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: 
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.

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: 
Yes. 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.

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_pos_0

HS_2
standard_description: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
problem_activity: Activity
The goal of this activity is for students to learn how to calculate
standard deviation
(
\(\sigma\)
or
\(\sigma_x\)
) using technology. Standard deviation is a measure of variability. The work in this activity prepares students to be successful in a future Algebra 1 lesson when they have to calculate the standard deviation of data sets.
Launch
Allow students to work individually. If technology is limited, students can work in pairs. Provide access to devices that can run GeoGebra or other statistical technology. Demonstrate how to use the technology available in your classroom to compute the standard deviation of a data set. For the purposes of exploration, use the population standard deviation, often denoted
\(\sigma\)
or
\(\sigma_x\)
.
Student Facing
[IMG]
Movie A ratings on a 10 point scale:
9, 8, 10, 10, 7, 1, 8, 1, 2, 8
Movie B ratings on a 10 point scale:
9, 8, 8, 7, 9, 7, 7, 9, 7, 8
Restaurant A ratings on a 100 point scale:
88, 87, 89, 90, 87, 85, 88, 91, 86, 86, 88, 89
Restaurant B ratings on a 100 point scale:
90, 65, 89, 50, 94, 93, 95, 95, 75, 70, 88, 89
Calculate the mean and standard deviation for each data set.
Based on these statistics, which movie and restaurant would you choose? Explain your reasoning.
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
Select students to share their solutions. Ask students how the standard deviation influenced their preferred movie and restaurants.


aligns: yes