Lesson 10

This warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved. While students may notice and wonder about many things, highlight observations or questions about the relative size of the measurements in different units.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses. 

• “¿Es posible comparar estas distancias?” // “Can these distances be compared?”

In this activity, students apply their knowledge of centimeters, meters, and kilometers, perform unit conversions, and reason multiplicatively to compare and order distances.

Students have the opportunity to decide which unit to use for making comparisons (that is, whether to convert all distances to meters, to centimeters, or to kilometers). They may find it most practical to use meters because two of the distances are already in meters, and because they know how the other two units are related to meters. 

Students reason abstractly and quantitatively as they think about which unit to use to make comparisons (MP2) and use place value understanding to make the conversions (MP7).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing

• Groups of 2
• “Han aprendido sobre metros, centímetros y kilómetros. ¿Cuál de estas unidades es la más grande?” // “You’ve learned about meters, centimeters, and kilometers. Which of these units is the largest?” (kilometer) “¿Cuál es la más pequeña?” // “Which is the smallest?” (centimeter)
• “¿Cómo se relacionan las tres unidades?” // “How are the three units related?” (One meter is 100 times as long as 1 centimeter. One kilometer is 1,000 times as long as 1 meter.)

• 5 minutes: partner work time on the first problem
• 5 minutes: independent work time on the last problem
• Monitor for:
  • the ways students reason about the relative size of the four distances
  • the unit students choose to use for comparison
  • the ways students reason about “80 times as far”

• Invite students who used different units for comparison to share their responses and reasoning about the first problem. Record or display their reasoning for all to see.
• If no students chose to use centimeters or kilometers as the unit of reference, ask them why they chose meters.
• To discuss the last problem, assign one part (a or b) to each partner.

MLR1 Stronger and Clearer Each Time

• “Respondan a la pregunta que les asignaron y compartan su respuesta con su compañero. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your response to your assigned part of the last problem with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
• 2–3 minutes: structured partner discussion 
• Repeat with 1–2 different partners.
• “Ajusten su respuesta inicial a la pregunta que les asignaron basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial response to your assigned part based on the feedback you got from your partners.”
• 2 minutes: independent work time
• Consider highlighting different ways students reasoned about “80 times as far” in the last problem, highlighting different ways to do so. (A couple of examples are shown in the Student Responses.)

This activity invites students to apply their knowledge of liters and milliliters and multiplicative reasoning to solve a problem about water bottles in different sizes. Students are prompted to express all the quantities in milliliters, so no decisions are needed in terms of the unit to use, but students do need to reason deductively or logically to solve the problem. As they work to eliminate possibilities, draw conclusions, and explain their thinking to others, students practice constructing logical arguments (MP3).

• Groups of 2–4

• “Tómense unos minutos en silencio para leer las pistas y trabajar en la actividad. Después, discutan con su grupo cómo pensaron” //  “Take a few quiet minutes to read the clues and to work on the activity. Then, discuss your thinking with your group.”
• 5–7 minutes: independent work time
• 5 minutes: group discussion

• Discuss the order in which students completed the missing values. Ask questions such as:
  • “Cuando averiguaron la cantidad que contenían las botellas, ¿por cuál empezaron? ¿Hubo alguna razón por la que empezaron con esa botella?” // “Which was the first bottle whose amount you figured out? Was there a reason you started with that bottle?” (E because \(3\times n =1,\!500\) and \(3\times500=1,\!500\))
  • “¿Cuál botella y cuál cantidad averiguaron después?” // “Which bottle and amount did you figure out next?” (F mL because 350 mL is less than 500 mL and there is only one bottle with less than bottle E)
  • “¿Cómo encontraron la cantidad que contiene la botella más grande? ¿Cómo encontraron el valor de 20 veces un número entre 100 y 999?” // “How did you find the amount that the largest bottle holds? How did you find 20 times a number in the hundreds?” (3,500 is ten times as much as 350 so 20 times as much is \(3,\!500+3,\!500\) or 7,000)