Lesson 21

This warm-up serves two goals: to elicit observations about equal groups in seating arrangements, and to identify variables that might be important when solving a real-world problem in which limited information is given. These conversations prepare students to design seating arrangements given some constraints later in the lesson. 

During the synthesis, highlight observations about equal groups and reveal that the image shows a seating chart. Ask students to identify the information they may need if they were to be in charge of planning the seating arrangement for a game night. As students brainstorm questions to help them gather necessary information and clarify the problem, they engage in aspects of mathematical modeling (MP4). 

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Alguien dibujó el diagrama para representar una situación de la vida real. ¿Cuál podría ser esa situación?” // “Somebody drew the diagram to illustrate a real-world situation. What could that situation be?” (Table arrangement. Game board. Sports arrangement.)
• “La imagen muestra organizaciones de mesas para una noche de juegos” // “The image shows table arrangements for a game night.”
• “Si estuvieran encargados de planificar la organización de los asientos para una noche de juegos, ¿qué tendrían que preguntar para tener suficiente información para hacer la planificación?” // “If you were in charge of planning the seating arrangement for a game night, what questions would you need to ask to have enough information to plan?” (How many tables are there? How many people can play each game? How many people can sit at each table? How many chairs are there? How many guests are going to the game night? How big are the tables?)
• Share and record responses. Keep this visible for the next activity.
• “En la siguiente actividad harán una gráfica de los asientos para una noche de juegos. Obtendrán las respuestas de algunas de estas preguntas. Para otras preguntas, tendrán que tomar algunas decisiones” // “In the next activity you will create a seating chart for a game night. You will get answers to some of these questions. For other questions, you will need to make some decisions.”

The purpose of this activity is for students to plan a seating arrangement. Students are only given the information of the number of players required for each game and the total number of tables. The numbers 2, 4, 5, and 10 have been chosen to reflect the multiplication work students have done in previous lessons. Students make their own decisions about other aspects of the scenario before planning their seating arrangement and also choose how to represent their seating arrangement (MP4).

Students may want answers from the teacher before making the arrangement. Encourage them to make their own assumptions as long as it does not contradict the given information.

• Groups of 2 or 4
• Give each group tools for creating a visual display and access to inch tiles, graph paper, and connecting cubes or counters.
• “La primera parte de la tarea responde algunas de nuestras preguntas, como el número de personas necesarias para cada juego y el número total de mesas. Pueden tomar decisiones sobre la información que no se da. En el póster que hagan, incluyan la información que supusieron y expliquen qué información nueva obtuvieron como resultado. Además, incluyan cuántas personas pueden jugar juegos en la sala con su distribución de los asientos” // “The first part of the task answers some of our questions such as the number of people needed for each game and the total number of tables. You can decide the information that is not given. In the poster you make, include the information you assumed and explain what new information you got as a result. Also, include how many people can play games in the room with your seating plan.”

• 20 minutes: small-group work time
• Monitor for groups that:
  • Describe their assumptions and explain how their assumption impacted the arrangement. For example, if they wanted to set up 6 games of Game A, then they need space for 12 people.
  • Make assumptions about the total number of people.

If students find it challenging to make decisions about unknown information, consider asking:

• “Dime cómo va el diseño de tu gráfica de los asientos hasta el momento” // “Tell me about how you've designed your seating chart so far?”
• “¿El problema te da información sobre lo que estás escogiendo? ¿Cuáles son las opciones que tienes para _____? ¿Cómo cambiaría tu gráfica de los asientos si tú _____?” // “Is there information given in the problem for what you're choosing? What are some choices you have about _____? How would it affect your seating chart if you _____?”

• Invite previously selected students to display their posters for all to see.
  • “¿Qué nos dice esta organización sobre la situación?” // “What does this arrangement tell us about the situation?” (It shows us how many of each game are played. It shows us how many people can play each game. It shows us how many people can play games in the room if it's set up like this.)
  • “¿Qué expresión de multiplicación representa el número de personas que pueden jugar el juego A?, ¿el juego B?, ¿el juego C?, ¿el juego D?” // “What multiplication expression represents the number of people that can play Game A? B? C? D?”

The purpose of this activity is for students to represent their game night plans on a scaled bar graph. In the synthesis, students consider how their graph communicates information about their game night plan.

• Each student needs a sheet of grid paper.

• Groups of 2 or 4
• Give each student grid paper.
• “Ahora van a hacer una gráfica de barras con escala que muestre cuántas personas pueden jugar cada juego, con su organización de la sala” // “Now you’re going to make a scaled bar graph that shows how many people can play each game with your room arrangement.”
• “Discutan qué escala va a usar su grupo para su gráfica” // “Discuss what scale your groups will use for your graph.”
• 1 minute: small-group discussion
• “Pueden trabajar en grupo, pero cada uno hará su propia gráfica. También pueden escoger una escala diferente a la del resto de su grupo” // “You can work with your group, but everyone in your group will make their own graph. You can also choose a different scale than the rest of your group.”

• 5-7 minutes: small-group work time

• Display graphs that used different scales.
• “¿Cómo cambiaron las gráficas al escoger escalas diferentes?” // “How did choosing different scales affect the graphs?” (Some of the graphs have shorter bars because each jump on the graph is worth more. Some of the graphs are easier to read than others.)
• “¿Qué información nos da esta gráfica de barras sobre la situación?” //  “What information does this bar graph give us about the situation?” (The number of people at each game, the types of games. We can find the total number of people if we add them all up.)