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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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:
[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: 
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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this activity is for students to develop mathematical questions about their school community. This walk could also take place on the playground or in the local community.
MLR8 Discussion Supports.
Synthesis: As students share their questions, include a drawing or annotation to clarify any questions about context. Invite students to notice common language used in mathematical questions such as: how many, how much, which, more than, taller than, etc.
Advances: Speaking, Representing
Required Materials
Materials to Gather
Clipboards
Paper
Launch
Give each student a clipboard with a blank piece of paper.
“We’re going to take another walk around the school. Your job is to think of math questions that you would like to answer about our school. Use your recording sheet to help you remember what questions you have.”
Activity
15 minutes: whole-class school walk
Student Facing
What math questions do you have about our school?
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 questions.
Record student questions on an anchor chart. Keep the chart display during the next activity.


aligns: yes