The purpose of this activity is for students to move back and forth between equations, situations, and diagrams. Each member of a group is assigned one of the representations to begin with and all of the representations can represent the same situation. This is the first time in this unit students have been asked to write situations that represent division equations or diagrams. As students work, ask them to explain how the diagram represents the number of objects being shared and the number of equal shares.

Students go back and forth between equations, situations, and diagrams, interpreting the diagrams and equations and creating situations that these diagrams and equations represent (MP2).

• “How does the situation represent the diagram or equation?”
• Show them the picture from the Launch. “If there are 4 pounds of blueberries shown here, how does this image represent the diagram or equation?”

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student representations.
• Display equation: .
• “How did you use the equation to help determine the number of objects and equal shares in your story?” (The numerator is the number of objects. The denominator is the number of shares. This story needs 4 objects and 6 equal shares.)
• Display image:

  

• “How did you use the diagram to help determine the number of objects and equal shares in your story?” (The number of objects is the number of wholes or large rectangles. The number of shares is the number of equal pieces each rectangle is divided into. There are 4 objects and 6 equal shares.)
• “How were your stories the same? How were they different?” (There were 4 objects in each and they were divided into 6 equal shares, but our contexts were different.)

The purpose of this activity is for students to solve problems about the same context. The context for both problems is equally splitting some gold. There are three related quantities:

• The total amount of gold collected
• The total number of friends who collect the gold
• The amount of gold each person gets

In previous lessons, students solved problems where the unknown was the amount each person gets after some people shared something equally. In this activity, the unknowns are the amount of gold the friends share and the number of friends sharing the gold. Students may need to draw diagrams to interpret the unknown. During the Activity Synthesis, connect the meaning of division to the meaning of a fraction.

• “What do you know about the problem? What are you still trying to figure out?”
• Draw a diagram of the situation. “How does this diagram represent the situation?”

• Invite previously selected students to share their responses.
• Display the first situation that describes 3 friends sharing gold and each friend gets grams of gold.
• “What do we know about the situation?” (There are 3 friends and each friend gets grams of gold.)
• Display:
• “How does represent the situation of friends sharing gold?” (It is the amount of gold each friend got.)
• “What does the 3 represent in ?” (Thirds. The amount they collected was split into 3 equal parts because there are 3 friends.)
• “What does the 4 represent in ?” (It represents how many thirds of gold each friend received and it represents the total amount of gold, in grams, being shared by the 3 friends.)