# Lesson 4

Interpretemos datos de medidas que están en diagramas de puntos

## Warm-up: Observa y pregúntate: Una lista y un diagrama de puntos (10 minutes)

### Narrative

The purpose of this warm-up is to remind students that measurement data can be shown on a line plot, preparing them to interpret a line plot that includes fractional measurements in a later activity. While students may notice and wonder many things about the given data, the general structure of the line plot and how it shows the measurement data in the table are the important discussion points.

### Launch

• Groups of 2
• Display the data and line plot.
• “¿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?

• 3
• 5
• 4
• 4
• 5
• 6
• 7
• 5
• 3
• 4
• 4
• 5
• 6
• 6
• 4

### Activity Synthesis

• “¿Qué le cambiaríamos al diagrama de puntos para mostrar una longitud de $$6\frac{1}{2}$$ pulgadas?” // “How would we adjust the line plot to include a length that is $$6\frac{1}{2}$$ inches?” (Add half inch marks to the scale. Partition the inches into two equal parts.)

## Activity 1: Un grupo de plántulas (20 minutes)

### Narrative

The purpose of this activity is for students to analyze a line plot that represents lengths that are measured to the nearest half inch. They make observations and write statements about the data represented in the line plot, and then generate questions that could be answered with the line plot. When students recognize how organizing data helps to read the information and to answer questions, they learn that line plots are a powerful tool to present data (MP5).

### Launch

• Groups of 2
• Display the list and line plot.
• “Tanto la lista como el diagrama de puntos muestran las alturas de unas plántulas. Una plántula es una planta joven. ¿En qué lugares han visto plántulas?” // “The list and the line plot both show the heights of seedlings. A seedling is a young plant. Where have you seen seedlings before?” (At the park. In a garden.)
• “Si miramos la lista, ¿podemos saber cuál es la altura de la plántula más baja?” // “Looking at the list, can we tell the height of the shortest seedling?” (Yes, $$\frac{1}{2}$$ inch). “¿Y la altura de la plántula más alta?” // “What about the tallest seedling?” (Yes, 5 inches)
• “Dibujen un bosquejo de la plántula más baja y de la plántula más alta con sus alturas reales. Usen lo que saben sobre la longitud de una pulgada” // “Draw a quick sketch of the shortest seedling and the tallest seedling at their actual heights. Use what you know about the length of an inch.”
• 1 minute: independent work time
• “Compartan sus bosquejos con su compañero” // “Share your sketches with your partner.”
• “¿Qué más podemos saber sobre las plántulas si miramos la lista?” // “What else can we tell about the seedlings from looking at the list?” (Twenty-two seedlings were measured. There are two seedlings that are 3 inches tall.)
• 1 minute: partner discussion
• Share responses.

### Activity

• “Ahora miren el diagrama de puntos con atención. Piensen en qué información podemos obtener del diagrama de puntos y qué preguntas nos puede ayudar a responder” // “Now, take a close look at the line plot. Think about what information we can gather from the line plot and what questions it can help to answer.”
• “Completen estos problemas con su compañero” // “Work with your partner to complete these problems.”
• 7–10 minutes: partner work time

### Student Facing

alturas de las plántulas (en pulgadas)

• $$\frac{1}{ 2}$$
• 1
• 1
• $$\frac{1}{ 2}$$
• $$1\frac{1}{ 2}$$
• $$2\frac{1}{ 2}$$
• 4
• $$\frac{1}{ 2}$$
• 3
• $$1\frac{1}{ 2}$$
• 5
• $$1\frac{1}{2}$$
• $$1\frac{1}{2}$$
• $$2\frac{1}{2}$$
• 3
• $$\frac{1}{2}$$
• $$2\frac{1}{2}$$
• $$1\frac{1}{2}$$
• 1
• $$1\frac{1}{2}$$
• 4
• 2
1. Escribe 3 afirmaciones sobre las medidas que están representadas en el diagrama de puntos.

2. ¿Qué preguntas se podrían responder más fácilmente con el diagrama de puntos que con la lista? Escribe por lo menos 2 preguntas.

