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: 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.

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

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.

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.

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

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 & 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.

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.

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.
problem_activity: Narrative
The purpose of this card sort is for students to connect words and phrases to visual representations of partitioned shapes. Students begin by sorting the cards in a way that makes sense to them, and then are invited to sort the shapes based on the language that can be used to describe them. In the activity synthesis, the phrases “two of the halves” and “four of the fourths” are introduced to describe shapes where all pieces are shaded in.
Keep cards D and N available to use during the lesson synthesis.
As students sort the shape cards they look for structure, namely the number of pieces making up each shape, whether or not the pieces are equal, and the number of those pieces that are shaded (MP7).
MLR2 Collect and Display.
Circulate, listen for and collect the language students use as they describe the shapes. On a visible display, record words and phrases such as: “shaded,” “half,” “fourth,” “quarter,” “equal,” “not equal,” “whole,” “shape.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Speaking
Required Materials
Materials to Copy
Shaded Parts Cards
Required Preparation
Create a set of Shaded Parts Cards for each group of 2.
Launch
Groups of 2
Give each group a set of cards.
“Sort your cards in a way that makes sense to you. Then explain how you sorted them.”
3 minutes: partner work time
Share responses.
Activity
“Now, sort the cards into the categories shown on your paper. Think about what words you can use to describe the shape on each card. Write the letter of each card in the space for it's category.”
5 minutes: partner work time
Student Facing
Sort the cards into categories in a way that makes sense to you. Explain how you sorted the cards.
[IMG]
Sort your cards into these categories.
Write the letter of each card in the space for its category.
A fourth or quarter is shaded
[IMG]
A half is shaded
The whole shape is shaded
[IMG]
Not equal pieces
Student Response
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Activity Synthesis
Display card J.
“How can we describe this shape?” (It is a square. It is cut into halves. The whole shape is shaded.)
“When a shape is split into halves and they are both shaded, we say the whole shape is shaded or two of the halves are shaded.”
Repeat with card E.
“When a shape is split into fourths and they are all shaded, we say the whole shape is shaded or four of the fourths are shaded.”


correct_option_index: 4