# Lesson 5

Problemas de conversión de varios pasos: Longitud en unidades métricas

## Warm-up: Verdadero o falso: Potencias de 10 (10 minutes)

### Narrative

The purpose of this True or False is for students to demonstrate strategies and understandings they have for multiplying and dividing by powers of 10. They will use these operations when they convert measurements between different metric length units.

### Launch

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategy.
• Repeat with each statement.

### Student Facing

En cada caso, decide si la afirmación es verdadera o falsa. Prepárate para explicar tu razonamiento.

• $$5,\!423 \times 10 = 50,\!423$$
• $$5,\!423 \div 10 = 542.3$$
• $$5,\!423 \div 100 = 54.23$$

### Activity Synthesis

• “¿Cómo decidieron si la ecuación $$5,\!423 \div 100 = 54.23$$ es verdadera?” // “How did you decide if the equation $$5,\!423 \div 100 = 54.23$$ is true?” (It's like dividing by 10 twice. $$5,\!423 \div 10 = 542.3$$ and $$542.3 \div 10 = 54.23$$. Each number has digits 5, 4, 2, 3 in the same order. The values of the digits' places in 54.23 are $$\frac{1}{100}$$ the values of the corresponding digits' places in 5,423.)

## Activity 1: Todo el día caminando (15 minutes)

### Narrative

The purpose of this activity is for students to solve multi-step distance problems using centimeters, meters, and kilometers. This gives students an opportunity to think about which units are most helpful for communicating a distance (MP6). When the distance is short, like the length of a single footstep, centimeters or meters both work well. For a longer distance, like the distance a person walks in a day, it is reasonable to use meters or kilometers, but the number of centimeters is very large and more difficult to visualize.

To add movement or make this activity interactive, consider providing groups of 2 or 4 with a centimeter ruler or meter stick to measure their or a classmate’s step before working on the task. While students could use the measurements of their own steps to complete the table, the arithmetic may be more complex and, as a result, it may be harder to observe patterns.

Engagement: Provide Access by Recruiting Interest. Optimize meaning and value. Invite students to share the places they could walk in the classroom, at home, in the community, and so on, that would be equivalent to the distances presented in the chart.
Supports accessibility for: Conceptual Processing; Visual-Spatial Processing

### Required Materials

Materials to Gather

### Launch

• Groups of 2 or 4
• “Si alguien quisiera medir la longitud de uno de sus pasos, ¿qué unidad creen que debería usar: milímetros, centímetros, metros o kilómetros?” // “If someone wants to measure the length of one of their footsteps, which unit do you think they should use? Millimeters, centimeters, meters, or kilometers?”
• Highlight that millimeters are too small and kilometers are too large. Both centimeters and meters make sense and the first part of this activity will use those two units of measure.
• “Hay 100 centímetros en un metro. ¿Aproximadamente cuántos pasos hay en 1 metro?” // “There are 100 centimeters in a meter. About how many steps are in 1 meter?” (2 or 3)
• “Hay 1,000 metros en un kilómetro. ¿Aproximadamente cuántos pasos hay en 1 kilómetro?” // “There are 1,000 meters in a kilometer. About how many steps are in a kilometer?” (2,000 or 3,000)

### Activity

• 5 minutes: independent work time
• 5 minutes: small-group work time
• Monitor for students who use the following strategies when determining how many kilometers Lin walks during the day:
• multiply 50 centimeters by 8,500 steps to determine the distance in centimeters that Lin walked and divide 425,000 by 100,000
• multiply 0.5 meters by 8,500 steps to determine the distance in meters that Lin walked and then divide 4,250 by 1,000

### Student Facing

Lin tiene un reloj que cuenta el número de pasos que da durante el día. El reloj muestra la distancia que recorre en centímetros, en metros o en kilómetros.

1. Esta es una lista de las actividades que hizo Lin el lunes. Al lado de cada actividad, escribe si tendría sentido mostrar la distancia en cm, m o km.

• caminó hasta el pupitre de su amiga
• caminó hasta la parte de adelante del salón
• caminó desde su salón hasta el bus
• corrió dos vueltas alrededor del patio de recreo
2. La tabla muestra la cantidad de pasos que mostró el reloj de Lin para cada actividad. Si cada uno de sus pasos mide 50 centímetros, ¿cuántos centímetros recorrió Lin en cada actividad?, ¿y cuántos metros?
actividad número de pasos distancia (cm) distancia (m)
caminó hasta el pupitre de su amiga 5
caminó hasta la parte de adelante del salón 12
caminó desde su salón hasta el bus 250
corrió dos vueltas alrededor del patio de recreo 1,000
3. Al final del día, el reloj de Lin mostró 8,500 pasos. ¿En qué unidades tendría sentido que su reloj registrara la distancia: en centímetros, en metros o en kilómetros? ¿Por qué?
4. ¿Cuántos kilómetros caminó Lin ese día?

