# Lesson 15

Hagamos diagramas de puntos

## Warm-up: Conversación numérica: Resta hasta 50 (10 minutes)

### Narrative

The purpose of this Number Talk is to activate students’ previous experiences with subtracting multiples of ten and subtracting by place. In previous lessons, students found the value of differences within 100 using base-ten blocks, tape diagrams, drawings, or equations. The ability look for ways to make use of the base-ten structure of numbers in expressions to find their values helps students build fluency (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.

• $$47 - 20$$
• $$47 - 24$$
• $$36 - 10$$
• $$36 - 15$$

### Activity Synthesis

• “¿Cómo les ayudó la primera expresión a encontrar el valor de la segunda expresión?” // “How did the first expression help you find the value of the second expression?” (I already knew that $$47 - 20 = 27$$, so I just took away 4 more.)
• “¿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: Midamos y grafiquemos longitudes de lápices (15 minutes)

### Narrative

The purpose of this activity is for students to generate measurement data and represent the data in a line plot. Students measure pencils in centimeters, check the accuracy of their measurements, and use a template to represent their data in a line plot. In the synthesis, students revisit the importance of labels on the line plot and also discuss the importance of keeping the Xs the same size and in rows to help make it easier to read the data (MP6).

Pencils are suggested for this activity because the measurements collected are likely to vary. Pencils could be substituted with other classroom items (for example, pipe cleaners, straws, or the sides of books) that might generate interesting measurement data for classroom discussion.

Action and Expression: Develop Expression and Communication. Give students access to grid paper to keep data organized and neat.
Supports accessibility for: Organization, Visual-Spatial Processing

### Required Materials

Materials to Gather

Materials to Copy

• Line Plot Template

### Required Preparation

• Collect 10–12 pencils of varying lengths for each group of 4.

### Launch

• Groups of 4
• Give each group a set of 10–12 pencils of various lengths.
• Give each student a centimeter ruler.

### Activity

• “Hoy van a recolectar datos de medidas y van a hacer un diagrama de puntos. Su primera tarea es medir la longitud en centímetros de cada uno de los lápices de su grupo. Dos personas deben medir cada lápiz para asegurar que sus medidas sean precisas” // “Today, you are going to collect measurement data and create a line plot. Your first job is to measure the length in centimeters of each of the pencils in your group. Two different people should measure each pencil to make sure your measurements are accurate.”
• 10 minutes: small-group work time
• “Ahora, usen los datos que recolectaron para hacer un diagrama de puntos. Traten de hacer sus Xs del mismo tamaño” // "Now, use the data you collected to create a line plot. Try to make your Xs the same size.”
• 5 minutes: independent work time
• Monitor for students who write a title and labels on their line plot.

### Student Facing

1. Mide los lápices en centímetros. Trabaja con un compañero y revisen las medidas de cada uno. Anoten cada medida en la tabla.
longitud del lápiz (cm)
2. Haz un diagrama de puntos que represente las longitudes de todos los lápices de tu grupo.

### Activity Synthesis

• Share the line plot of a student who wrote a title and labels.
• “¿Sabemos qué datos representa el diagrama de puntos de _______? ¿Cómo lo sabemos?” // “Do we know what data _____’s line plot is representing? How do we know?”
• Share a line plot that uses same-size Xs arranged in rows.
• “¿Qué observan acerca de las Xs en el diagrama de puntos de _______?” // “What do you notice about the Xs in _____’s line plot?”
• “¿Por qué es importante mantener las Xs del mismo tamaño y en filas?” // “Why is it important to keep the Xs the same size and in rows?” (It can make it look like some measurements have more because the tower looks taller.)
• As needed, draw or display an example of a line plot where the Xs are not in rows (for example, draw different-size Xs and/or draw with a different amount of space above and below each X).

## Activity 2: Grafiquemos longitudes de lápices (20 minutes)

### Narrative

The purpose of this activity is for students to represent measurement data in a line plot with a scale that does not start at 0. In the launch, students compare line plots that show the same data, but have line plots that start and end with different numbers. They learn that line plots do not have to start with 0, but that the numbers still represent lengths from 0, just like their work with torn tape measures in previous lessons.

