# Lesson 8

Metros y kilómetros

## Warm-up: Conversación numérica: Por cientos y por miles (10 minutes)

### Narrative

This Number Talk encourages students to use what they know about multiples of 100, the relationship between hundreds and thousands, and properties of operations to mentally solve problems. The reasoning students do here will be helpful later in the lesson when students explore the relationship between kilometers and meters and convert measurements from the former to the latter.

### 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.

• $$3 \times 100$$

• $$40 \times 100$$

• $$43 \times 100$$

• $$43 \times 1,\!000$$

### Activity Synthesis

• “Sabemos el valor de $$43 \times 100$$. ¿Cómo nos ayuda eso a encontrar el valor de $$43 \times 1,\!000$$?” // “How does knowing $$43 \times 100$$ help you find $$43 \times 1,\!000$$?” (1,000 is 10 times 100, so if we know $$43 \times 100$$, we can multiply that by 10 to find $$43 \times 1,\!000$$.)

## Activity 1: ¿Qué tan largo es un kilómetro? (20 minutes)

### Narrative

The purpose of this activity is to build students’ intuition for 1 kilometer. Previously, students used centimeter grid paper and counted 100 units to build a length of 1 meter. Since building a kilometer is impractical, here students relate 1 kilometer to the length of other objects that may be more familiar. For instance, if an Olympic-size pool is 50 meters long, the length of 2 pools is 100 meters and the length of 20 pools is 1,000 meters or 1 kilometer.

The blackline master shows copies of a few objects: a soccer field, the Statue of Liberty, an Olympic-size pool, or a basketball court. Students work with their group to cut out these images and use the copies of each object to reason about the length of 1 kilometer.

Here are the images on the blackline master for reference:

### Required Materials

Materials to Gather

Materials to Copy

• How Long is One Kilometer?, Spanish

### Launch

• Groups of 4
• “¿Qué tan largo piensan que es 10 metros?” // “How long do you think 10 meters is?”
• Consider asking students to use the meter strips to illustrate 10 meters.
• “¿Qué tan largo es 100 metros? ¿Cuántas tiras de 1 metro de largo necesitamos para completar 100 metros?” // “How long is 100 meters? How many meter-long strips do we need to make 100 meters?” (100 of the meter-long strips, or 10 of the 10-meter-long strips)

### Activity

• “Ahora vamos a trabajar con kilómetros. Lean el primer problema y resuélvanlo individualmente” // “Now we will work with kilometers. Read the first problem and solve it on your own.”
• 2 minutes: independent work time
• Invite students to share their responses and reasoning.
• Highlight that if we take 10 of the 100-meter sections of the track and lay them end to end in a straight line, the total length would represent 1,000 meters or 1 kilometer.
• Give each group a pair of scissors and a copy of the blackline master.
• “Van a usar la longitud o la altura de algunos objetos para representar 1 kilómetro: un campo de fútbol, la Estatua de la Libertad, una piscina olímpica y una cancha de baloncesto” // “You will now use the length or height of some other objects to represent 1 kilometer: a soccer field, the Statue of Liberty, an Olympic-size pool, and a basketball court.”
• “Con su grupo, completen el resto de la actividad” // “Work with your group to complete the rest of the activity.”
• “Cada integrante del grupo debe escoger un objeto diferente y debe pensar en cuántos de ellos se necesitan para representar exactamente o aproximadamente 1 kilómetro” // “Each group member should choose a different object and think about how many of them are needed to represent exactly or approximately 1 kilometer.”
• “Si no tienen suficientes copias para llegar a 1 kilómetro, piensen en cuántas más necesitarían para representarlo” // “If you don’t have enough copies to reach 1 kilometer, think about how many more you’ll need to represent it.”
• 10–12 minutes: group work time

### Student Facing

Hay 1,000 metros en 1 kilómetro.

1. La sección sombreada más oscura de la pista corresponde a la longitud de una carrera de 100 metros. ¿Cuántas carreras de 100 metros se tendrían que correr para recorrer 1 kilómetro?

2. Tu profesor te dará imágenes de algo con una longitud o una altura medida en metros.

¿Aproximadamente cuántos de los objetos que te dieron se necesitan para completar 1 kilómetro? Explica o muestra cómo lo sabes.

