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: Count within 1000; skip-count by 5s, 10s, and 100s.
problem_activity: Narrative
The purpose of this activity is for students to compare methods that can be used to count numbers between 100 and 999. Students see images of beans that are put in groups of 5 and another in groups of 10. A third image uses groups of 100, groups of 10, and single beans. Students make connections to place value and their understanding of the base-ten structure (MP2, MP7). They also consider opportunities for accuracy and efficiency when they articulate pros and cons for each method.
Launch
Groups of 2
Display image of a cup of beans or display a cup of beans.
Read the context aloud.
Activity
1 minute: quiet think time
5 minutes: small-group discussion
Monitor for students who:
describe the organization and group sizes in each method
describe Clare’s method in terms of hundreds, tens, and ones
discuss ideas such as efficiency (how long it takes) and accuracy (chances of mistakes)
Student Facing
[IMG]
Clare, Noah, and Jada counted a cup of dried beans. They each came up with 529 beans. The following pictures show how each of them counted.
Jada’s counting strategy:
[IMG]
Noah’s counting strategy:
[IMG]
Clare’s counting strategy:
[IMG]
What do you notice about each of their strategies?
What is helpful about each strategy?
What is challenging about each strategy?
Student Response
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Activity Synthesis
Invite previously selected students to share their observations.
“Which of these strategies do you believe would be the fastest or slowest? Explain.”
“Do you think it would be easier to make a mistake using one of these strategies? Which one and why?”
“Which strategy do you prefer? Why?”


aligns: yes