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.

• Invite students who used different units for comparison to share their responses and their 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

• “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.
• “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).

• Discuss the order in which students completed the unknown values. Ask questions such as::
  • “Which was the first bottle whose amount you figured out? Was there a reason you started with that bottle?” (E, because and )
  • “Which bottle and amount did you figure out next?” (F is 350 mL because 350 mL is less than 500 mL and Bottle F is the only bottle with less than Bottle E)
  • “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 , or 7,000)