3. Con tu grupo, escribe un número en cada espacio en blanco para que la afirmación sea verdadera.

1. Un kilómetro es la longitud de (aproximadamente, exactamente) __________ campos de fútbol.

2. Un kilómetro es la longitud de (aproximadamente, exactamente) __________ Estatuas de la Libertad.

3. Un kilómetro es la longitud de (aproximadamente, exactamente) __________ piscinas olímpicas.

4. Un kilómetro es la longitud de (aproximadamente, exactamente) __________ canchas de baloncesto.

4. Estima hasta dónde llegarías si recorrieras 1 kilómetro desde la puerta principal de tu escuela.

### Activity Synthesis

• Select students to share their work on how the four objects compare to 1 kilometer.
• For each response, ask: “¿Cómo supiste cuántos de ese objeto se necesitarían para completar una longitud de 1 kilómetro?” // “How did you know how many of that object it would take to make a length of 1 kilometer?” (Sample responses for the soccer field:
• I added 110 repeatedly until it reached 1,000.
• I know that 5 soccer fields make 550, and thought about how many of that length would make 1,000.
• I tried multiplying 110 feet by different numbers to reach 1,000.
• I thought about how many 110s would go into 1,000.)
• Invite students to share their responses to the last problem.
• Consider giving or showing students a map showing one or more points that are 100 meters from school and asking them to identify a place that is 1 kilometer away from school.
• Emphasize that 1 kilometer is 1,000 times as long as 1 meter. If we use 1 meter as a unit of measurement, we’ll need 1,000 of it to make 1 kilometer. Explain that “kilo” means a thousand.

## Activity 2: Metros y kilómetros (15 minutes)

### Narrative

The purpose of this activity is for students to convert measurements from kilometers into meters and reason the other way around. When the given measurement is a whole number of kilometers, students are likely to multiply the whole number by 1,000 to find its equivalent in meters. For $$\frac{1}{2}$$ kilometer, they are likely to reason that half of 1,000 is 500, or that 1,000 divided by 2 is 500. Students are not expected to reason multiplicatively or to know that $$\frac{1}{2} \times 1,\!000$$ is 500. The lesson synthesis focuses on discussing Andre's reasoning from the task.

MLR7 Compare and Connect. Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “¿Qué tenían en común las estrategias?” // “What did the strategies have in common?”, “¿En qué eran diferentes?” // “How were they different?”, and “¿Por qué al usar distintas estrategias obtuvimos el mismo resultado?” // “Why did the different approaches lead to the same outcome?”
Action and Expression: Internalize Executive Functions. Invite students to choose a starting place that feels most comfortable to them, then to verbalize their strategy before they begin. Students can speak quietly to themselves, or share with you or a partner.
Supports accessibility for: Conceptual Processing, Language, Organization

### Launch

• Groups of 2
• Display the table for all to see.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 30 seconds: quiet think time
• 30 seconds: partner discussion
• Students may have noticed and wondered about the “km” and “m” in the table. Clarify that these are abbreviations for kilometers and meters.

### Activity

• 6–7 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for the different ways students reason about 27 kilometers. For instance, they may:
• count by 1,000 27 times
• reason that 10 groups of 1,000 make 10,000, 20 groups make 20,000, and 7 more groups make 7,000
• use the previous values in the table: reasoning that $$27 = 12 + 10 + 5$$ and adding the corresponding values in meters ($$12,\!000 + 10,\!000 + 5,\!000$$)
• multiply 27 by 1,000

### Student Facing

1. Completa la tabla con las longitudes que faltan, en metros o kilómetros.
kilómetros (km) metros (m)
$$\frac{1}{2}$$ $$\phantom{000000000000}$$
1 1,000
5
6,000
$$8\frac{1}{2}$$
10
12,000
27
2. Andre dice que 100 metros es más largo que 10 kilómetros. ¿Estás de acuerdo o en desacuerdo? Explica o muestra tu razonamiento.
3. ¿Cuál es mayor? Prepárate para explicar cómo lo sabes.

1. 2,000 metros o 3 kilómetros

2. 500 metros o 1 kilómetro

3. 14 kilómetros o 14,000 metros

4. 8 kilómetros u 80,000 metros

### Student Response

Students may multiply the number of kilometers by 1,000 without attending to the units of meters an kilometers, that is they may just conduct the multiplication without making a connection. Consider asking, “¿Cuántos metros forman 1 kilómetro?” // “How many meters make 1 kilometer?” and “¿Cómo podemos usar esto como ayuda para pensar en el número de metros que forman $$\frac{1}{2}$$ kilómetro?” // “How can we use this to help us think about the number of meters that make $$\frac{1}{2}$$ kilometer?”

### Activity Synthesis

• Display the table.
• Invite selected students to share their reasoning on how they converted each whole-number measurement. Start with students who reasoned by counting and end with those who reason multiplicatively.
• Discuss how students found the number of meters in $$\frac{1}{2}$$ and $$8\frac{1}{2}$$ kilometers. Record their reasoning.

## Lesson Synthesis

### Lesson Synthesis

“Hoy aprendimos sobre la relación que hay entre metros y kilómetros” // “Today we learned about the relationship between meters and kilometers.”

“¿Estuvieron de acuerdo con Andre en que 100 metros es más largo que 10 kilómetros? ¿Cómo supieron si lo que él dijo era cierto o no?” // “Did you agree with Andre that 100 meters is longer than 10 kilometers? How did you know whether what he said was true?” (No, because a kilometer is 1,000 meters, which is already longer than 100 meters)

“¿Por qué Andre habrá creído que esto era cierto?” // “Why might Andre have believed this was true?” (He compared the numbers 100 and 10 and saw that 100 was larger.)

Highlight explanations that made it clear that we cannot simply compare the number measurements without considering the units in which they were measured.