few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Topic options: 
A. 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.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
C. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
D. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
E. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
F. 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.
G. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
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. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
J. 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.
K. 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.


Your response:
Thought: This problem teaches students different ways of writing numbers that express the same value. This helps students better understand the complex number system, which includes rational numbers.
Answer: I

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_001097

7
options: Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

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.

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

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

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.

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

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

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

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: Activity
The goal of this activity is for students to be introduced to the idea that variability is important when analyzing and comparing data sets. Students will compare data sets, and make a decision as to which data set represents a better scenario. This activity prepares students to calculate variability in order to compare data sets in a later lesson. Monitor for students who calculate any
statistics
to inform their decisions. Make note of the students who only calculate a measure of center vs. students who calculate both a measure of center and a measure of variability.
Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Students will work individually. Tell them to use statistics to inform their decision.
Student Facing
In order from least to greatest, here are the prices per gallon of gas at two different gas stations over the past 7 days.
Station A:
2.38, 2.68, 2.82, 2.86, 2.99, 3.26, 3.59
Station B:
2.84, 2.85, 2.88, 2.95, 2.98, 3.03, 3.05
Suppose that these gas stations were the closest to your house, but not near each other. Which gas station would you go to for gas? Explain your reasoning.
Student Response
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Activity Synthesis
The purpose of this discussion is to understand that the variability is worth paying attention to. If any students chose to compute the mean, median, IQR, MAD, or range for the two stations, ask them to share their results and how those values help them decide. Interestingly, the mean is the same for the gas stations. But any measure of variability shows that the prices at station B are more stable and predictable than the prices at station A. If no students suggest computing measures of center and variability and comparing them, be prepared to demonstrate.
Here are the summary statistics for each set of data:
For Station A:
Mean: 2.94
Five-number summary: 2.38, 2.68, 2.86, 3.26, 3.59
Range: 1.21
IQR: 0.58
MAD: 0.29
For Station B:
Mean: 2.94
Five-number summary: 2.84, 2.85, 2.95, 3.03, 3.05
Range: 0.21
IQR: 0.18
MAD: 0.07
If time permits, discuss which measures are helpful. Here are sample questions:
“Was the mean helpful in deciding the gas station from which you would purchase gas?”(No, because both means were the same.)
“How did the range (or IQR, MAD, five-number summary) help you decide which gas station you would go to?” (Whichever gas station had the highest range [or IQR, MAD] is the gas station I chose.)
“In the real world, how would you use the gas prices at each gas station to make a decision?” (I would think about which one generally had lower prices and choose that one, or I would see which one had more predictably cheaper prices and choose that one.)


correct_option_index: 1