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:
{
  "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:
{
  "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:
{
  "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: 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.

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.

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

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.

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

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

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

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.

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.

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

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
problem_activity: Narrative
The purpose of this activity is for students to practice division within 100 by playing a game called Race to 1. The goal of the game is to repeatedly divide numbers until they reach one.
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community.
Supports accessibility for: Social-Emotional Functioning, Organization
Required Materials
Materials to Gather
Number cubes
Launch
Groups of 2
“Take a minute to read the directions for Race to 1.”
1 minute: quiet think time
“Let’s look at a sample game. Jada rolled a 3 on her first turn, then rolled 2 a few times afterwards. Talk with your partner about what her next move should be if she rolls 2 on her next turn.” (She should divide 4 or 6 by 2 because those moves get her really close to one.)
1 minute: partner discussion
Share responses.
Give each group a number cube.
Activity
“Play Race to 1 with your partner.”
10–15 minutes: partner work time
If students finish early, have them play again. Students can fill in the same numbers from the first game at the top of the columns of the second game or use the numbers 24, 36, 48, and 72 for a challenge.
Student Facing
Directions for Race to 1
On your first turn:
Roll a number cube. The number you roll is your divisor. (If you roll a 5, roll again.)
Choose one number from the top row of your table. Divide it by your divisor.
Write a division expression and record the quotient in the table. Your turn is done.
On all your other turns:
Roll a number cube. The number you roll is your divisor. (If you roll a 5, roll again.)
Choose either a quotient from one of your past turns or a new number from the top row of the table. Divide it by your divisor.
Write a division expression and record the quotient in the table.
The first player to get a quotient of 1 wins.
Sample Game
Jada rolled 3 on her first turn, then rolled 2 a few times afterwards.
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "thead": [{"tr": [{"th": [{"p": [{"_attributes": {"style": "text-align:center"}, "_value": "start number"}]}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "12"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "16"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "18"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "24"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math"]}, "_value": "\\(12\\div3\\)"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math"]}, "_value": "\\(16\\div2\\)"}]}, {}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math"]}, "_value": "\\(24\\div2\\)"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {"_attributes": {"style": "text-align:center"}, "_value": "4"}, {"_attributes": {"style": "text-align:center"}, "_value": "8"}, {}, {"_attributes": {"style": "text-align:center"}, "_value": "12"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math"]}, "_value": "\\(12\\div2\\)"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {"_attributes": {"style": "text-align:center"}, "_value": "6"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}]}]}]}
Game 1
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "thead": [{"tr": [{"th": [{"p": [{"_attributes": {"style": "text-align:center"}, "_value": "start number"}]}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "12"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "16"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "18"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}, "_value": "24"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}]}]}]}
Game 2
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "thead": [{"tr": [{"th": [{"p": [{"_attributes": {"style": "text-align:center"}, "_value": "start number"}]}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}}, {"_attributes": {"scope": "col", "style": "text-align:center; width:18%"}}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "division expression"}, {}, {}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "_value": "quotient"}, {}, {}, {}, {}]}]}]}]}
Activity Synthesis
“How was having an efficient way to divide helpful as you played Race to 1?” (I had to decide which number I was going to divide, so it was helpful to be able to do it quickly. I had to divide a few times on each turn.)
“What was a helpful strategy as you played Race to 1?” (I had to think about which number I could divide by the number I rolled. I divided the smallest number by the largest divisor to try to get to the quotient to be as small as possible so I could get to 1 first.)


correct_option_index: 1