The purpose of this activity is for students to estimate products, using the context of volume introduced in the Warm-up. Students estimate the number of cubic centimeters of milk different-size groups of students might consume. For example, at first, students multiply the amount of milk they consume by the number of students in the class. Next, students multiply the amount consumed by one class by the number of classes. Because these are all estimates, the fact that not every student in one class drinks the same amount of milk or that different classes or grades or schools have different numbers of students can be overlooked. When students make simplifying hypotheses such as this, they model with mathematics (MP4).

As currently structured, the activity is quite open-ended so that students can use their own school to make their estimates. There is a lot of variation in school size. The average size of an elementary school in Montana, for example, is less than 200, while in California, it is 600. Some large elementary schools in New York City have close to 2,000 students. The important mathematical part of this activity does not depend on the exact numbers for a particular school. The key is which numbers students choose as they make estimates, focusing on multiples of powers of 10.

• Invite students to share responses and estimates.
• “How did you use your estimates from each question to help answer the next question?” (Once I knew how much milk I drank, I multiplied by the number of students in our class. Then I multiplied that by the number of fifth-grade classes.)
• “How did you make an estimate for your class?” (I think there are between 20 and 30 students in the class but not everyone likes milk. So I estimated that 20 students drink milk with lunch.)

The purpose of this activity is for students to make estimates about how long it would take different groups of students to drink 10,000,000 cubic centimeters of milk. Unlike the previous activity, in which students multiplied the 250 cubic centimeters of milk by greater and greater numbers, in this activity, students divide 10,000,000 cubic centimeters of milk by smaller and smaller numbers to find out how long it would take each group to drink 10,000,000 cubic centimeters of milk. If students attempt to calculate exact answers, remind them that they are looking only for an estimate and the amount of milk consumed by each group in the previous activity is also only an estimate. Making an estimate, or a range of reasonable answers, with incomplete information, is a part of modeling with mathematics (MP4).

• “How did you estimate the number of days it takes 10 schools to drink 10,000,000 cubic centimeters of milk?” (We estimated that they drink about 1,000,000 cubic centimeters a day, so in 10 days that’s 10,000,000.)
• “How did you use this estimate to estimate how long it takes your school to drink 10,000,000 cubic centimeters of milk?” (I multiplied by 10 because it takes 1 class 10 times as long as it takes 10 classes.)
• “Do you think that you ever will drink 10,000,000 cubic centimeters of milk?” (No, 40,000 days is a lot. There are only 365 days in a year, so that would be more than 100 years.)