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: 
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to ten objects).
problem_activity: Narrative
The purpose of this warm-up is for students to experience a new part of the Questions About Us routine. Students consider concepts of number in a familiar context. This warm-up focuses on cardinality, or knowing that the last number tells us how many, and keeping track of which images have been counted. In the activity, students share methods for counting the images. After counting the group of images as a class or inviting a student to demonstrate how to count the images, ask students,  “How many students chose cats?” to confirm that students know that the last number tells us how many.
The images included in the Questions About Us Chart blackline master K.2.B are examples of what to display for the Questions About Us warm-ups in Section B. In order to create a display that will be visible to the whole class, print and cut out enough 5-frames so that there is a square for each student in the class. For example, if there are 23 students in the class, cut out four 5-frames and 3 squares out of a fifth 5-frame. Consider laminating the display and using a dry erase marker to write the two choices and record students' responses. If available, the provided images can also be enlarged.
Required Materials
Materials to Copy
Questions About Us Chart
Launch
Groups of 2
Display Questions About Us Chart.
“Which animal do you like better: dogs or cats?”
30 seconds: quiet think time
Record each student's choice with a circle in a 5-frame.
Activity
“How can we figure out how many students like cats better?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students like cats better?”
“How can we figure out how many students like dogs better?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students like dogs better?”
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
Count how many students chose cats again. After counting 10 dots, pause and ask, “How many dots have I counted?” and “Which dots have I already counted? Which dots do I still need to count?”


aligns: no