When students represent measurement data in their own line plot, they use a template that does not have enough tick marks for students to start at 0 and represent each length in the data table. This encourages students to consider ways to label their line plot without starting at 0. Students may choose to use the least or greatest lengths to decide how to start or end their number line, but they do not need to. The synthesis discussion will focus on strategies they used to determine how to label, including how they used what they know about a ruler.

This activity uses MLR8 Discussion Supports. Advances: Speaking

### Launch

• Groups of 2
• Display the image (2 line plots).
• “¿En qué se parecen estos diagramas de puntos? ¿En qué son diferentes?” // “What is the same about these line plots? What is different?”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Monitor for a student who notices that the line plot for Group B doesn’t start at 0, but there are the same number of Xs.
• Share responses.
• “Cuando hacemos un diagrama de puntos, podemos escoger el número con el que empezamos, basándonos en los datos que tenemos. Una vez que escogemos un número para empezar, tenemos que asegurarnos de no saltarnos ningún número, aunque no haya datos ahí” // “When we make a line plot, we can choose the number to start with, based on the data we have. Once we pick a starting number, we need to make sure we don’t skip any numbers, even if there’s no data there.”

### Activity

• “Van a hacer un diagrama de puntos que represente algunos datos que hay en una tabla. Piensen cómo quieren escribir los números debajo de las marcas. Asegúrense de marcar las partes de su diagrama y traten de hacer todas las Xs del mismo tamaño” // “You are going to create a line plot to represent some data given in a table. Think about how you want to label the marks with numbers. Be sure to include labels, and try to make your Xs the same size.”
• 10 minutes: independent work time

MLR8 Discussion Supports

• “Comparen su diagrama de puntos con el de su pareja” // “Compare your line plot with your partner.”
• Display and review the following sentence frames to support partner discussion:
• “Los diagramas de puntos de ______ y de ______ se parecen porque. . .” // “_____ and _____ line plots are the same/alike because. . . .”
• “Los diagramas de puntos de ______ y de ______ son diferentes porque. . .” // “______ and _____ line plots are different because. . . .”
• 2 minutes: partner discussion
• Monitor for students who used two different start and end numbers.

### Student Facing

Usa estos datos para hacer una gráfica de puntos.
Grupo C longitud del lápiz (centímetros)
Andre 12
Clare 10
Diego 10
Elena 10
Han 13
Kiran 14
Noah 16
Priya 14
Tyler 13

### Student Response

If students label their line plot using only the measurements in the table (for example, they only label 10, 12, 13, 14, 16 without labeling the numbers in between), ask students to look at the line plots from the launch. Consider asking:

• “¿En qué se parece un diagrama de puntos a una regla?” // “How is a line plot like a ruler?”
• “¿Cómo decidiste cómo marcar los números en tu diagrama de puntos? ¿Cómo podrías ajustar tu diagrama de puntos para que represente las medidas como una regla?” // “How did you decide how to label the numbers on your line plot? How could you revise your line plot so that it represents lengths like a ruler?”

### Activity Synthesis

• Show two line plots that use different start and end numbers.
• “¿Como decidieron con qué número empezar?” // “How did you decide which number to start with?”
• “¿Cómo usaron lo que ya sabían de una regla para marcar su diagrama de puntos y ubicar cada x?” // “How did you use what you know about rulers to label your line plot and place each x?”
• “¿En qué se parecen estos diagramas de puntos a una cinta métrica rota?” // “How are these line plots like a torn tape measure?” (They are missing 0 and some other numbers, but they still show numbers in order. There's still the same length between each number.)

## Lesson Synthesis

### Lesson Synthesis

Display a completed student line plot from the second activity that starts with a number other than 0 or display:

“¿Qué aprendieron sobre las longitudes de los lápices a partir del diagrama de puntos?” // “What did you learn about the lengths of the pencils based on the line plot?”

Share and record responses.

“Diego dijo que la mayoría de los lápices medían 10 cm de largo. Kiran dijo que el lápiz más largo medía 16 cm. ¿Los dos tienen razón?” // “Diego said that the most pencils were 10 cm long. Kiran said the longest pencil was 16 cm. Are they both correct?”