
The info gap routine requires students to make sense of problems by determining what information is necessary and then ask for information they need to solve them. This may take several rounds of discussion if their first requests do not yield the information they need (MP1).
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Launch
Groups of 2
“The problems in this lesson are about setting up for a special event at a school. What’s your favorite special event at school or in your community?”
Share responses.
Activity
MLR4 Information Gap
Display the Sample Problem Card.
Read the problem aloud.
Listen for and clarify any questions about the context.
“Some of the information you need to solve this problem is missing, and I have it here. What specific information do you need?”
1–2 minutes: quiet think time
“With your partner, decide what information you need to solve the problem, and create a list of questions you can ask to find out.”
2–3 minutes: partner discussion
Invite students to share 1 question at a time.
Record each question on a display, and respond with: “Why do you need to know (restate the information requested)?” Students should provide a justification for how they will use the information before the information is revealed.
Answer questions using only information stated on the Sample Data Card (do not reveal).
Record information that is shared on the display. Give students time to decide whether they have enough information to solve the problem.
Repeat until students decide they have enough information to solve, then ask students to solve.
2–4 minutes: independent work time
Student Facing
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Student Response
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Activity Synthesis
Invite 1–2 students to share how they solved the problem.
“Which questions helped you find out how many chairs were in the room?” (How many chairs were in the corner? How many chairs were in each row? How many rows were there?)
If there were any questions that the data card cannot answer, discuss them here.


aligns: no