# Lesson 14

¿Qué es un diagrama de puntos?

## Warm-up: Observa y pregúntate: Gráficas “a la mano” (10 minutes)

### Narrative

The purpose of this warm-up is to have students consider a new type of data representation, the line plot. While students may notice and wonder many things about the two data representations, describing the differences between the data represented in a bar graph (categorical) and the data represented in a line plot (numerical) should be the focus. This warm-up will provide a foundation for discussions about the features of a line plot and an understanding of how data is represented in this type of graph.

### Launch

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

### Activity

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

### Student Facing

¿Qué observas? ¿Qué te preguntas?

### Activity Synthesis

• “¿De qué se tratan estas dos gráficas? ¿Cómo lo saben?” // “What are these two graphs about? How do you know?” (One graph is about the size of gloves. The other graph is about hand spans. I can tell from the title and labels on the graphs.)
• As needed, clarify the meaning of hand span.
• “Hoy vamos a aprender una nueva forma de mostrar datos que recolectamos midiendo longitudes de objetos. Van a tener la oportunidad de medir sus palmos y hacer una presentación con los datos de la clase” // “Today we are going to learn a new way to display data that is collected by measuring the lengths of objects. You are going to get a chance to measure your own hand spans and create a class data display.”

## Activity 1: Midamos nuestros palmos (20 minutes)

### Narrative

The purpose of this activity is for students to generate numerical data by measuring their hand spans in inches. Students trace their hands and measure their hand spans (the length from the tip of the pinky to the tip of the thumb). The student-generated data is used to demonstrate creating a line plot, as they work collectively to represent their hand spans measured in inches. Students add a representation of the length of their hand spans by drawing an x on a sticky note and adding it to the line plot. They make sense of the way the line plot represents a number of measurements and the size of each measurement (MP2). The class line plot will be used in the next activity to discuss the purpose and features of a line plot.

Engagement: Provide Access by Recruiting Interest. Provide choice and autonomy. Provide access to colored pencils, markers, colored paper, etc. for students.
Supports accessibility for: Attention

### Required Materials

Materials to Gather

### Required Preparation

• Create a blank line plot with a scale from 0 to 10 for students to place their measurements on.
• Ensure the tick marks are equally spaced with enough room for students to place their sticky notes.

### Launch

• Groups of 2
• Give students 12-inch rulers.

### Activity

• “Vamos a seguir midiendo en pulgadas. Cada uno de ustedes va a medir su palmo” // “We are going to continue measuring in inches. Each of you will measure your hand span.”
• Display the image of the traced hand.
• “Van a medir su palmo, que es la longitud desde su dedo meñique hasta su dedo pulgar. Primero, tracen su mano y después mídanla, redondeando a la pulgada más cercana” // “You are going to measure your hand span, which is the length from your pinky to your thumb. First, you’ll trace your hand and then measure it to the nearest inch.”
• “Después de medir su palmo, revisen las medidas de su pareja” // “After measuring your own hand span, check your partner’s measurements.”
• 6 minutes: partner work time
• “Ahora, vamos a hacer una representación para mostrar las medidas de los palmos de todos” // “Now, we are going to make a representation to show everyone’s hand span measurements.”
• Give each student a sticky note that is the same size.
• “Ahora tenemos que representar los datos que hemos recolectado. Dibujen una X grande en su nota adhesiva” // “Now we need to represent the data we have collected. Draw a big x on your sticky note.”
• As needed, demonstrate drawing an x on a sticky note.
• Display the blank line plot.
• “Si queremos que esta representación le muestre a otros la longitud de todas nuestras medidas, ¿en dónde creen que debe ir la medida de sus palmos?” // ”If we want this display to show others the lengths of all our measurements, where do you think the length of your hand span should go?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Invite students to come up to add their sticky notes to the chart above the corresponding measurement.
• Consider asking students to explain how they place their sticky notes.

### Student Facing

1. Traza tu mano (separa y estira tus dedos).
2. Dibuja una línea desde tu dedo pulgar hasta tu dedo meñique. Esta línea representa tu palmo. Mide la longitud de tu palmo en pulgadas.

### Activity Synthesis

• “Acabamos de hacer un diagrama de puntos. Un diagrama de puntos es una forma de mostrar cuántas hay de cada medida, usando una X para cada medición. La recta y los números sobre la recta representan las unidades que usaron para medir. La recta debe verse como los números de la herramienta que usan para medir” // “We just made a line plot. A line plot is a way to show how many of each measurement using an x for each measurement. The line and the numbers on it represent the units you used to measure. The line should look like the numbers on the tool you use to measure.”
• “¿Qué representa cada x en el diagrama de puntos?” // “What does each x on the line plot represent?” (Each x represents a measurement of a student hand span.)
• “¿Qué representa el número total de Xs?” // “What does the total number of Xs represent?” (Everybody's measurement. Its the same number as the number of people in our class today.)
• As needed, “El número total de Xs representa el número total de mediciones. No es necesario que cada una de ellas sea hecha por personas diferentes” // “The total number of Xs represents the total number of measurements. They don't have to each be done by different people.”
• “¿Cuántas medidas recolectamos para nuestro diagrama de puntos? Expliquen cómo ven sus datos” // “How many measurements did we collect for our line plot? Explain how you see the data.”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

## Activity 2: Interpretemos nuestros datos numéricos (15 minutes)

### Narrative

The purpose of this activity is for students to interpret data represented in a line plot. They engage in a discussion about what they notice and how a line plot can be used to interpret data. After highlighting the features of a line plot, students answer questions about the lengths of students’ hand spans. In the synthesis, the importance of making Xs the same size in order to accurately reflect our data is stressed (MP6), as students will create their own line plots in later lessons.

