The purpose of this lesson is to remind students of the tangible meaning of volume: that it’s the amount of space contained in a three-dimensional figure. Students estimate the amount of stuff different containers hold, recalling units of measurement commonly used for volume, like fluid ounces, cups, liters, gallons, cubic feet, and cubic centimeters (also known as milliliters). They revisit the names of figures learned prior to this unit: cylinders, cones, rectangular prisms, and spheres, and see some physical containers that can be modeled with these. It is important for students to make these connections between physical and mathematical objects so that, later on, real-world objects can be modeled with idealized figures (MP4).

Students also learn a method for quickly drawing a cylinder. Later in the unit, they also learn quick methods for sketching a cone and a sphere. This skill was included both because it is a handy thinking tool to have access to in problem solving and also because it helps students better understand the meaning of terms, like “radius” and “height,” as they apply to these mathematical objects.