Lesson 1

The purpose of this warm-up is to elicit students’ prior understandings about categorical data representations, which will be useful when students engage with single-unit scale picture and bar graphs in later activities. While students may notice and wonder many things about this graph, it is important to pay attention to the ways in which students make sense of a picture graph, the questions they have about the categorical data, and the contexts that make sense for the categorical data shown.

For all warm-up routines, consider establishing a small, discreet hand signal that students can display to indicate they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or another subtle signal. This is a quick way to see if students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class. Since this is the first warm-up of the year, we allocated 15 minutes, instead of 10, to establish the structure of a routine.

• Groups of 2
• Display the graph.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 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.

• ”¿Qué situaciones podría representar la gráfica?” // “What situations could the graph represent?” (Favorite day of the week. Favorite type of food. Types of animals that people saw in the park.)
• Math Community: Ask students to reflect on both individual and group actions while considering the question “¿Qué ven y qué escuchan cuando hacemos matemáticas juntos como una comunidad matemática?, ¿qué estoy haciendo yo?, ¿qué están haciendo ustedes?” // “What does it look and sound like to do math together as a math community? What am I doing? What are you doing?” (We talked to each other and to the teacher. We had quiet time to think. We shared our ideas. We thought about the math ideas and words we knew. You were writing down our answers. You were waiting until we gave the answers.)
• Record and display their responses under the “Doing Math” header.

The purpose of this activity is to elicit students’ prior understandings about essential parts of a picture graph. The graph in this activity is the same as the one in the warm-up, but includes a title. Students are encouraged to consider what categories could be in the graph. Students contextualize and make sense of the data based on the title, the given values, and their own experiences (MP2). This is an opportunity for students to connect their lived experience to the mathematics, supporting the development of their math identities.

• Groups of 2
• Display the graph.
• “¿Qué es distinto en esta gráfica con relación a la primera gráfica que discutimos?” // “What is different about this graph from the first graph that we discussed?” (It has a title. We know what the graph is about.)
• 30 seconds: quiet think time
• Share responses.
• “El título de la gráfica nos ayuda a entender los datos que se muestran en ella” // “The title of the graph helps us make sense of the data shown in the graph.”
• As needed, remind students that data is information about the things or people in a group.
• “¿Cómo van ustedes y otros estudiantes de nuestra comunidad de la escuela a la casa?” // “How do you and other students in our community get home from school?”
• Share responses.

• “Esta es una gráfica de dibujos que representa cómo los estudiantes van a casa desde la escuela. En una gráfica de dibujos se usan dibujos de objetos o símbolos para mostrar cuántos hay en cada grupo o categoría. Las gráficas de dibujos tienen leyendas que muestran lo que representa cada dibujo” // “This is a picture graph that represents how students get home from school. A picture graph shows how many in each group or category using pictures of the objects or symbols. Picture graphs have keys that tell what each picture represents.”
• “¿Cuáles podrían ser las categorías de esta gráfica de dibujos? Prepárense para explicar su razonamiento” // “What could the categories be in this picture graph? Be prepared to explain your reasoning.”
• 2–3 minutes: partner work time

• Display the graph.
• Invite students to share possible categories for the graph.
• Consider asking: “¿Cuántas categorías hay en esta gráfica? ¿Cómo lo saben?” // “How many categories will there be for this graph? How can you tell?”

The purpose of this activity is to prepare students for work with scaled bar graphs in upcoming lessons. Now that students have reasoned about the parts of a picture graph, they look at how picture graphs and bar graphs are alike and how they are different. Students use the information presented on the axes of the bar graph to read the graph, interpret the categorical data presented in the graphs, and generate questions that can be answered using the graphs.

• Groups of 2
• Display the picture graph and the bar graph.
• “La segunda imagen es una gráfica de barras. En una gráfica de barras se usa la longitud de los rectángulos para mostrar cuántos hay en cada grupo o categoría. ¿En qué se parecen las gráficas? ¿En qué son diferentes?” // “The second image is a bar graph. A bar graph shows how many in each group or category using the length of rectangles. How are the graphs alike? How are they different?”
• 2 minute: partner discussion
• Share and display responses.

• “¿Qué nos pueden enseñar las gráficas sobre cómo los estudiantes van a casa? Escriban dos preguntas que podrían responder con las gráficas” // “What could you learn from the graphs about how students get home? Write two questions that the graphs could answer.”
• 7–10 minutes: partner work time

If students write questions that can't be answered with the graphs, consider asking:

• “¿Cómo se te ocurrió tu pregunta?” // “How did you come up with your question?”
• “¿Cómo podríamos inventar una pregunta que se pueda responder con la gráfica?” // “How could we come up with a question that could be answered with the graph?”

• Display the graphs.
• “Si usamos las gráficas completas, ¿qué podemos aprender sobre cómo los estudiantes regresan a casa desde la escuela?” // “What can we learn about how students get home from school based on the complete graphs?”
• “¿Qué preguntas se pueden hacer basándose en las gráficas sobre cómo los estudiantes regresan a casa desde la escuela?” // “What questions could you ask about how students get home from school based on the graphs?”