MLR8 Discussion Supports. Synthesis: Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.

### Launch

• Display the class line plot.
• “Acabamos de representar los datos que recolectamos, pero si alguien más los mira, no va a saber de qué se trata este diagrama de puntos” // “We just represented the data we collected, but if someone else looks at it, it is not clear what this line plot is about.”
• “Sabemos que las gráficas necesitan un título. ¿Cuál puede ser un buen titulo para estos datos?” // “We know graphs need a title. What could be a good title for this data?” (Class hand spans)
• 1 minute: quiet think time
• Share responses and record a title.
• “Cuándo hicimos gráficas de dibujos y gráficas de barras, marcamos las categorías para que otros supieran lo que representaba cada grupo de dibujos o cada barra” // “When we made picture graphs and bar graphs we labeled the categories so others would know what each group of pictures or each bar represented.”
• “¿Qué representan los números de nuestro diagrama de puntos? ¿Qué les recuerda la forma en la que los números están organizados?” // “What do the numbers on our line plot represent? What does the way the numbers are arranged remind you of?” (The numbers represent lengths in inches. It reminds of a ruler. It has tick marks and each tick mark is the same length apart.)
• “La línea de la gráfica de puntos representa la unidad que usaron para medir. Ella muestra los números en orden y con la misma longitud entre números, como en una regla” // “The line on a line plot represents the unit you use to measure. It shows numbers in order and the same length apart, just like on a ruler.”
• “¿Qué unidad de medida representan los números de nuestro diagrama de puntos? ¿Cómo podemos marcar esto?” // “What length unit do the numbers on our line plot represent? How could we label this?” (The lengths of our hand spans in inches. “measurement in inches”)
• 1 minute: quiet think time
• Share responses and record a label.
• “La longitud de la línea entre los dos números no tiene que coincidir con la unidad que usaron, por eso es importante marcar la línea del diagrama de puntos con la unidad” // “The length of the line between two numbers do not have to match the unit you used, so it's important to label the line on the line plot with the unit.”

### Activity

• Hemos usado gráficas para responder preguntas. Ahora, ustedes van a usar este diagrama de puntos para responder preguntas basadas en estos datos, que representan los palmos de nuestra clase. Piensen en lo que representan las Xs mientras responden cada pregunta. Asegúrense de anotar la unidad en sus respuestas” // “We have used graphs to answer questions. Now, you will use this line plot to answer questions based on our class data representing hand spans. Think about what the Xs represent as you answer each question. Make sure you record the unit in your answers.”
• 3–4 minutes: independent work time

### Student Facing

1. ¿Cuál fue el palmo más largo?
2. ¿Cuál fue el palmo más corto?
3. Escribe otra afirmación sobre los palmos de nuestra clase basándote en el diagrama de puntos.

### Student Response

If students count the number of Xs to determine the longest hand span, consider asking:

• “¿En qué parte del diagrama de puntos ves las longitudes de los palmos?” // “Where do you see the lengths of hand spans in the line plot?”
• “¿Qué nos dice el número de Xs que hay encima de un número?” // “What does the number of Xs above a number tell us?”

### Activity Synthesis

• Invite students to share the longest and shortest hand span and how they used the line plot.
• Invite 34 students to share the statements they wrote about the data.
• “¿Cual longitud de palmo fue la más común?” // “Which hand span length was most common?” (The measurement that has the most Xs represents the length that was most common in our class. This is different from having the most votes. _____ inches was the most common measurement.)
• “¿Qué medida de longitud de palmo no tuvo ninguna persona de nuestra clase?” // “What is a measurement that no one in our class had for their hand span?” (Any number with no Xs.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos una nueva forma de mostrar datos: un diagrama de puntos” // “Today we learned a new way to display data—a line plot.”

Display the images from the warm up.

“¿En qué se parecen y en qué son diferentes las gráficas de barras y los diagramas de puntos?” // “What is the same and different about the bar graphs and line plots?”

“¿Qué nos dicen los números de cada gráfica?” // “What do the numbers tell us in each graph?”

Sample Responses:

Same:

• Both are graphs and have numbers.
• Both give us information (data).
• The numbers go by ones.
• The bars or the Xs go up in the graphs.

Different:

• One graph is about glove sizes and the other is about hand span.
• One has bars and the other has Xs.
• The bar graph has 3 bars.
• There are Xs in five different numbers on the number line.
• In the bar graph, numbers are on the side. In the line plot, the numbers are on the bottom.

The numbers in the Glove Size graph tell us how many people have each of the glove sizes.

The numbers in the hand span line plot tell us the length in inches of people’s hand spans.