few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Topic options: 
A. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
B. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
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. 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.
F. 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.
G. 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.
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. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
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. 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 problem asks students to reason about ratios of butter amounts to sugar amounts.",
  "answer": "D"
}

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: fl_problem_000972

6
options: 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 & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

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.

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

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

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.

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.

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.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
problem_activity: Narrative
The purpose of this activity is for students to add and subtract multiples of 10 and 100 within 1,000. Students interpret situations with base-ten blocks and base-ten diagrams and use equations to represents sums and differences. In the activity synthesis, students relate the situation, base-ten diagram, and equation and notice, through repeated reasoning, that when adding and subtracting, one can add or subtract hundreds and hundreds and tens and tens (MP7, MP8).
MLR7 Compare and Connect.
Synthesis: Lead a discussion comparing, contrasting, and connecting their different ways of representing the value of Mai and Lin’s blocks together. Ask, “How do these different representations show the same information?” “How are they different?”
Advances: Representing, Conversing
Representation: Access for Perception.
Invite students to act out the scenario of giving and taking hundreds on a number line. Discuss the individual jumps of 100 if a jump of 400 is too much to begin.
Supports accessibility for: Conceptual Processing, Language, Organization
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“These students were using base-ten blocks to find the value of sums and differences.”
“For each problem, represent the student’s value in a way that makes sense to you. You can use base-ten blocks, diagrams, or equations.”
10 minutes: partner work time
For Priya and Jada’s blocks, monitor for students who:
write equations to show the sums and differences.
use base-ten diagrams to show subtraction.
Student Facing
Mai has 2 hundreds, 2 tens, and 3 ones. Lin has 4 hundreds.
Represent their values with base-ten blocks or diagrams.
What is the value of their blocks altogether? Show your thinking.
Andre has 4 hundreds, 2 tens, and 8 ones.
Represent his value with base-ten blocks or diagrams.
Andre gives 2 hundreds to Clare.
What is the value of his blocks now? Show your thinking.
Diego has 6 tens. Tyler has 8 hundreds, 3 tens, and 6 ones.
What is the value of their blocks together? Show your thinking.
Elena has 5 hundreds, 7 tens, and 2 ones. She gives 2 tens to Kiran.
What is the value of her blocks now? Show your thinking.
Priya has 6 hundreds, 5 tens, and 8 ones. Han gives her 3 hundreds.
What is the value of her blocks now? Show your thinking.
Jada has 4 hundreds, 8 tens, and 2 ones. She gives 3 hundreds to Noah.
What is the value of her blocks now? Show your thinking.
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 draw diagrams that do not match the situation or write equations that are not true, consider asking:
“Can you explain what you did?”
“Do you notice any patterns when you add or subtract hundreds and hundreds? Tens and tens?”
Activity Synthesis
Invite a student to share their representation and equation for Jada’s blocks. If no students use a base-ten diagram, select a student to share how they use base-ten blocks, and use a base-ten diagram to record their steps.
“How does the base-ten diagram show Jada’s blocks?” (The blocks show how many Jada started with. The lines show the 3 hundreds that were taken away.)
Display
\(482 - 300 = 182\)
“How does the equation show Jada’s blocks?” (482 is what Jada started with and 300 is the 3 hundreds she gave away. 182 is how much she has left.)


correct_option_index: 4