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

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

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.

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.

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

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.

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 Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
problem_activity: Narrative
The purpose of this activity is for students to compare two numbers in context, to explain or show their reasoning, and record the results of the comparisons with the symbols >, =, or < (MP2). The numbers may be fractions with the same numerator or the same denominator, or a fraction and a whole number.
Students are likely to generate different comparison statements for the same situation. For example, they may write
\(\frac{5}{8} > \frac{3}{8}\)
or
\(\frac{3}{8}<\frac{5}{8}\)
to represent
\(\frac{5}{8}\)
being the greater fraction. During synthesis, discuss how both statements capture the comparison and are valid.
MLR8 Discussion Supports.
Synthesis: As students share the similarities and differences between the representations and comparison statements, use gestures to emphasize what is being described. For example, show with your fingers the partitions such as fourths or eighths that are the same in the representations that are being compared.
Advances: Listening, Representing
Engagement: Provide Access by Recruiting Interest.
Synthesis: Optimize meaning and value. Invite students to share a connection between activity content and their own lives. Ask “How can I use this in my own life?”
Supports accessibility for: Conceptual Processing
Launch
Groups of 2
“Let’s use what we learned about comparing fractions and recognizing equivalent fractions to solve problems about lengths.”
Activity
“Work independently to solve the problems. For each one, be sure to show your thinking and to write a comparison statement.”
6–8 minutes: independent work time
“Share your responses and reasoning with your partner.”
2–3 minutes: partner discussion
Monitor for:
different representations or reasoning strategies used for the same problem, such as diagrams, fraction strips, number lines, or explanations in words
different statements written for the same problem, such as
\(4=\frac{12}{3}\)
and
\(\frac{12}{3}=4\)
, or
\(\frac{2}{3} > \frac{2}{8}\)
and
\(\frac{2}{8} < \frac{2}{3}\)
Student Facing
For each problem:
Answer the question and explain or show your reasoning.
Represent your answer with a statement that uses the symbols >, <, or =.
A beetle crawled
\(\frac{2}{8}\)
of the length of a log. A caterpillar crawled
\(\frac{2}{3}\)
of the length of the same log. Which insect crawled farther?
A grasshopper is 4 centimeters long. A caterpillar is
\(\frac{12}{3}\)
centimeters long. Which insect is longer?
[IMG]
A ladybug crawled
\(\frac{3}{8}\)
the length of a branch. An ant crawled
\(\frac{5}{8}\)
the length of the same branch. Which insect crawled farther?
A grasshopper jumped
\(\frac{5}{8}\)
the width of the sidewalk. A frog jumped
\(\frac{5}{6}\)
the width of the same sidewalk. Which jumped a longer distance?
Student Response
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Activity Synthesis
Select 2–3 students to share their reasoning strategies or representations for at least one of the situations.
“How did you use what you’ve learned in earlier lessons to compare fractions?” (If the fractions had the same numerator, I thought about the size of the denominators. If they had the same denominator, I compared the numerators.)
Select students who wrote different but equally valid comparison statements (for instance,
\(\frac{2}{8}<\frac{2}{3}\)
and
\(\frac{2}{3} > \frac{2}{8}\)
) to share.
Discuss how to read each statement and ask students whether both accurately represent the comparison.
Emphasize that we can write comparison statements in more than one way, but we need to check that the statements make sense given the numbers we write and the symbols we use.


correct_option_index: 2