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


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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).

Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

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 $P$.


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.

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, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

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: Multiply a vector by a scalar.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the Geoblocks center. Students describe solid shapes using their own language. Students provide clues so that their partner can identify the shape out of a set of 4-6 solid shapes. While students may correctly name the solid shapes, it is not expected in this lesson. Students may describe the shapes in many ways. Monitor for students who:
reference a familiar object: “This shape looks like a ball.”
describe attributes or parts of the shape, such as point and circle for a cone.
use the name of the shape: “This shape is a cube.”
use positional words: “This shape is next to the one that looks like a box.”
The purpose of the activity synthesis is to highlight the language students use to describe shapes (MP6).
MLR8 Discussion Supports.
Synthesis: For each response that is shared, invite students to turn to a partner and restate what they heard, using descriptions and gestures.
Advances: Listening, Speaking
Action and Expression: Internalize Executive Functions.
Invite students to plan how they will describe the shape to their partner.
Supports accessibility for: Organization, Conceptual Processing
Required Materials
Materials to Gather
Geoblocks
Solid shapes
Required Preparation
Each group of 2 students needs 4–6 different solid shapes.
Launch
Groups of 2
Give each group of students 4–6 different solid shapes.
“We are going to learn a new way to do the Geoblocks center. It is called Geoblocks, Describe and Find.”
“Put the solid shapes in the middle, between you and your partner.”
30 seconds: partner work time
Activity
“Think of a shape but don’t tell your partner. Describe one of the shapes to your partner. Your partner’s job is to guess which shape you are describing. Once your partner figures out which shape you are describing, switch roles.”
7 minutes: partner work time
Monitor for students who describe the shapes in the ways described in the activity narrative.
Advancing Student Thinking
If students guess a shape that is not being described, consider asking:
“What clues did your partner give you?”
If needed, consider prompting students to eliminate some of the shapes. For example, ask “Your partner said that the shape has a round part. Are there any shapes that do not have round parts?”
Activity Synthesis
Invite previously identified students to share.
“Which clues did your partner give that were helpful to you?” (My partner said their shape was tall and had a circle on the top and bottom.)


aligns: no