few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Example 2:
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).

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
No. This task does not involve an equation in two variables. There is only 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_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).
problem_activity: Narrative
The purpose of this warm-up is for students to participate in part of the Questions About Us routine. Students have worked with 5-frames in previous sections and as an option during counting collections. In this activity, 5-frames are introduced as a way to represent how many students are here today. A blackline master is provided, but the 5-frames should be modified to match the number of students in the class. For example, if there are 24 students in the class, four 5-frames and 4 extra squares should be displayed. This will allow students to use the representation to also determine how many students are absent in future lessons by referring to the empty squares. This display will be used during the  Questions About Us warm-up in later lessons, so create the display in a place in the classroom that can easily be seen by students.
In the synthesis, students look at the new 5-frame representation and compare it to the representations based on student ideas created in the previous lesson.
Required Materials
Materials to Gather
Chart paper
Materials to Copy
Questions About Us 5-Frames
Required Preparation
Gather the poster created during Questions about Us in the previous lesson.
Launch
“How can we use the 5-frames to show how many of us are here?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
Demonstrate a student suggestion for how to use the 5-frames.
“How can we figure out how many of us are here?” (We can count each person. We can count each circle in the 5-frame.)
Count each student.
“How many of us are here today?”
Count each circle.
“How many of us are here today?”
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Display one of the representations based on student ideas from the previous lesson and the new representation with 5-frames.
“These are both different ways that we showed how many of us are here. What do you notice?”


aligns: no