# Lesson 5

Representemos datos de medidas en diagramas de puntos

## Warm-up: Conversación numérica: Multipliquemos números del 11 al 19 (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying within 100 and to help students develop fluency.

When students use known multiplication facts to multiply larger numbers, 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.

• $$3\times10$$
• $$3\times13$$
• $$6\times13$$
• $$3\times26$$

### Activity Synthesis

• “¿Cómo usaron los hechos de multiplicación que ya conocen para encontrar algunos de los otros productos?” // “How did you use multiplication facts that you already know to find some of the other products?” (I knew that $$3\times10$$ is 30, so $$3\times13$$ would be 3 groups of 10 and 3 groups of 3 which is 39. Once I knew $$3\times13$$, I was able to find $$6\times13$$ by doubling 39 which is 78.)

## Activity 1: Hagamos un recorrido para medir (20 minutes)

### Narrative

The purpose of this activity is for students to generate measurement data using rulers marked with half inches and quarter inches. Students go on a walk in nature, around the school, or on the playground to measure the length of items they chose. If time is limited, this activity could also be done in the classroom.

Students may record and organize their data in the provided tables or on lined paper.

MLR8 Discussion Supports. Synthesis: Revoice student ideas to demonstrate and amplify mathematical language use. For example, revoice the student statement “It lined up with one of the half thingies” as “Se alineó con una de las marcas de mitad de pulgada” // “It lined up with one of the half inch marks,” or “We recorded it in halves” as “Lo anotamos en mitades de pulgada” // “We recorded it in half inches.”

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 4 needs a ruler marked with half inches and quarter inches from a previous lesson.

### Launch

• Groups of 4
• “Hoy vamos a hacer un recorrido por la escuela (o por el patio de recreo, o por el salón) para medir la longitud de algunos objetos” // “Today we are going to take a walk around the school (or the playground, or the classroom) to measure the length of some objects.”
• “Con su grupo, mencionen algunos objetos a los que les podemos medir su longitud durante el recorrido” // “Talk to your group about some objects whose length we could measure on our walk.” (sticks, leaves, pine needles, plants)
• 1 minute: group discussion
• Share responses.
• Make sure each group has a ruler that shows halves and fourths of an inch (from an earlier lesson).
• If not using the table in the workbook, give students blank lined paper for recording measurements.

### Activity

• “Discutan con su grupo qué objetos van a medir durante el recorrido. Deben recolectar por lo menos 10 medidas de longitudes” // “Discuss with your group what to measure on our walk. You’ll need to gather at least 10 length measurements.”
• “Más adelante, cada grupo va a crear un diagrama de puntos con estas medidas y lo va a mostrar en un póster” // “Later, each group will create a line plot with these measurements and display it on a poster.”
• 2 minutes: group work time
• Share responses.
• “Escriban y organicen sus medidas en la tabla (o en un papel con rayas)” // “Record and organize your measurements in the table (or on lined paper).”
• 20 minutes: whole-class walk around the school

### Student Facing

1. ¿Qué objetos vas a medir?
2. Escribe las longitudes de los objetos en la tabla (o en otra hoja de papel).

### Activity Synthesis

• “Ahora que tenemos nuestros datos de las medidas, hagamos un diagrama de puntos” // “Now that we have our measurements data, let’s make a line plot.”

## Activity 2: Hagamos un diagrama de puntos (20 minutes)

### Narrative

In this activity, students create a line plot using the measurement data that they generated earlier and display their group’s line plot for all to see.

Encourage students to plan their line plot using the blank line in the activity statement before creating a poster version for display in a gallery walk. A template for a larger line plot is provided in the blackline master. Students can join the number lines on two copies of the blackline master to create a longer number line.

As students visit others’ data displays, they consider how the line plots are alike and how they are different, as well as why different scales might have been chosen for different objects measured.

