few_shots: 
Example 1:
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.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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:
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).

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

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: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Narrative
The purpose of this activity is for students to find all of the compositions and decompositions of 10 in the context of a Put Together/Take Apart, Both Addends Unknown story problem. Monitor for students who:
change the number of red and yellow counters on a 10-frame (MP5).
move the beads on a bead tool (MP5).
use their knowledge, possibly from memory, of different decompositions of 10.
use patterns such as switching the number of pigeons in the fountain and on the bench (MP7).
The purpose of the activity synthesis is to use the 10-frame and the bead tool to visualize how the parts that make 10 are related, specifically that adding one to one number takes one away from the other number in the decomposition.
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, to figure out all the different ways to make 10. Students can take turns verbally sharing their plan with their partner and work on an overall plan to find all the ways to make 10.
Supports accessibility for: Organization, Conceptual Processing
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Materials from a previous activity
Required Preparation
Students can use their bead tool from a previous lesson.
Create a chart displaying solutions to be used during the lesson synthesis.
|                                                                               pigeons in the                       fountain                                                                               |                                                                                pigeons on the                       bench                                                                                 |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 9                        8                        7                        6                        5                        4                        3                        2                        1 | 1                        2                        3                        4                        5                        6                        7                        8                        9 |
Launch
Groups of 2
Give students access to connecting cubes or two-color counters, bead tools, and 10-frames.
Display and read the task statement.
“Work with your partner to show all of the ways that the 10 pigeons could be in the fountain and on the bench.”
Activity
7 minutes: partner work time
Student Facing
There were 10 pigeons.
Some of the pigeons were in the fountain.
The rest of the pigeons were on the bench.
How many of the pigeons were in the fountain?
Then how many of the pigeons were on the bench?
Show your thinking with objects, drawings, numbers, or words.
Student Response
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Activity Synthesis
Display a 10-frame with 9 red counters and 1 yellow counter and a bead tool with 9 beads on the left and 1 on the right.
[IMG]
[IMG]
“How do the 10-frame and the bead tool show a solution for the story problem?” (There can be 9 pigeons in the fountain and 1 pigeon on the bench.)
Switch one red counter to yellow, as pictured, and move 1 bead from the right to the left.
[IMG]
[IMG]
“What if I change one of the red counters to yellow? What if I move one bead over?” (Then 8 pigeons are in the fountain and 2 pigeons are on the bench.)
“Can I keep changing red counters to yellow? Can I keep moving the beads to the other side? What will happen?” (Yes, more pigeons will be on the bench and fewer pigeons will be in the fountain.)


aligns: yes