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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
problem_activity: Narrative
The purpose of this activity is for students to fluently add and subtract within 5. Students look at the expression on their card and move quickly to the corner that is labeled with the correct answer. There are 16 expression cards included in the blackline master.
MLR8 Discussion Supports.
Invite students to read the expression card aloud to each partner. Listen for and clarify any questions about the the expressions.
Advances: Conversing
Required Materials
Materials to Gather
Materials from a previous lesson
Required Preparation
Each student needs one card from the Expression Cards set used in a previous lesson.
Label each corner of the classroom with a large number: 2, 3, 4, and 5.
Launch
Give each student an expression card.
“Find the value of the expression on your card. Go to the corner that is labeled with the value of the expression.”
Activity
30 seconds: independent work time
“Find a partner in your corner. Show them your card and tell them how you found the value of your expression.”
2 minutes: partner discussion
“Walk back to the center of the room. Trade your card with a partner.”
Repeat the steps above 3–4 times, as time allows.
Activity Synthesis
Display the expression
\(3 - 1\)
.
“Noah saw this expression and went to the corner labeled 4. Was he correct? How do you know?” (No, because this is 3 take away 1 and that is 2.)
“Why do you think he went to the corner labeled 4?” (He might have thought it was
\(3 + 1\)
instead of
\(3 - 1\)
.)


aligns: no