### Activity Synthesis

• Display the list and the line plot.
• “¿En qué son diferentes la información que se muestra en el diagrama de puntos y la que se muestra en la lista?” // “How is the information displayed in the line plot different from that in the list?” (In the line plot, all the measurements that are the same length are together. The measurements go from smallest to largest along the bottom. In the line plot, we don’t keep writing the numbers over and over, we would just use an x for each measurement.)
• “¿Qué preguntas se podrían responder más fácilmente con el diagrama de puntos que con la lista?” // “What were some questions that could be more easily answered with the line plot than the list?” (“¿Cuántas plántulas miden 3 pulgadas de alto?” // “How many seedlings were 3 inches tall?” because we could just count the x’s at 3 instead of searching through the list. “¿Cuál es la plántula más baja?” // “What’s the shortest seedling?” because we can find the x on the left end of the scale. “¿Cuál altura de las plántulas es la más común?” // “Which seedling height was the most common?” because we can see which number has the most x’s.)

## Activity 2: Todo sobre las ramas (15 minutes)

### Narrative

The purpose of this activity is for students to use a line plot to answer questions about a set of length data. The data show measurements to the nearest quarter inch. Students may apply their understanding of fraction equivalence to interpret the data and answer the questions.

Engagement: Provide Access by Recruiting Interest. Leverage choice around perceived challenge. Invite students to select complete 6 out of the 8 line plot questions.
Supports accessibility for: Organization, Attention, Social-emotional skills

### Launch

• Groups of 2
• “Este diagrama de puntos tiene datos sobre las longitudes de algunas ramas. ¿Qué observan? ¿Qué se preguntan?” // “This line plot has data about the lengths of some twigs. What do you notice? What do you wonder?” (Students may notice: The twigs were measured to the nearest quarter inch. The longest twig is $$7\frac{2}{4}$$ inches. Students may wonder: Where were the twigs found? How many twigs are shown on the line plot?)

### Activity

• “Respondan individualmente las preguntas sobre los datos que se muestran en el diagrama de puntos” // “Work independently to answer the questions about the data shown in the line plot.”
• 5 minutes: independent work time
• “Con su compañero, terminen de responder todas las preguntas sobre los datos que se muestran en el diagrama de puntos” // “Work with your partner to finish answering all the questions about the data shown in the line plot.”
• 5–7 minutes: partner work time

### Student Facing

1. ¿Cuántas longitudes de ramas están representadas en el diagrama de puntos?
2. ¿Cuántas de las ramas miden $$6\frac{1}{2}$$ pulgadas de largo?
3. ¿Cuántas de las ramas miden menos de 6 pulgadas de largo?
4. ¿Cuántas de las ramas miden más de 6 pulgadas de largo?
5. ¿Cuál es la longitud de la rama más corta?
6. ¿Cuál es la longitud de la rama más larga?
7. ¿Cuál es la longitud de rama más común?
8. Agrega una “x” al diagrama de puntos para representar una rama que tiene una longitud de entre 3 y 4 pulgadas.

¿Cuál es la longitud de la rama que agregaste al diagrama de puntos?

### Activity Synthesis

• “Discutan con su compañero cómo respondieron las últimas dos preguntas” // “Discuss with your partner how you answered the last two questions.” (Since the inches are partitioned into 4 equal parts, I knew the scale shows quarters of an inch. I used the quarter inch marks to add an x for a twig that is $$3 \frac {1}{4}$$ inches long because that is between 3 and 4 inches.)
• “¿Cómo usaron la equivalencia de fracciones para responder las preguntas?” // “How did you use fraction equivalence to answer the questions?” (When the question asked how many of the twigs were $$6\frac{1}{2}$$ inches long, I used the mark that was at $$6\frac{2}{4}$$, because the lengths are equivalent. When I added a twig to the line plot, it was at the $$3\frac{2}{4}$$ inch mark, but I wrote $$3\frac{1}{2}$$ because the fractions are equivalent.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy hicimos y respondimos preguntas sobre las medidas que se muestran en un diagrama de puntos” // “Today we asked and answered questions about measurements shown in a line plot."

“¿Qué representa cada x en un diagrama de puntos?” // “What does each x in a line plot represent?” (A measurement)

“¿Cómo sabemos qué medida está representada por una x?” // “How do we know what measurement an x represents?” (The line plot has a number line with labels and tick marks. Where an x falls on the number line tells us the measurement.)

“¿Qué más nos puede decir un diagrama de puntos sobre los datos que muestra?” // “What else can the line plot tell us about the data it displays?” (The number of x’s tells us how many measurements are in the data. The x on the far left tells us the smallest measurement. The x on the far right tells us the greatest measurement. We can see which measurements are common based on how many x’s there are at certain locations.)