The goal of this activity is for students to use concepts of volume and unit conversion to enhance their understanding of density. During the Activity Synthesis, students must attend to precision (MP6) as they discuss the relationship between mass, volume, and density

Students may calculate density in grams per cm³, then be unsure how to convert to kg per m³. Prompt them to either convert the measurements to cubic meters and kilograms prior to calculating density, or to use dimensional analysis to convert the density.

The purpose of this discussion is to draw out relationships between mass, volume, and density. Ask students:

• “How did you deal with the different units in this problem?” (If possible, select a student who calculated the feather density in grams per cm³ then converted to kg per m³, and another who converted the measurements to kilograms and cubic meters prior to calculating the density.)
• “How did you calculate the densities of each material?” (Divided the mass by the volume.)
• “How much space is 400 cubic meters? Would the feathers fill this room?” (A classroom of 30 feet by 30 feet by 12 feet has a volume of about 300 cubic meters.)
• “How much space is 0.124 cubic meters? Would the steel fit in the bed of a pickup truck?” (1,000 kg of steel would make a cube with an edge length of about 0.5 meters.)

This task presents a different way to think about density. Instead of considering mass per unit volume, students analyze animal population density. They use unit conversion and volume calculations to solve a problem. As students choose and track common units of measurement, they are attending to precision (MP6).

While students work, monitor for a variety of strategies such as:

• Converting the density of 16 fish per 100 gallons of water to 0.16 fish per 1 gallon.
• Multiplying the tank’s volume in gallons by 16, then dividing by 100.
• Calculating that if 275 fish were used, the density would be about 14 fish per 100 gallons.

The goal of this discussion is to highlight different ways to solve the problem. Ask students what the density of fish per 100 gallons would be if 275 fish were put in the tank, and what that means in this situation. Invite students to share how they approached rounding. For example, if the calculations show that 315.8 fish are needed, should we round up or down? Both answers can be supported.