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: 
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_pos_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 decompose 6 into 2 parts. Students see that the total number of cubes remains the same when it is decomposed into 2 parts. Although students may notice that they can do this in different ways, that idea is not the focus until the next activity.
MLR8 Discussion Supports.
Display and encourage students to use the following sentence frames: “I have _____ cubes in my hand”, “I have _____ cubes on my desk,” and “I have _____ cubes altogether.”
Advances: Speaking, Reading, Representing
Required Materials
Materials to Gather
Connecting cubes
Required Preparation
Each student needs 6 connecting cubes.
Launch
Groups of 2
Give each student 6 connecting cubes.
Activity
“You have 6 cubes. Put some of the cubes in your hand and some on your desk.”
30 seconds: independent work time
“Tell your partner how many cubes are in your hand. Show them the cubes.”
“Tell your partner how many cubes are on your desk. Show them the cubes.”
“Tell your partner how many cubes you have altogether.”
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Invite a student to share.
“How many cubes did you have in your hand? How many cubes were on your desk?”
Write an expression to represent the parts.
“How many cubes did you have in all?” (6)
“The total number of cubes stays the same when we break them up into 2 parts.”


aligns: no