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, such as the length of a single footstep, centimeters or meters both work well. For a longer distance, such as 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 students with a centimeter ruler or meter stick to measure each other’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.

• “How did you determine how many kilometers Lin walked during the day?”
• Ask previously selected students to share their solutions.
• Display students’ work, or write these equations, for all to see:
• “How does each equation represent the situation?” ( represents 8,500 steps, each of which is 50 centimeters long, so that would be a total of 425,000 centimeters. represents 8,500 steps, each of which is 0.5 meter long, so that would be a total of 4,250 meters.)
• “What is the same about these equations?” (They have the same number of steps. Both are multiplication equations.)
• “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:
• “How does each equation represent the situation?” (Both represent the number of kilometers that Lin walked. 425,000 is the distance she walked in centimeters so if we divide it by 100,000, we 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 Lin walked.)
• Display: 4.25 km, 4,250 m, 425,000 cm
• “Which measurement do you think best communicates how far Lin walked this day?” (4.25 kilometers because I can picture how long a kilometer is.)

The purpose of this activity is for students to convert between meters and kilometers to decide which of two measurements is greater. 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.

• 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.
• “What worked well in this solution?” (All of the numbers are whole numbers.)
• “What was difficult?” (The numbers were all big.)
• Invite a student who converted from meters to kilometers to share.
• “What worked well?” (The numbers were a good size to visualize.)
• “What was difficult?” (I needed to add and subtract decimals to find out how much farther Tyler ran than Clare.)