Lesson 18

The purpose of this What Do You Know About ____? is to invite students to share what they have learned about bar graphs and how they can use them.

• “¿Qué saben sobre las gráficas de barras?” // “What do you know about bar graphs?”
• 1 minute: quiet think time

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

• “Den un ejemplo de cómo podríamos usar una gráfica de barras” // "What is an example of how we might use a bar graph?" (You can use it to show data that you collected after asking a question or counting things. You could show favorite ice cream flavors or how many of each kind of animal we saw at the zoo.)
• “¿De qué otras maneras pueden representar datos?” // "What are other ways you can represent data?" (picture graphs, lists, tallies, tables)

The purpose of this activity is for students to create a survey, collect and organize their data, and represent their data as a picture or bar graph.

To add movement to this activity, consider a gallery walk for students to see and compare the different representations of their data.

• Groups of 2.
• “Estos son algunos temas que exploramos en lecciones anteriores” // “These are some topics we explored in previous lessons.”
• Display list of topics:
  • How we get to school
  • Favorite sport
  • Favorite season
  • Field trip choice
  • Recess activity
  • Favorite pet
  • Food for a party
  • Fruits we love
  • Veggies we love
• “En parejas, piensen y discutan ideas sobre cosas que quieren saber acerca de sus compañeros de clase” // “With your partner, brainstorm other ideas for things you want to learn about your classmates.”
• 2 minutes: partner discussion.
• Invite a few students to share and record responses.
• “Revisen ambas listas de posibles temas para encuestar a sus compañeros. Con su pareja, escojan un tema y escriban una pregunta de encuesta. Elijan 3 o 4 respuestas posibles para su pregunta” // “Look through both lists of possible topics for surveying our classmates. With your partner, pick one topic and write a survey question. Decide on 3 or 4 possible responses for your survey question.”
• “Por turnos, hagan su pregunta a su pareja y anoten ambas respuestas en su cuaderno de trabajo” // “Take turns asking your survey question to your partner and record both of your responses in your workbook.”  

• “Ahora van a hacer su pregunta de encuesta a otros estudiantes de nuestra clase y a anotar los datos que recolecten” // "Now you will ask other students in our class your survey question and record the data you collect."
• 5 minutes: partner work time
• Monitor to ensure students have collected sufficient data.
• While students survey, give each student the graph template and access to colored pencils.
• “Usen sus datos para crear una gráfica de dibujos o de barras” // “Use your data to create a picture or bar graph. “
• 10 minutes: partner work time.
• Monitor for students who create:
  • a picture graph that use pictures that represent each category (for example, drawing each kind of animal for a survey about pets)
  • a picture graph that uses the same abstract picture for each category (for example, drawing a circle to represent each pet in a survey about pets)
  • a bar graph with a clear title, scale, and category labels

• Invite previously selected students to share their graphs.
• “¿En qué se parecen estas gráficas? ¿En qué son diferentes?” // “How are these graphs the same? How are they different?” (The bar graph has numbers on it, but the picture graphs don’t. Some have 3 and some have 4 different responses. Some are up and down and some are side-to-side.)
• “¿Qué decisiones tuvieron que tomar estos matemáticos en cuanto a sus gráficas?” // “What choices did these mathematicians make with their graphs?” (They had to decide what kind of graph to make, a title, which direction to show the bars in how to represent their data so it is clear with a title, labels, or pictures.)

The purpose of this activity is for students to create their own relevant mathematical questions and use their understanding of addition and subtraction to answer questions about their own and their peers' survey data.

• Combine pairs into groups of 4

• “Intercambien las gráficas. Usen las frases genéricas o hagan sus propias preguntas acerca de las gráficas del otro grupo” // “Switch graphs. Use the sentence stems or create your own questions about the other group’s graphs.”
• 1–2 minutes: independent work time
• 4 minutes: partner work time.
• “Por turnos, hagan las preguntas que se inventaron y usen su propia gráfica para responder” // “Take turns to ask each other the questions you came up with and use your own graph to answer.”
• “Si es posible, escriban una ecuación para mostrar cómo pensaron” // “When possible, write down an equation to show your reasoning.”
• 5 minutes: group discussion.
• Monitor for students who write equations to show the categories they combine or compare when answering their peers' questions.

If students rely on counting to find solutions rather than adding or subtracting, consider asking “¿Qué ecuación puedes escribir para representar las categorías de la pregunta?” // "What equation could you write to represent the categories in the question?"

• Invite previously selected students to share.
• “¿En qué parte de esta gráfica vemos las ecuaciones? ¿Qué significa la ecuación?” // “Where do we see the equations in their graph? What does the equation mean?”
• “¿Cuál es la diferencia entre responder las preguntas usando una gráfica de barras y responderlas usando una gráfica de dibujos?” // “What’s the difference between answering the questions from a bar graph and answering them from a picture graph?”

The purpose of this activity is for students to analyze what they have learned from the data and representations in the previous activities and to share their findings. In this activity, students select two things they learned and illustrate them using a tape diagram.  

Monitor for tape diagrams that can be displayed during the lesson synthesis and compared to the bar graph selected in a previous activity. While the graph and diagram do not have to be from the same pair, it would be helpful for students to see data from the same survey displayed with different representations.

To add movement to this activity, consider a gallery walk. Students can make their diagrams on poster paper. As students walk around the room, they select a few diagrams and determine what information they learn about their class based on the diagram and equation.

• Groups of 2
• “Con su pareja van a dibujar un diagrama. Su diagrama debe comparar dos cosas que hayan aprendido de su encuesta” // “You and your partner are going to draw a diagram. Your diagram should compare two facts you learned from your survey.”
• “Con su pareja decidan cuáles 2 cosas quieren compartir con la clase y cómo las van a comparar” // “Decide with your partner which 2 facts you want to share with the class and how you will compare the two facts.”
• 1 minute: partner discussion.

• 5 minutes: independent work time
• Students check in with their partners to be sure their representations make sense and are accurate.
• 3 minutes: partner discussion
• Monitor for a few examples of accurate tape diagrams and equations.

• Display selected student work.
• “¿Qué información sobre nuestros compañeros nos da este diagrama o ecuación?” // “What information does this diagram or equation tell us about our classmates?”
• “¿En qué parte del diagrama ven esta ecuación?” // “Where do you see this equation in the diagram?”