# Lesson 3

Gráficas de dibujos con escala

## Warm-up: Conversación numérica: Suma (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to add up the total number of students represented in a picture graph. When students use strategies based on place value to add they look for and make use of structure (MP7).

### Launch

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Encuentra mentalmente el valor de cada expresión.

• $$50 + 10$$
• $$50 + 12$$
• $$60 + 13$$
• $$65 + 13$$

### Activity Synthesis

• “¿Cómo les ayudó el valor posicional cuando sumaron estos números?” // “How was place value helpful as you added these numbers?” (I was able to use tens and ones to help me find the sum.)
• “¿Quién puede expresar el razonamiento de _____ de una forma diferente?” // “Who can restate _____’s reasoning in a different way?”
• “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
• “¿Alguien pensó en el problema de otra forma?” // “Did anyone approach the problem in a different way?”
• “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to _____’s strategy?”

## Activity 1: Tantas respuestas (15 minutes)

### Narrative

The purpose of this activity is for students to read a scaled picture graph. A scale of 5 is used to encourage skip-counting because students skip-counted by 5 in grade 2. The questions in the task focus on the structure of a scaled picture graph and strategies for reading them.

### Launch

• Groups of 2
• “¿Cuál es su deporte o actividad favorita afuera de la escuela?” // “What is your favorite sport or activity outside of school?”
• Share responses.
• Display the first image of the single-unit scale picture graph.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (Students may notice: The graph is about students’ favorite sports. There are a lot of smiley faces. Each smiley face represents 1 student. It takes a lot of time to count up the students in each category. Students may wonder: How many student responses are shown in the whole graph? How could we make the graph take up less space?)
• 1 minute: quiet think time
• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Activity

• “Con su pareja, encuentren cuántos estudiantes están representados en la gráfica” // “Work with your partner to find how many students are represented in the graph.”
• 3–5 minutes: partner work time
• Monitor for students who group the smiley faces by 2, 5, or 10 to make them easier to count.
• Have students who grouped the smiley faces share their strategies for how they found the total number of students represented in the graph.
• If no students use this strategy ask, “¿Cómo puede ayudarnos agrupar los dibujos de la gráfica a contar más fácilmente?” // “How could grouping the pictures in the graph make them easier to count?” (We could circle tens so we could count by ten. It would be easier to keep track of your count than by counting by ones.)
• Display the second image of the scaled picture graph.
• “¿Cómo podríamos contar el número total de estudiantes en esta gráfica?” // “How could we count the total number of students in this graph?”
• 2 minutes: partner work time
• Math Community: As students work, monitor for examples of the “Doing Math” actions.

### Student Facing

1. A un grupo de estudiantes le preguntaron: “¿Cuál es tu deporte favorito?”. Sus respuestas se muestran en esta gráfica de dibujos:

¿Cuántos estudiantes están representados en la gráfica?

2. Sus respuestas también se muestran en esta gráfica:

¿Cuál es la diferencia entre contar el número total de estudiantes en esta gráfica y contar el número total de estudiantes en la primera gráfica?

### Student Response

If students count the students in the scaled picture graph and get a total other than 65, consider asking:

• “¿Cómo encontraste el número total de estudiantes representados en la gráfica?” // “How did you find the total number of students represented in the graph?”
• “¿Cómo te ayudaría contar de 5 en 5 a encontrar el número total de estudiantes representados en la gráfica?” // “How could you use counting by 5 to find the total number of students represented in the graph?”

### Activity Synthesis

• “Cuando una gráfica tiene muchos datos, podemos ajustar la escala para que cada dibujo represente más de 1 objeto. Si cada dibujo representa algo que no es 1, decimos que la gráfica es una gráfica de dibujos con escala. La leyenda nos dice que, en esta gráfica, cada carita feliz representa 5 estudiantes” // “In a graph where there’s a lot of data we can adjust the scale so each picture represents more than 1 object. When each picture represents something other than 1, we say that it’s a scaled picture graph. The key tells us that in this graph, each smiley face represents 5 students.”

## Activity 2: Preguntas sobre gráficas de dibujos con escala (20 minutes)

### Narrative

The purpose of this activity is for students to interpret a scaled picture graph and write questions that can be asked based on the data represented in a scaled picture graph.

