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: 
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 following problem or activity 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

HS_1

im_task_001160_pos_0

HS_2
standard_description: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
problem_activity: Narrative
The purpose of this activity is for students to answer questions about the data represented by their picture graphs and bar graphs. Students switch workbooks with a new partner, which is an opportunity for students to view each other’s work and see different representations of data. While students are answering questions based on different graphs, identify the questions that are harder for students to answer. These questions can be discussed in the lesson synthesis. In upcoming lessons, students will have more opportunities to work with questions that require comparing categories.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “The next time I answer questions about a graph, I will . . . .“
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Gather
Materials from a previous lesson
Required Preparation
Each student needs the picture graph and bar graph they created in the previous lesson.
Launch
Groups of 2: different partner than previous activity
“Tear out the page in your books labeled ‘Answering Questions Using Graphs.’”
Activity
“Now you are going to answer questions a different partner has written about their graphs.”
“Write your name and your partner’s name on the top of the page.”
“Trade graphs and questions with your partner. Answer each of the questions your partner wrote.”
6 minutes: independent work time
“Discuss the questions and answers with your partner to see if you agree.”
6 minutes: partner discussion
Monitor for students who mention the graph features like the title or labels when answering, "How did you know where to find the answer to each question?"
Student Facing
Answer your partner’s questions from Activity 1 using the graphs.
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
How did you know where to find the answer to each question?
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
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
Select 2
–
3 identified students to share a question they answered and how they knew where to find the answer.


aligns: no