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: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this warm-up is to allow students to connect language to mathematical representation, which will be useful when students need to compare quantities and numbers in later activities. In the synthesis, students have the opportunity to practice using the language “more” to compare quantities.
This warm-up gives students opportunities to make sense of a problem by acting it out first before thinking about how to solve the problem (MP1).
Launch
Groups of 2
Display and read the story.
“What is the story about?”
30 seconds: quiet think time
Share responses.
Read the story again.
“How can you act out this story?”
30 seconds: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share responses.
Choose a way to represent the story as a class.
Read the story together.
Student Facing
Lin and her brother are setting the table for dinner.
Lin put 8 cups on the table.
Her brother put 6 plates on the table.
Did Lin or her brother put more things on the table?
[IMG]
Student Response
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Activity Synthesis
“Did Lin or her brother put more things on the table? How do you know?” (Lin put more things on the table. When we acted it out, there were 2 plates that did not have any cups, so there were more plates. 8 is more than 6.)
“Tell your partner about 8 and 6 using ‘more.’” (8 is more than 6.)
“8 plates is more than 6 cups. 8 is more than 6.”


aligns: no