MLR8 Discussion Supports. Use multimodal examples to show the meaning of a symbol. Use verbal descriptions along with gestures, drawings, or concrete objects to show how each flower on the graph is a symbol that represents five flowers that were seen in the park.
Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were needed to solve the problem. Display the sentence frame, “La próxima vez que lea una gráfica de dibujos con escala, prestaré atención a . . .” // “The next time I read a scaled picture graph I will pay attention to . . . .“
Supports accessibility for: Conceptual Processing

### Launch

• Groups of 2
• Display the graphs for all to see.
• “¿Qué estrategias podrían usar para leer estas gráficas?” // “What are some strategies you could use to read the graphs?” (In the Flowers I Saw on the Way Home graph I could count each category by 5 since each picture represents 5 flowers.)
• 1 minute: quiet think time
• Share and record responses.

### Activity

• “Ahora, vamos a responder preguntas sobre las gráficas de dibujos con escala. También tendrán la oportunidad de escribir sus propias preguntas basándose en cada gráfica” // “Now, we’re going to answer some questions about the scaled picture graphs. You will also have a chance to write your own question that can be asked based on each graph.”
• 8–10 minutes: partner work time
• If there is time, have groups trade books and answer each other’s questions.
• Math Community: As students work, monitor for examples of the “Doing Math” actions.

### Student Facing

1. Andre recolectó datos para saber cuántas flores de cada tipo vio camino a casa. Los datos se muestran en esta gráfica de dibujos:

1. ¿Cuántas flores de cada tipo vio Andre camino a casa?

rosas _____

tulipanes _____

margaritas _____

violetas _____

2. Escribe 2 preguntas que puedas hacer sobre las flores que Andre vio camino a casa.
2. A un grupo de estudiantes le preguntaron: “¿Cuál es tu tipo de libro favorito?”. Sus respuestas se muestran en esta gráfica de dibujos:

1. ¿A cuántos estudiantes les gusta cada tipo de libro? ¿Cómo lo sabes?
2. Observa la gráfica y escribe 2 preguntas que puedas hacer sobre los tipos de libro favoritos.

### Student Response

• “¿Cómo hiciste para responder las preguntas sobre la gráfica?” // “How did you answer the questions about the graph?”
• “¿Qué nos dice la leyenda sobre cada dibujo en la gráfica?” // “What does the key tell us about each picture in the graph?”

### Activity Synthesis

• Have students share responses to the questions they answered and explain their reasoning.
• “¿Cómo usaron la escala para responder las preguntas?” // “How did you use the scale to answer the questions?” (I counted by the number that each picture represented, like by 5 for the flowers and by 2 for the students.)
• Share a variety of student written questions.
• “¿Cómo supieron que su pregunta se podía contestar con la gráfica?” // “How did you know your question could be answered with the graph?” (The data you needed to answer the question was in the graph.)
• If time ask, “¿Qué preguntas no se pueden contestar con esta gráfica?” // “What questions cannot be answered by this graph?” (How many students' favorite type of book is graphic novels?)

## Lesson Synthesis

### Lesson Synthesis

Display the images of the two “Favorite Sports” graphs.

“Hoy aprendimos sobre las gráficas de dibujos con escala. ¿Por qué razones haríamos una gráfica de dibujos con escala?” // “Today we learned about scaled picture graphs. Why would we make a scaled picture graph?” (When there is a lot of data to represent, it is faster to use a scale.)

“¿En qué es diferente leer gráficas de dibujos con escala a leer gráficas que tienen una escala de 1?” // “How is reading scaled picture graphs different from reading graphs that have a scale of 1?” (Each picture doesn’t represent 1 thing so you need to look at the scale. In a scaled picture graph you can count by the scale to find the total in each category instead of counting by 1.)

Math Community

After the cool-down, ask students to individually reflect on the question “¿Cuál acción de 'Hacer matemáticas' sintieron que fue la más importante al trabajar hoy? ¿Por qué?” // “Which ‘Doing Math’ action did you feel was most important in your work today, and why?” Have students write their responses on the bottom of their cool-down paper, on a separate sheet of paper, or in a math journal.

Collect and read their responses after class. These responses will offer insight into how students feel about their own mathematical work and help you make personal connections to the norms they will be creating during days 4–6.