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: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
problem_activity: Activity
In this info gap activity, students practice analyzing box plots and thinking carefully about what questions they could help to answer. They connect features of box plots to information about IQR, range, median, and minimum and maximum values of several data sets on sea turtles (MP7). Along the way, they see the usefulness of box plots in comparing distributions and characteristics of different populations.
The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly precise questions until they get the information they need (MP6).
Here is the text of the cards for reference and planning:
[IMG]
Launch
Tell students that they will now practice using box plots to answer questions about populations of sea turtles. Provide students with the following background information: Sea turtles are air-breathing amphibians that spend most of their time floating in seaweed beds. Females come on shore to lay their eggs. One nesting place for several species of sea turtles is the Outer Banks of North Carolina. All sea turtles are considered to be endangered and only about 1 in 1,000 newly hatched sea turtles survives, which is why their nesting areas are protected.
Arrange students in groups of 2. Give each group a pair of cut-up cards from the blackline master—a Problem Card for one partner and a Data Card for the other. Remind students of the protocol for asking and answering questions, as shown on the task statement. Give students 10 minutes to complete the activity. If any groups finish early, offer a second pair of cards and ask the partners to switch roles.
Engagement: Develop Effort and Persistence.
Display or provide students with a physical copy of the written directions. Check for understanding by inviting students to rephrase directions in their own words. Keep the display of directions visible throughout the activity.
Supports accessibility for: Memory; Organization
Conversing
: This activity uses
MLR4 Information Gap
to give students a purpose for discussing information necessary to connect features of a box plot to information about the five-number summary. Display questions or question starters for students who need a starting point such as: “Can you tell me . . . (specific piece of information)”, and “Why do you need to know . . . (that piece of information)?”
Design Principle(s): Cultivate Conversation
Student Facing
Your teacher will give you either a Problem Card or a Data Card about sea turtles that nest on the Outer Banks of North Carolina. Do not show or read your card to your partner.
[IMG]
If your teacher gives you the
problem card
:
Silently read your card and think about what information you need to be able to answer the question.
Ask your partner for the specific information that you need.
Explain how you are using the information to solve the problem.
Continue to ask questions until you have enough information to solve the problem.
Share the
problem card
and solve the problem independently.
Read the
data card
and discuss your reasoning.
If your teacher gives you the
data card
:
Silently read your card.
Ask your partner
“What specific information do you need?”
and wait for them to
ask
for information.
If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
Before sharing the information, ask “
Why do you need that information?
” Listen to your partner’s reasoning and ask clarifying questions.
Read the
problem card
and solve the problem independently.
Share the
data card
and discuss your reasoning.
Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
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
Invite students to share their experiences with the Info Gap activity. Consider discussing some of the following questions.
For students who had a Problem Card:
“How did you decide what information to ask for? How did the information on your card help?”
“How easy or difficult was it to explain why you needed the information you were asking for?”
“Give an example of a question that you asked, the clue you received, and how you made use of it.”
“How many questions did it take for you to be able to solve the problem? What were those questions?”
“Was anyone able to solve the problem with a different set of questions?”
For students who had a Data Card:
“When you asked your partner why they needed a specific piece of information, what kind of explanations did you consider acceptable?”
“Were you able to tell from their questions what statistical question they were trying to answer? If so, how? If not, why might that be?”


aligns: no