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: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
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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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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

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im_task_000870_pos_0

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standard_description: Correctly name shapes regardless of their orientations or overall size.
problem_activity: Narrative
The purpose of this activity is for students to identify and name shapes in the environment. The shape walk can take place in the playground, library, or another area of the school. It may be easier for students to use their recording sheet if it is on a clipboard.
When students recognize mathematical features of objects in the real world, they model with mathematics (MP4).
Engagement: Develop Effort and Persistence.
Students may benefit from chunking this task into smaller parts. Invite students to look for one shape at a time. Check in with students to provide feedback and encouragement after recording each shape.
Supports accessibility for: Conceptual Processing
Required Materials
Materials to Gather
Clipboards
Launch
Groups of 2
“We are going to take a walk around the playground. Look for examples of triangles, rectangles, and circles around the playground. Tell your partner about the shapes you find and draw pictures or write words to record what you find.”
Activity
10 minutes: shape walk
“Write a number to show how many of each shape you found.”
2 minutes: independent work time
Student Facing
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Synthesis:
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Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Invite students to share their recording sheets and the shapes that they found.
Display the image or an example from the playground:
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“Han found this swing on the playground. Where should he draw this on the recording sheet?” (The swing looks like a rectangle so he could draw it with the rectangles. The sides of the swing look like triangles.)


aligns: yes