The purpose of this activity is to compare measurements in inches, feet, and yards. Four different lengths are used and each length is presented in inches, feet, and yards. Students sort these measurements in three different ways. First they sort the measurements in a way that makes sense to them. Then students find equivalent lengths. Finally, they organize lengths that use the same unit in increasing order. The Activity Synthesis highlights why expressing all the measurements, with one unit, is a convenient way to communicate and compare measurements (MP6).

• Invite 2–3 previously selected groups to share a set of equivalent lengths.
• Consider asking: “How did you decide that these cards show the same length?”
• Attend to the language that students use to describe their matches, giving them opportunities to describe how they know the measurements are equal.
• “How did you order the measurements? Why?” (I chose one of the units, feet, and compared all of the measurements in that unit.)
• “Why was it important for all of the measurements to be in the same unit in order to compare?” (That way I can just compare the numbers because they all have the same unit of measure.)

The goal of this activity is to solve multi-step conversion problems, using customary length units. The given information for both problems is in fraction form. Students need to find the perimeter of the different fields and then investigate how many times around each field is a given number of miles. The first problem involves 3 steps:

• Find the perimeter of the rectangular field.
• Find the total distance of 6 laps around the field.
• Convert from yards to feet or feet to yards.

The second problem has only two steps, but the number of laps is unknown and students need to find how many laps make at least 2 miles.

When students critically analyze Priya's claim that six laps of the soccer field is more than a mile, they critique the reasoning of others (MP3).

If students don’t have a strategy to solve the first problem, consider asking:

• “Can you represent a person running one lap around the field?”
• “How can you figure out the distance of one lap around the field?”

• Invite students to share their solutions to the first problem.
• “How did you find how far 1 lap around the field is?” (I multiplied the length and the width by 2 and added them.)
• “How far is one lap?” ( yards)
• “How far is 6 laps? How do you know?” (1,587 yards, I multiplied by 6.)
• “How did you find the product ?” (I multiplied 264 by 6. I know that is 3 so I added that.)
• “Is 6 laps more than or less than a mile?” (Less, because it’s less than 5,000 feet. Less, because a mile is more than 1,700 yards.)