The purpose of this activity is for students to practice using precise language to describe how they estimated volumes of objects (MP6). Starting from an object of known volume, students must consider the difference in dimensions between the two objects. The focus here is on strategies to estimate the volume and units of measure used, not on exact answers or calculating volume using a formula (which will be the focus of later lessons).

Students may think there is a single right answer. Measurements are always approximate. Some of the measurements given by the authors of this activity were calculated using estimates from the photos, and may not be very precise. Measurements listed on the sides of packages are more accurate, but actual contents may vary slightly.

For each set of containers, display the image, and ask previously identified groups to share their strategies for estimating the volume. Once strategies for each set of containers are shared, discuss:

• “How do the estimates differ if we measure using water instead of rice?” (Measuring with rice leaves a bit of empty space between the grains, while water, being liquid, leaves no empty space, so it’s more accurate.)
• “If the containers we used were much larger (like water tanks), would our units of measure change? Why?” (If we were measuring larger volumes, we might want to use larger units, like gallons. 4,000 ml sounds big, but it’s only a bit more than 1 gallon, which isn’t that much water.)

Conclude the discussion by asking students to compare some other units of measure for volume that they know of. Ask students to recall what they know about unit conversion between some of the following units of measure:

• Fluid ounces, quarts, cups, liters, and milliliters
• Cubic feet, cubic meters, and cubic yards
• Note that cubic centimeters are special because 1 cc = 1 ml.

If it comes up, here is information about ounces: Units called “ounces” are used to measure both volume and weight. It is important to be clear about what quantity you are measuring! To differentiate between them, people refer to the units of measure for volume as “fluid ounces.” For water, 1 fluid ounce is very close to 1 ounce by weight. This is not true for other substances! For example, mercury is much denser than water. 1 fluid ounce of mercury weighs about 13.6 ounces! Motor oil is less dense than water (that’s why it floats), so 1 fluid ounce of oil weighs only about 0.8 ounces. The metric system is not so confusing for quantities that would be measured in ounces, since it’s common to measure mass instead of weight and measure it in grams, whereas volume is measured in milliliters.

The purpose of this activity is for students to learn or remember the names of the figures, and some features of those figures, that they worked with earlier and to practice a quick method for sketching a cylinder. Students start by determining the shapes that are the faces of the four figures. They also determine which shape would be considered the base of each figure shown. This allows students to connect what they have previously learned about two-dimensional figures to the three-dimensional figures in this activity and will help later when establishing volume formulas for cylinders, cones, and spheres.

The last question introduces students to a way to sketch a cylinder. This is a skill they will continue to use throughout the unit when working on problems that do not provide a visual example of a situation.

If students struggle to visualize the shapes of the faces, position the object so that students can only see two dimensions. Ask students what two-dimensional shape they see.

If using physical objects, display each object one at a time for all to see. If using images, display the images for all to see, and refer to each object one at a time. Ask students to identify:

• Which figure the object is an example of.
• The different shapes that make up the faces of the figure.
• The shape that is the base of the figure.

Invite previously selected students to share their sketches of cylinders. The goal is to ensure that students see a variety of cylinders: short, tall, sideways, narrow, etc. If no student drew a “sideways” cylinder, sketch one for all to see, and make sure students understand that even though it is sideways, the height is still the length perpendicular to the base.

Tell students that we will be working with these different three-dimensional figures for the rest of this unit. Consider posting a display in the classroom that shows a diagram of each object labeled with its name, and where appropriate, with one side labeled “base.” As volume formulas are developed, the formulas can be added to the display.