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: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
problem_activity: Optional activity
In the final phase of the drawing project, students reflect on and revise their work. Students who chose the same paper option confer in small groups to analyze and compare their floor plans. They discuss their decisions, evaluate the accuracy of their drawings, and then revise them as needed.
After revision, students debrief as a class and discuss how the choice of scale, units, and paper affected the drawing process and the floor plans they created.
Launch
Arrange students who use the same type and size of paper into small groups. Give them 8–10 minutes to share and explain their drawings. Display and read aloud questions such as the following. Ask students to use them to guide their discussion.
What scale did you use? How did you decide on the scale?
Do the scaled measurements in each drawing seem accurate? Do they represent actual measurements correctly?
Did the scale seem appropriate for the chosen paper? Why or why not?
What was the first thing you drew in your drawing? Why?
How did you decide on the objects to show in your drawing?
What aspects of your drawings are different?
How could each floor plan be revised to better represent the classroom?
Student Facing
Trade floor plans with another student who used the same paper size as you. Discuss your observations and thinking.
Trade floor plans with another student who used a different paper size than you. Discuss your observations and thinking.
Based on your discussions, record ideas for how your floor plan could be improved.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Before debriefing as a class, give students 4–5 minutes of quiet time to reflect. Ask them to write down ideas for revising their floor plan and strategies for creating accurate scale drawings based on their conversation.
Though much of the discussion will take place within the groups, debrief as a class so students can see floor plans created at a variety of scales and on different paper types or sizes. Display a range of scale drawings for all to see and discuss the following questions. (Alternatively, consider posting all students’ work for a gallery walk and ask students to reflect on these questions.)
What are the differences in these drawings?
How did different scales impact the final drawing?
How did the size of paper impact the choice of scale?
What choices were really important when creating the scale drawing?
Would these choices be the same if you were doing a different room in the school? Or some other building?
Representing, Conversing: MLR7 Compare and Connect.
Use this routine to prepare students for the whole-class discussion. Invite students to quietly circulate and read at least 2 other posters or visual displays in the room prior to the whole-class discussion. Give students quiet think time to consider what is the same and what is different about the visual displays of the floor plans created at a variety of scales and on different paper types or sizes. Next, ask students to find a partner to discuss what they noticed. Listen for and amplify observations that include mathematical language and reasoning about how the choice of scale, units, and paper affect the process of creating scaled drawings.
Design Principle(s): Cultivate conversation


aligns: no