The purpose of this activity is for students to write and interpret division expressions and equations that represent equal sharing situations. They explain the relationships between the dividend and the numerator and divisor and the denominator. Students may draw diagrams to help them make sense of these relationships (MP1).

The last problem provides an opportunity for students to think critically about a proposed solution to a problem (MP3). Different ways to think about the proposed solution include:

• Estimation: with 3 friends sharing 2 liters equally, each friend gets less than 1 liter.
• Thinking about the meaning of the numerator (how many liters are being shared) and denominator (how many people are sharing the water equally).

This activity uses MLR3 Critique, Correct, Clarify. Advances: reading, writing, representing

• Invite previously selected students to share.

MLR3 Critique, Correct, Clarify

• Display the response for students to consider:
• Mai said that each dancer gets liter water because 3 divided into 2 equal groups is .
• Read the explanation aloud.
• “What parts of this response are unclear, incorrect, or incomplete?” (The 3 represents the number of dancers, not the amount of water. So, Mai would be dividing dancers instead of liters of water.)
• 1 minute: quiet think time
• 2 minute: partner discussion
• Invite 2–3 groups share what they discussed. Record for all to see.
• “With your partner, work together to write a revised explanation.”
• Display and review the following criteria:
  • Use “dancers” and “liters of water.”
  • Create a labeled equation or diagram.
• 3–5 minute: partner work time
• Select 1–2 groups to read their revised draft aloud slowly enough to record for all to see. Scribe as each group shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.
• “What is the same and different about the explanations?” (Some people labeled the diagram to show what is being divided and some people labeled the numbers in the equation.)

In previous activities, students interpreted diagrams and expressions that represented equal sharing situations. The purpose of this activity is for students to interpret division expressions without the support of diagrams in order to deepen their understanding about the relationship between fractions and division expressions. The activity is designed to highlight the relationship between the number of objects being shared and the numerator, and the number of people sharing and the denominator (MP7).

• Display the table from the activity.
• “What are some of the numbers you used for the last two rows?”
• Record the answers as additional rows to the table.
• “What are some patterns that you notice in the table?”
• Ask previously selected students to share their solutions.