# Lesson 7

Metros y centímetros

## Warm-up: Observa y pregúntate: Bicho grande, bicho pequeño (10 minutes)

### Narrative

The purpose of this warm-up is to elicit what students know about length measurement and about units of measurement. While no unit is specified for the ruler in the image, students are likely to bring up centimeters (given the way each 1 unit is partitioned into 10 smaller parts, as seen on centimeter rulers). The work here prepares students to think about the relationship between meters and centimeters later in the lesson.

### 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 compañero 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

• Consider sharing that the large insect is a stick insect. (The longest species ever found measured more than 60 cm.) The small insect is a green potato bug.
• “Si cada unidad de la regla mide 1 centímetro, ¿aproximadamente cuánto mide la chinche de papa?” //  “If each unit in the ruler is 1 centimeter, about how long is the potato bug?” (1 cm) “¿Y el insecto palo?” // “What about the stick insect?” (About 16 cm with the antennae, about 12 cm otherwise.)

## Activity 1: ¿Qué tan largo es un metro? (25 minutes)

### Narrative

The purpose of this activity is for students to develop an intuition of 1 meter as 100 times as long as 1 centimeter. Students build a 1-meter long strip out of centimeter grid paper. They use this tool to identify objects or distances that are about 1 meter long.

MLR8 Discussion Supports. Synthesis: At the appropriate time, give groups 2–3 minutes to plan what they will say when they present to the class. “Practiquen lo que van a decir cuando compartan sus predicciones y sus resultados con toda la clase. Hablen sobre qué es importante decir y decidan quién va a compartir cada parte” // “Practice what you will say when you share your predictions and results with the class. Talk about what is important to say, and decide who will speak and who will share each part.”

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Grid Paper - Standard

### Launch

• Groups of 3–4
• Give each group 2–3 sheets of centimeter grid paper, 2–3 pairs of scissors, and some tape.
• “Cada cuadrado de la cuadrícula de la hoja mide 1 centímetro de largo” // “Each grid on the paper is 1 centimeter long.”
• “En grupo, corten el papel cuadriculado de 1 centímetro en tiras. Después, únanlas para hacer una tira de papel que mida exactamente 1 metro de largo” // “Work with your group to cut the centimeter grid paper into strips and then join them to make a strip of paper that is exactly 1 meter long.”

### Activity

• “Después de que hayan hecho su tira de 1 metro de largo, identifiquen algunos objetos en el salón de clase o algunas distancias que crean que miden aproximadamente 1 metro de largo. Después, usen su herramienta para comprobar sus predicciones” // “After your 1-meter-long strip is made, identify some objects in the classroom or some distances you think are about 1 meter long. Then, use your tool to check your predictions.”
• 15 minutes: group work on the first two problems
• 2–3 minutes: independent work on the last problem

### Student Facing

1. Usa el papel cuadriculado de 1 centímetro para armar una tira que mida 100 centímetros de largo. Vas a necesitar tijeras y cinta.

Si lo haces de manera precisa, tu tira de papel tendrá 1 metro de largo.

2. Haz una lista de 5 cosas del salón de clase que creas que miden aproximadamente 1 metro de largo.

Después, usa tu tira de papel para comprobar qué tan cerca de 1 metro está tu predicción.

3. Decide si cada uno de los siguientes mide más de 1 metro, menos de 1 metro o aproximadamente 1 metro.

1. El insecto palo de la actividad de calentamiento
2. El paso que das al caminar
3. El paso que das al correr
4. La distancia que abarcan tus brazos

Prepárate para explicar cómo lo sabes.

### Student Response

Students may make a counting error and put together a strip that is shorter or longer than 1 meter. Consider asking:

• “¿Cómo organizaste las partes de 1 centímetro? ¿Cómo las contaste?” // “How did you organize and count the centimeter pieces?”
• “¿Cómo puedes asegurarte de que hay 100 partes de 1 centímetro? ¿Agrupar las partes puede ayudar?” // “How can you make sure there are 100 centimeter pieces? Can grouping the pieces help?”

### Activity Synthesis

• Invite groups to share their predictions and the results of their measurement.
• Select students to share their responses to the last problem. If time permits, allow students to measure the arm span or step length of a few students.
• “¿Cuántos cuadrados de la cuadrícula de 1 centímetro unieron para formar 1 metro?” // “How many 1 centimeter grid squares did you put together to make 1 meter?”

## Activity 2: En la escuela y alrededor de ella (10 minutes)

### Narrative

In this activity, students analyze student work converting meters to centimeters to develop the understanding that a meter is “100 times as long” as a centimeter. They correct errors in reasoning centering around place value (MP3).

Representation: Access for Perception. Begin by demonstrating how to measure the height of the classroom door with a meter stick (or a student’s meter strip from the previous activity) to support understanding of the context. Pause after measuring each meter to ask students, “¿Cuántos centímetros medimos?” // “How many centimeters have we measured?” As students begin working independently, invite them to imagine using their meter strip to find each measurement.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

### Launch

• Groups of 2
• Read the opening paragraph as a class. Ask 1–2 students to reframe the context in their own words.

### Activity

• “Tómense 5 minutos en silencio para identificar y corregir los errores de Priya y para encontrar la medida que falta. Después, compartan con su compañero cómo pensaron” // “Take 5 quiet minutes to spot and correct Priya’s errors and find the missing measurement. Then, share your thinking with your partner.”
• 5 minutes: independent work time
• 3–4 minutes: partner discussion
• Monitor for students who place zeros for the measurement in centimeters and those who explicitly reason in terms of 100 times the value in meters.

### Student Facing

Priya tomó algunas medidas, en metros, y las anotó en la tabla. Pero cometió algunos errores al convertirlas a centímetros. También le faltó una medida.

medida en metros medida en centímetros
a. altura de una puerta 2 200
b. altura del pasillo 3 30
c. ancho del pasillo 5 500
d. longitud del gimnasio 18 180
e. longitud del pasillo 27 2,700
f. longitud del patio de recreo 50
1. Encuentra y corrige los errores de conversión de Priya. Prepárate para explicar cómo lo sabes.
2. Completa la longitud del patio de recreo, en centímetros. Escribe una ecuación que represente cómo pensaste.

### Student Response

If students place zeros for the measurement in centimeters, ask them to explain their rationale and check if they do so as a result of observing a pattern (for instance, “I noticed that every time we convert from meters to centimeters, the number in centimeters ends in two zeros”) or because they have internalized the value in centimeters as 100 times as much as that in meters.

### Activity Synthesis

• See lesson synthesis.

## Lesson Synthesis

### Lesson Synthesis

“Hoy examinamos centímetros y metros, y los relacionamos con nuestro trabajo sobre la multiplicación” // “Today we looked at centimeters and meters and related them to our multiplication work.”

“Escriban una oración que describa la relación que hay entre las dos unidades. Traten de ser lo más específicos y lo más precisos que puedan en las palabras que escojan” // “Write one sentence to describe the relationship between the two units. Be as specific and precise as you can in your word choice.”

While students’ statements may emphasize the equivalence of 1 meter and 100 centimeters (“one meter is 100 centimeters”), highlight explanations that articulate the multiplicative relationship of the two units (“1 meter is 100 times as long as 1 centimeter”).

Display the table showing Priya’s measurements. Invite students to share their responses to the last activity.

Reiterate the multiplicative relationship of the values in the two columns, revoicing students’ responses as needed. (For instance, “If 1 meter is 100 times 1 centimeter, then 3 meters must be $$3 \times 100$$ centimeters or 300 centimeters, rather than 30 centimeters.”)