few_shots: Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Topic options: 
A. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
C. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
D. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
E. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
F. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
G. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
H. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
I. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
J. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
K. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.


Your response, in json format:
{
  "explanation": "This problem pertains to functions because it asks students to find the general solution to a trigonometric function.",
  "answer": "B"
}

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


Topic options: 
A. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
B. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
C. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
D. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
E. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
F. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
G. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
H. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
I. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
J. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
K. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.


Your response, in json format:
{
  "explanation": "This task asks students to reason with equations, specifically a quadratic equation. Since the problem asks for as many different methods as possible, it's possible that students would discover solution methods that include graphing both sides of the equation with a graphing calculator and finding the x coordinates of where the two functions intersect.",
  "answer": "B, G"
}

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 $P$.


Topic options: 
A. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
B. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
C. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
D. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
E. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
F. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
G. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
H. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
I. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
J. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.
K. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.


Your response, in json format:
{
  "explanation": "This task involves geometric concepts including angles, circles, and rays.",
  "answer": "H"
}

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
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.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center"}, "br": [{}], "_values": ["pigeons in the", "fountain"]}, {"_attributes": {"scope": "col", "style": "text-align:center"}, "br": [{}], "_values": ["pigeons on the", "bench"]}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "p": [{"_value": "9"}, {"_value": "8"}, {"_value": "7"}, {"_value": "6"}, {"_value": "5"}, {"_value": "4"}, {"_value": "3"}, {"_value": "2"}, {"_value": "1"}]}, {"_attributes": {"style": "text-align:center"}, "p": [{"_value": "1"}, {"_value": "2"}, {"_value": "3"}, {"_value": "4"}, {"_value": "5"}, {"_value": "6"}, {"_value": "7"}, {"_value": "8"}, {"_value": "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
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
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.)


correct_option_index: 1