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).

• Select 2–3 students to share their problems and solutions. Show a variety of accurate student representations.
• Display equation: .
• “¿Cómo les ayudó la ecuación a encontrar el número de objetos y de partes iguales en su historia?” // “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:

  

• “¿Cómo les ayudó el diagrama a encontrar el número de objetos y de partes iguales en su historia?” // “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.)
• “¿En qué se parecen sus historias? ¿En qué son diferentes?” // “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.

• 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.
• “¿Qué sabemos sobre la situación?” // “What do we know about the situation?” (There are 3 friends and each friend gets grams of gold.)
• Display:
• “¿Qué representa  en esta situación en la que unos amigos comparten oro?” // “How does represent the situation of friends sharing gold?” (It is the amount of gold each friend got.)
• “¿Qué representa el 3 en ?” // “What does the 3 represent in ?” (Thirds. The amount they collected was split into 3 equal parts because there are 3 friends.)
• “¿Qué representa el 4 en ?” // “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.)