few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


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


Your response:
{
  "explanation": "In this problem, students learn to recognize equivalent fractions. Each lap around the school is 1/4 mile, while each lap around the playground is 1/12 mile. Three laps around the playground is 3/12 mile, which is equivalent to 1/4.",
  "answer": "D"
}

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: im_task_000212

4
options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

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.

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.

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

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.

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

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.
problem_activity: Narrative
The purpose of this activity is for students to make a reasonable estimate for a given product.
In addition to estimating the product, students also decide whether the estimate is too large or too small. In the activity synthesis, students consider about how far their estimate is from the actual product.
I
n the next activity, students will evaluate the expressions using a strategy of their choice.
Students choose between several different possible estimates and justify their choice before they calculate the product (MP3).
Engagement: Provide Access by Recruiting Interest.
Synthesis: Revisit math community norms to prepare students for the whole-class discussion.
Supports accessibility for: Social Emotional Functioning, Language
Launch
Groups of 2
Activity
5–7 minutes: independent work time
2–3 minutes: partner discussion
Monitor for students who:
relate the given expression to each proposed answer by rounding or changing one or both factors.
estimate by rounding the factors.
use benchmark numbers.
use place value reasoning or the properties of operations to explain why their estimate is reasonable.
Student Facing
Which estimate for the product
\(18 \times 149\)
is most reasonable? Explain or show your reasoning.
\(2,\!000\)
\(4,\!000\)
\(3,\!000\)
\(1,\!500\)
Are any of the estimates unreasonable? Explain or show your reasoning.
Do you think the actual product will be more or less than your estimate? Explain or show your reasoning.
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 do not choose a reasonable estimate for
\(18 \times 149\)
, ask, “Can you explain how you chose your estimate?”
Activity Synthesis
Invite students to share their estimates for the product and their reasoning.
“Why do you think
\(3,\!000\)
is a good estimate?” (18 is close to 20 and 149 is very close to 150 and I know
\(20 \times 150 = 3,\!000\)
.)
“Is the value of
\(18 \times 149\)
greater than or less than
\(3,\!000\)
? How do you know?” (Less, because 18 is less than 20 and 149 is less than 150.)
“Can you estimate how much less?” (About 300, because I added 2 to 18 to get 20 and
\(2 \times 149\)
is about 300.)
Display:
\(18 \times 149\)
is about
\(2,\!700\)
.
“In the next activity, we’ll check to see how good our estimate is.”


correct_option_index: 9