The purpose of this activity is for students to make reasoned estimates about the volume of recyclable goods a school produces in a day, a week, a month, and a year. Students have seen cubic feet and cubic meters briefly in an earlier unit, and it may be helpful to build a cubic foot to enable them to visualize this unit of measure and improve their estimates.

Answers to the questions here will vary widely, based on the size of the school, the size of the recycling bins, and the exact estimates students make. Mathematically, the important point is that students use multiplication appropriately in their estimates and develop a sense for the staggering size of the waste that they will consider in the second activity.

• Invite students to share their estimates for the volumes of the different recycling bins.
• “How did you estimate the volume of the small bins?” (A bin looks like it’s about 2 feet tall, and I think the base is maybe a square foot. So that’s 2 cubic feet.)
• “How did you estimate the volume of the large recycling bins?” (I think they’re about 3 feet tall, with a base of about 4 square feet, so that would be 12 cubic feet.)

The purpose of this activity is to use estimation to compare the amount of recyclable plastic produced by all elementary schools in the United States with the amount of recyclable plastics the United States exports every year for processing. In this task, an estimate for each school is provided. The new parts of this activity are considering all of the schools in the country, for which an estimate is provided, and the total amount of plastics exported by the United States each year, for which an estimate also is provided.

The numbers in this activity go beyond those expected for the grade 5 division standard, but they are friendly and the quotient is small enough that students could find it by repeated subtraction or addition. It also is possible that they will use their place-value understanding and their understanding of single-digit multiplication facts.

• Invite students to share their solutions for finding the number of days it would take a school to fill one of the cargo containers with plastic.
• “How can you use the equation to find the value of ?” (They have the same value because if 32 groups of 4 is 128, putting 10 times as many in each group will give 10 times as much for the total.)
• Invite students to share their response for the number of cargo containers each school will fill.
• “How did you find the value of ?” (I know that , and this is also true for thousands.)
• Invite students to share their reasoning for the last question about all elementary schools’ plastic recyclables.
• “Much of the debris that is in the Great Pacific Garbage Patch is plastic. Today we got a sense of how much recyclable plastic all of the schools in our country produce.”