Representation: Access for Perception. Synthesis: Use gestures during the explanation of the line plot to emphasize important aspects of the line plot.
Supports accessibility for: Conceptual Processing, Attention

### Required Materials

Materials to Gather

Materials to Copy

• Let's Make a Line Plot

### Launch

• Groups of 4
• “Examinen los datos que recolectaron con su grupo. ¿Qué necesitan saber para hacer un diagrama de puntos que represente los datos?” // “Look at the data your group collected. What do you need to know to make a line plot that represents the data?” (The longest and shortest measurements. Whether the lengths are whole numbers or include halves and fourths of an inch.)
• 1 minute: group discussion
• Share responses.
• Give each group 2 copies of the blackline master, scissors, glue or tape, and tools for creating a visual display.

### Activity

• “Con su grupo, hagan un diagrama de puntos que represente sus datos. Más adelante van a compartir su diagrama de puntos con el resto de la clase” // “Work with your group to create a line plot that represents your data. You will share your line plot with the class later.”
• “Pueden usar la recta numérica que está en blanco, en su página, para planear cómo van a hacer su diagrama de puntos antes de crear el diagrama final que van a presentar” // “You can use the blank number line on your page to plan your line plot before creating a final one to display.”
• “¿Cómo planean hacer la escala del diagrama de puntos para que pueda mostrar todas sus medidas?” // “How do you plan to make the scale for the line plot so that it can show all your measurements?”
• “¿Qué información o qué marcas pueden incluir para ayudar a los demás a entender su diagrama de puntos?” // “What information or labels could be included to help others understand your line plot?”
• Demonstrate how to join and tape (or glue) the 2 copies of the blackline master to make a large line plot.
• “Después de que completen la versión final de su diagrama de puntos, péguenlo con cinta (o con pegamento) en un póster” // “After you complete your final line plot, tape (or glue) your line plot on a poster.”
• 12–15 minutes: group work time

### Student Facing

Hagan un diagrama de puntos que represente los datos de las medidas que recolectaron. Más adelante, van a mostrar y a compartir su diagrama de puntos con la clase.

Pueden usar esta recta numérica que está en blanco para hacer un borrador. Piensen en:

• cómo escribir los números que corresponden debajo de cada marca para que puedan incluir todas las medidas
• incluir detalles que ayuden a los demás a entender los datos que recolectaron

### Activity Synthesis

• Ask students to display their posters.

MLR7 Compare and Connect

• “Cuando vayan a ver los pósteres con su grupo, piensen en qué se parecen y en qué son diferentes los diagramas de puntos. Prepárense para compartir sus observaciones” // “As you visit the posters with your group, think about how the line plots are alike and how they are different. Be prepared to share your observations.”
• 5 minute: gallery walk
• See lesson synthesis.

## Lesson Synthesis

### Lesson Synthesis

Discuss students' observations from the gallery walk.

“¿En qué se parecen los diagramas de puntos?” // “How are the line plots alike?” (They all show lengths in inches and at least 10 x’s. They all show at least one stack of x’s that is taller.)

“¿En qué son diferentes?” // “How are they different?” (They represent lengths of different objects. Some line plots show more or fewer x’s than others. The numbers on the ends of the lines are different. The locations of x’s and how they are spread out are different. On some line plots, each space represents $$\frac{1}{2}$$ inch. On others, it represents $$\frac{1}{4}$$ inch.)

“¿Por qué los diagramas de puntos tenían escalas diferentes?” // “Why did the line plots have different scales?” (Some types of objects are usually longer than others. For example, twigs are usually longer than leaves. Some data include only lengths in half inches. Others include quarters of an inch.)

Consider asking: “¿Qué aprendieron sobre los diagramas de puntos en las últimas lecciones?” // “What did you learn about line plots in the past few lessons?” (They are used to show measurements, including fractions an inch. We can choose the scale of the line plot based on the measurements. We can get some information about the data more easily from a line plot than from a list.)