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

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options: 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.

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

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.

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

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.

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

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.

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.
problem_activity: Narrative
The purpose of this activity is for students to ask a question that can be answered with the given information and then answer the question. There are many different questions students can ask including:
Who picked the most apples?
How many apples did they pick together?
Did Elena or Diego pick more apples?
How many apples did Diego pick?
These questions require all the given information to solve. Students may also ask questions which require only some of the information to solve, such as, “How many apples did Han pick?” The activity synthesis focuses on sharing different questions students asked and how they found the answer, with a focus on the multi-step problem “How many apples did they pick altogether?” Images are provided for display, however, student work should be used as much as possible in the synthesis.
Launch
Groups of 2
“Sometimes people buy apples at the market or grocery store, but sometimes people go to an apple orchard to pick apples.”
“Each person gets a basket to collect the apples they pick, and then they pay for the apples.”
“Apple picking can be a fun outing for families and friends.”
“You will be reading a story and asking questions about friends who went apple picking together.”
Activity
Read the problem.
“Think about the questions you could ask someone that this story could help them answer.”
5 minutes: independent work time
“Switch questions with your partner and find the answer.”
“Share your thinking and check to see if you agree about the answer.”
5 minutes: partner work time
Monitor for students who represent how many apples Han picked and students who represent how many apples Diego picked compared to Han to share in the synthesis as shown.
Student Facing
Elena picked 29 apples. Elena picked 14 fewer apples than Han. Han picked 15 more apples than Diego.
Write a question someone could answer based on this information.
Answer your question. Show your thinking using diagrams, symbols, or other representations.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students write a question that can’t be answered with the information given, consider asking:
“What is the story about?”
“What can be counted in the story?”
“What quantities do you know? What is unknown?”
Activity Synthesis
Invite students to share their questions.
Display a diagram that represents the number of apples Han picked, such as:
[IMG]
“What does the diagram represent?” (The number of apples Han picked since he picked 14 more than Elena.)
“How did you find how many apples Han picked?” (I added 30 to 14 to get 44 and then took away 1 to get 43.)
Display a diagram that represents the number of apples Diego picked compared to Han, such as:
[IMG]
“What does the diagram represent?” (How many apples Diego picked compared to Han.)
“How did you find how many apples Diego picked?” (I took 15 away from 43.)
“How did you find how many apples Elena, Han, and Diego picked altogether?” (I added 29, 43, and 28. I put all the tens together to get 80 and all the ones together to get 20 then added 80 and 20.)


correct_option_index: 5

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