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: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with 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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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_pos_0

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im_task_001160_neg_0

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standard_description: Estimate lengths using units of inches, feet, centimeters, and meters.
problem_activity: Narrative
The purpose of this activity is for students draw their own picture graphs to represent given data. Each student receives a data table to use. After drawing their own graphs, they share their graph with a partner and receive feedback on what is clear and what they could improve. As students represent the data and share their graphs with others, they notice and describe the features of picture graphs that make it easy for others to understand (MP3, MP6). While students are making their graphs, monitor for any features that many students leave out (for example, titles or category labels) to emphasize when sharing in the synthesis.
The data tables will be used again in the next activity.
This activity uses
MLR8 Discussion Supports
. Advances: reading, writing, and conversing.
Required Materials
Materials to Copy
Data Tables
Picture and Bar Graph Template
Required Preparation
Each student needs 1 data table from the blackline master. Each student in a group of 2 may receive different data tables.
Launch
Groups of 2
Display “2nd Graders’ Favorite Sports” graph.
“What can you learn about 2nd graders’ favorite sports from this graph?”
“What are some features of this graph that help us understand the data?”
Share responses.
Highlight the important features (title, labels, and pictures or symbols).
Activity
"Now you are going to create your own picture graph."
Give each student 1 data table and a graph template from the blackline master.
“Write the number of the data table on your page.”
“This graph uses smiley faces, but you may choose something different when you make your graph."
"Think about what picture you are going to use, then represent the data shown in your table in a picture graph.”
10 minutes: independent work time
Monitor for students who use symbols that are easy to draw.
“Switch graphs with your partner.”
“Tell your partner 1 thing you think they did really well and 1 thing you still have a question about.”
MLR8 Discussion Supports
Display sentence frames.
“You did _____ really well in your graph.”
“Why did you . . . ?”
“Can you say more about . . . ?”
5 minutes: partner work time
Student Facing
A group of 2nd graders were asked, “What is your favorite sport?” Their responses are shown in this picture graph.
[IMG]
Represent the data shown in your table in a picture graph.
Table # _______
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 graphs of previously selected students.
“What is same about these graphs? What is different?”
1 minute: quiet think time
1
–
2 minutes: partner discussion
Share responses.
Consider asking selected students:
“Why did you choose that symbol?”
"What other features did you add to your graph to help others' understand it?"


aligns: no