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: 
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: 
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 following problem or activity 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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to use their own language and the language generated by the class in the last activity to describe how objects were sorted and tell how many objects are in each category. Students walk around the room and look at how other students sorted their objects. Consider using a signal to let students know when it is time to rotate.
Action and Expression: Internalize Executive Functions
. Check for understanding by inviting students to rephrase directions in their own words. Keep a display of directions visible throughout the activity.
Supports accessibility for: Memory, Attention
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
The math tool sorts from the previous activity are needed for this gallery walk.
Launch
Groups of 2
“Now you’re going to walk around to other tables to look at how other students sorted their tools. For each group’s work, talk to your partner about how they sorted the math tools and how many objects are in each category.”
Students move so they are looking at another group’s work.
“Look at the objects on your own. How did they sort the math tools? How many objects are in each category? When you are ready to share your thinking with your partner, put your thumb up.”
30 seconds: quiet think time
“Take turns sharing your thinking with your partner.”
1 minute: partner discussion
Activity
“Move to the next group’s work. Talk to your partner about how they sorted and how many tools are in each category.”
Repeat as time allows.
8 minutes: partner discussion time
Student Response
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Activity Synthesis
“What are some different ways you saw the math tools sorted?”


aligns: no