few_shots: Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

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


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Thought: This task shows one quadratic equation with one variable, x.
Answer: B

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 $P$.


Standard options: 
A. 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.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Thought: 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.
Answer: A

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

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: Task
Statistical questions are questions that can be answered by collecting data and where we anticipate that there will be variability in that data. The data collected can be summarized in a distribution that can then be described in terms of center and in terms of spread. For some statistical questions, to answer the question you need to consider center. For other questions you might need to consider spread.
For each of the five statistical questions below, decide if you would answer the question by considering center or considering variability in the data distribution.
Example 1: The records office at an elementary school keeps daily attendance records.
Question 1: For students at this school, what is a typical number of school days missed in the month of April?
Example 2: Suppose that third graders at your school took both a math test and a social studies test. Scores on both tests could be any number between 0 and 100.
Question 2: On average, did the students score better on the math test or the social studies test?
Question 3: Were the students’ scores more consistent (more similar to one another) on the math test or on the social studies test?
Example 3: Bags of M&Ms don’t all have exactly the same number of candies in each bag. Suppose you count the number of candies in each of 25 bags of plain M&Ms and in each of 25 bags of peanut M&Ms, and make two dot plots—one for the number of candies in the plain M&M bags and one for the number of candies in the peanut M&M bags.
Question 4: If you wanted to give each student in your class a bag of M&Ms and you wanted to try to make sure that each student got the same number of candies, should you give them bags of plain M&Ms or bags of peanut M&Ms?
Question 5: If you wanted to give each student in your class a bag of M&Ms and you wanted to try to give students bags with the greatest number of candies, should you give them bags of plain M&Ms or bags of peanut M&Ms?


correct_option_index: 1

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