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: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
problem_activity: Activity
In this activity, students extend their thinking about distribution shapes to using the shape to justify making a decison from a set of repesentations. In previous lessons, students matched distribution shapes to situations. Students practice applying the situations when they choose a representation and are able to eliminate the others. This activity prepares students to compare specific measures of several distribution shapes in a later lesson.
Student Facing
Restaurant A
[IMG]
Restaurant B
[IMG]
Restaurant C
[IMG]
Restaurant D
[IMG]
Each histogram represents the number of star ratings for a different restaurant. The ratings range from 0–4, with 0 representing a very poor experience and 4 representing an excellent experience. For each question, explain your reasoning.
Which restaurant do reviewers like the most?
Which restaurant do reviewers like the least?
Which restaurant received mostly mixed reviews?
Which restaurant would you choose to try?
Student Response
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Activity Synthesis
Discuss how students use the data distribution shapes to choose their answers. Here are sample questions to promote class discussion:
“How did you determine at which restaurant you would eat?” (I thought the restaurant with the highest ratings is the one at which I would want to eat.)
“How can you tell which restaurant has the best ratings?” (I can tell which one has the best ratings by looking for the histogram with the greatest frequency of 4 or 4-star ratings indicated by tall bars on the right side of the histogram.)
“How does shape influence your decisions?” (Shape influences my decisions because as I am looking for the amount of ratings, I am looking at how tall the bars are on each histogram. The skewed histograms show me that reviewers tend to agree that the restaurant is either very good or very bad. The uniform shape shows me that the restaurant has an equal amount of each rating, which might mean the experience is somewhat random. The bimodal shape shows me that reviewers are split on the restaurant, with some rating the quality very good while others are rating it as very poor.)


aligns: no