The purpose of this activity is for students to compare two numbers in context, to explain or show their reasoning, and to record the results of the comparison with the symbol >, <, 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 or to represent  as the greater fraction. During the Activity Synthesis, discuss how both statements capture the comparison and are valid.

• Select 2 or 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, and ), 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. 

The purpose of this activity is for students to generalize what they have learned about comparing fractions to complete comparison statements and to generate new ones, using the symbols >, <, and =. Students first consider all numbers that could make an incomplete comparison statement true. Then they find fractions greater than, less than, and equivalent to a given fraction, and write statements to record the comparisons. As in the previous activity, students see that there are different ways to record the same comparison of two numbers.

• “You found one number that made the statement true. How did you find that number and know that it made the statement true?”
• “How could you use a similar strategy to find another number that would make the statement true?”

• Invite students to share their responses to the last set of problems.
• “How did you find a fraction that was less than (or greater than or equivalent to) the given fraction?”

The purpose of this activity is for students to use their knowledge of fractions to locate fractions with different denominators on the number line. Students may use a variety of reasoning to locate the fractions, including their knowledge of equivalence, strategies about the same numerator or the same denominator, or benchmark numbers with which they are familiar. The Activity Synthesis focuses on the variety of strategies that make sense, and students should be encouraged to use different strategies for different fractions as needed.

Although students have represented fractions on number lines (including those with two different denominators, when reasoning about equivalence), this activity is optional because representing multiple fractions of different denominators on the same number line involves a deeper understanding than is required by the standards.

• Invite students to share a variety of strategies for placing fractions on the number line.
• Consider asking:
  • “Which fractions were easier to place on the number line?”
  • “Which fractions were more difficult?”
  • “Did anyone have the same strategy but would explain it differently?”