The purpose of this activity is for students to visualize and make sense of the context of problems they will solve in the next activity. They will also consider representations that can be used to model the quantities and actions in the situation (MP4) and try creating them. Students will not have time to make a complete representation, so the focus is on making sense of the situation and persevering in finding effective representations (MP1).

• While discussing each representation, ask students:
  • “¿Dónde están los casilleros en esta representación?” // “Where are the lockers in this representation?” (Numbers or pictures used to indicate lockers)
  • “¿Cómo podemos saber si un casillero está abierto o cerrado en esta representación?” // “How can we tell if a locker is open or closed in this representation?” (Symbols or colors were used to indicate open or closed.)
  • “¿Cómo se muestra en esta representación qué estudiante está tocando los casilleros?” // “How does this representation show which student is touching the lockers?” (Students and their actions were listed in a table or a T-chart.)
• “En la siguiente actividad, van a responder preguntas sobre el juego. Pueden usar su representación o alguna que haya sido compartida por un compañero como ayuda para pensar en los problemas” // “In the next activity, you will answer questions about the game. You may use your representation or one shared by a classmate to help you think through the problems.”

The purpose of this activity is for students to solve problems about a locker game by using the ideas of factors and multiples and by observing patterns in the numbers. The situation offers many possible explorations, but the questions around which lockers are touched and by how many people are designed to elicit understandings about multiplication.

Discussion about which lockers will be open or closed or by whom will likely move students away from thinking about factors and multiples and should not be the focus. The final question challenges students who are ready for more to look for additional patterns and generalize their observations. It is not expected that all students complete the final problem. Students who are ready may simulate opening and closing the lockers in different ways, such as:

• Using actual lockers, if available.
• Using a printed set of squares labeled 1 through 20.
• Using two color counters and 10-frames, if available.
• Using the head and tail sides of coins

• “Durante unos minutos, compartan sus respuestas con los estudiantes de otro grupo” // “Take a few minutes to share your answers with students in a different group.”
• Invite students to share how they kept track of the number of touches for each locker.