In previous grades, students worked with metric units of length. The purpose of this activity is to reason about the size of a kilometer. Students consider the distance they might walk or run, perhaps to and from school or during sports practice, and they also consider other lengths with which they might be familiar, such as going across town or taking a bike ride, or the distance to a friend's house. Building a sense and an understanding of large numbers or distances or other measurements takes time and practice. The intent of this activity is to begin this work informally. A variety of answers should be expected, and the goal of the Activity Synthesis is to share this variety and come to a general agreement of approximately how far is a kilometer, or some number of kilometers.

• Invite students to share their responses for how far it is from school to where they live.
• “How many meters are there in a kilometer?” (1,000)
• “About how many steps does it take to go 1 meter?” (2)
• “About how many steps does it take to go 1,000 meters or 1 kilometer?” (2,000)
• “Does 2,000 steps help communicate the length of 1 kilometer?” (Yes. That's a lot, but I can count to 1,000 and take that many steps, so it’s not too far. No. 1,000 steps is a lot, too much for me to imagine.)

• Communicate the enormity of the Great Pacific Garbage Patch.
• Continue to build a sense of distances by looking at a map of the United States and thinking about the sizes of different American states.
• Multiply large numbers, likely using the standard algorithm.
• Calculate a product of 2 three-digit numbers for the first time.

Students calculate the areas of different American states in order to grasp the enormity of a floating area of trash in the Pacific Ocean. It turns out that this area is substantially larger than most American states! Students will use the standard multiplication algorithm and estimation as they calculate the areas of different states. Estimation plays an important role because the area of New Mexico is a product of 2 three-digit numbers. Students are prepared to make and understand this calculation, which also provides them an opportunity to see the power of estimation. The area of New Mexico can be readily compared with the area of the Great Garbage Patch, without calculating the exact area. For the last question, students use the area of the states they calculated and apply that to a map of the United States.

Students model with mathematics when they make assumptions about the states, for example that they are approximated by rectangles, in order to calculate or estimate their areas, and when they choose states with areas approximately equal to the area of the Great Pacific Garbage Patch (MP4).

• Invite students to share their calculations for Delaware.
• “Is Delaware close in size to the garbage patch? How do you know?” (No, it is not close at all. 1,600,000 square kilometers is a lot more than 7,392 square kilometers.)
• “Is the garbage patch greater than or less than 10 times as large as Delaware?” (Much greater, because that’s only about 70,000 square kilometers, which is way less than a million.)
• “Is the garbage patch greater than or less than 100 times as large as Delaware?” (Greater, because that’s about 700,000 square kilometers, and the garbage patch is more than double that.)
• “How could you estimate the area of New Mexico?”(596 is close to 600, which is a nice number. 552 is harder, but if I say that’s about 500, then I get an estimate of or 300,000.)
• “How did you decide which area to circle on the map?”(5 New Mexicos would make about 1,600,000 square kilometers, so I circled New Mexico and 4 other states close in size to it.)