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 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_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
problem_activity: Narrative
The purpose of this Choral Count is for students to practice counting by 10 and 100 and notice patterns in the count. This is the first time students are introduced to the number 1,000. Although students in grade 2 do not need to understand the unit of a thousand, students will work with 1,000 on a number line in this lesson to deepen their understanding of the structure of the base-ten system.
Launch
“Count by 10, starting at 0.”
Record in a column as students count.
Stop counting and recording at 100.
“Count by 100, starting at 0.”
Record the count in a new column next to the first.
Stop counting and recording at 1,000.
Activity
“What patterns do you see?”
1–2 minutes: quiet think time
Record responses.
Student Response
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Activity Synthesis
Draw three number lines that show counting by 1, 10, and 100, such as:
[IMG]
[IMG]
[IMG]
“What patterns do you see?” (All 3 number lines show 10 jumps. They all start at zero, but end with different numbers.)


aligns: no