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: 
Construct a tangent line from a point outside a given circle to the circle.

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: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

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_neg_0

HS_2
standard_description: Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
problem_activity: Narrative
The purpose of this activity is for students to compare the length of two objects using a third object. When students decide if the teacher's desk will fit through the door or compare other large pieces of furniture, they will need to be precise about which lengths they are measuring as objects like the teacher's desk, a rug, and a bookcase, have a length, width, and in some cases a height (MP6). Next, they will need to select an appropriate third object to use to compare the lengths they have chosen. Teachers may choose to assign different questions for different groups to start with to facilitate student movement around the room. Teachers may also change any question that does not apply to their classroom.
MLR8 Discussion Supports.
Synthesis: For each observation that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide which problem to start with and the order to complete the task.
Supports accessibility for: Attention, Social-Emotional Functioning
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group needs measuring materials from the previous activity.
Launch
Groups of 2
Give students access to measuring materials.
“Have you ever seen someone move a large piece of furniture, like a couch, from one room to another? Is it easy to move big pieces of furniture? Why or why not?”
30 seconds: quiet think time
Share responses.
“I have been thinking about getting a new desk. If I do, I will have to move this desk out of the room. I am not sure if this desk will fit through the door. How can we check to see if it will fit?” (We could measure with a string.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“You are all going to check to see if my desk will fit through the door. You are also going to compare the length of some other objects in the room.”
Activity
15 minutes: partner work time
Monitor for a group that measures the width of the teacher's desk and one that measures the length.
Student Facing
Will the teacher’s desk fit through the door?
Show your thinking using drawings, numbers, or words.
Will a student desk fit through the door?
Show your thinking using drawings, numbers, or words.
Which is longer, the bookshelf or the rug?
Show your thinking using drawings, numbers, or words.
Which is longer, the file cabinet or the bookshelf?
Show your thinking using drawings, numbers, or words.
Which is shorter, the bookshelf or the teacher’s desk?
Show your thinking using drawings, numbers, or words.
Will the teacher’s desk fit next to the bookshelf?
Show your thinking using drawings, numbers, or words.
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
Invite previously identified students to share.
For each student, ask: “How did they compare the length of the objects? What tool did they use? What part of each object did they measure?”


aligns: no