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: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = �� ÷ 3, 6 × 6 = ?.
problem_activity: Narrative
The purpose of this activity is for students to facilitate the Notice and Wonder they created in the previous activity. Each group takes turns facilitating their Notice and Wonder for another group (or two groups, if time permits).
MLR8 Discussion Supports.
During group work, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “I heard you say . . .” Original speakers can agree or clarify for their partner.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Chart paper
Markers
Required Preparation
Each group of 3-4 from the previous activity needs 1 piece of chart paper and a marker.
Launch
Groups of 3–4 from the previous activity
Give each group a piece of chart paper and a marker to record responses.
“Now, work with another group and take turns facilitating the Notice and Wonder activity you created.”
Activity
10–12 minutes: small–group work time
Remind groups to switch roles after 5–6 minutes.
Student Facing
Display your image for your classmates.
Ask them, “What do you notice? What do you wonder?”
Give them a minute to discuss together.
Ask them to share what they notice and wonder.
Record their ideas.
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
“What did you learn as you facilitated your Notice and Wonder?” (Others might notice or wonder things we did not think of. Recording the ideas helps people understand what is being shared.)


aligns: yes