### Activity Synthesis

• “¿Cómo decidieron cuántos kilómetros caminó Lin durante el día?” // “How did you determine how many kilometers Lin walked during the day?”
• Ask previously selected students to share their solutions.
• Display student work or write these equations for all to see:
• $$8,\!500 \times 50= 425,\!000$$
• $$8,\!500 \times 0.5 = 4,\!250$$
• “¿Cómo está representada la situación en cada ecuación?” // “How does each of these equations represent the situation?” ($$8,\!500 \times 50= 425,\!000$$ represents 8,500 steps that are each 50 centimeters long so that would be a total of 425,000 centimeters.$$8,\!500 \times 0.5 = 4,\!250$$ represents 8,500 steps that are each 0.5 meter long so that would be a total of 4,250 meters.)
• “¿En qué se parecen estas ecuaciones?” // “What is the same about these equations?” (They have the same number of steps. They are both multiplication equations.)
• “¿En qué son diferentes estas ecuaciones?” // “What is different about these equations?” (One multiplies the number of steps by 50 centimeters and one multiplies the number of steps by 0.5 meter. The products are different. 4,250 is 100 times smaller than 425,000 because it represents meters instead of centimeters.)
• Display:
• $$425,\!000 \div 100,\!000= 4.25$$
• $$4,\!250 \div 1,\!000 = 4.25$$
• “¿Cómo está representada la situación en cada ecuación?” // “How does each of these equations represent the situation?” (They both represent the number of kilometers that Lin walked. 425,000 is the distance she walked in centimeters so if you divide it by 100,000, you get the number of kilometers she walked. 4,250 is the distance in meters that she walked so we only have to divide by 1,000 to figure out how many kilometers she walked.)
• Display: 4.25 km, 4,250 m, 425,000 cm
• “¿Cuál de estas creen que comunica mejor cuánta distancia caminó Lin este día?” // “Which of these do you think best communicates how far Lin walked this day?” (4.25 kilometers because I can picture how long a kilometer is.)

## Activity 2: ¿Quién corrió más lejos? (20 minutes)

### Narrative

The purpose of this activity is for students to convert between meters and kilometers to decide which of two measurements is larger. Monitor for students who convert from kilometers to meters, which will give two large whole-number measurements, and for students who convert from meters to kilometers, which will give two decimal numbers. The goal of the activity synthesis is to connect these two different solution strategies.

MLR1 Stronger and Clearer Each Time. Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to who ran farther, Tyler or Clare. Invite listeners to ask questions, to press for details and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.

• Groups of 2

### Activity

• 5 minutes: independent work time
• 5 minutes: partner discussion
• For the third problem, monitor for students who:
• convert from kilometers to meters to find the difference between Clare and Tyler’s runs
• convert from meters to kilometers to find the difference between Clare and Tyler’s runs

### Student Facing

1. Usa la tabla para encontrar la distancia total que Tyler corrió durante la semana. Explica o muestra cómo razonaste.

día distancia (km)
lunes 8.5
martes 6.25
miércoles 10.3
jueves 5.75
viernes 9.25

2. Usa la tabla para encontrar la distancia total que Clare corrió durante la semana. Muestra cómo razonaste.
día distancia (m)
lunes 5,400
martes 7,500
miércoles 8,250
jueves 6,750
viernes 7,250

3. ¿Quién corrió más lejos: Clare o Tyler? ¿Cuánto más lejos? Explica o muestra cómo razonaste.

### Student Response

If a student does not realize that they have to convert the units to compare them, refer to the letters next to the word “distance” in the table headers and ask the student to explain what they mean.

### Activity Synthesis

• Invite students to share strategies for how they added the two sets of numbers (that is, looking for “friendly” pairs of numbers to combine first or adding by place value).
• Invite a student who converted from kilometers to meters to share their solution to the last problem.
• “¿Qué funcionó bien en esta solución?” // “What worked well in this solution?” (All of the numbers are whole numbers.)
• “¿Qué fue difícil?” // “What was difficult?” (The numbers were all big.)
• Invite a student who converted from meters to kilometers to share.
• “¿Qué funcionó bien?” // “What worked well?” (The numbers were a good size to visualize.)
• “¿Qué fue difícil?” // “What was difficult?” (I needed to add and subtract decimals to find out how much farther Tyler ran than Clare.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy resolvimos problemas y convertimos medidas de longitud que estaban en unidades métricas. Resolvimos problemas sobre cuánta distancia caminaron o corrieron algunos estudiantes” // “Today we solved problems and converted length measurements in metric units. We solved problems about how far students walked or ran.”

“¿Cuánta distancia creen que caminan ustedes en un día?” // “How far do you think you walk in a day?” (2 or 3 kilometers because I walk to and from school each day and I think that’s a kilometer and then I run around on the playground a lot during recess. 5 kilometers because I walk to and from school every day and I also usually take my dog out for a walk once or twice a day.)

Consider giving students time to respond in their journals.

Collect some responses and ask students to explain how they know their answers are reasonable.