Introducing Volume
Volume, or the capacity of an object, is sometimes confused with surface area. At first glance, the formulas appear somewhat similar. A helpful way to compare the concepts is to explain surface area as the amount of room on the outside of a shape, and volume as the amount of space inside a shape. Discuss the value of measuring volume, giving such examples as knowing how much water a pool will hold, how much air a SCUBA tank will hold, or how much cement a cement mixer will hold. Ask students for other examples.
Students will benefit from practice with building, measuring, and filling containers to understand volume. The Power Solids have a removable base and can be filled with water, sand, rice, or other materials. By filling one Power Solid and pouring its contents into another Power Solid, students can explore volume relationships between shapes. If you intend to have students perform exact measurements using a graduated cylinder, be sure they are comfortable reading the bottom edge of the water level, or meniscus.
Students can measure volume by reading sand levels in a graduated cylinder before and after filling a Power Solid. Have your students take the average of three trials to eliminate some errors. First, fill a large graduated cylinder nearly to the top and take a reading. Use the sand in the cylinder to fill the Power Solid. Take a reading for the sand remaining in the cylinder and subtract it from the starting quantity. The difference is the volume of sand poured into the Power Solid.
Challenge students to order the Power Solids from largest to smallest volume by estimation. You may want to allow them to fill their Power Solids or use cube models to make more accurate estimations. As you introduce the formulas for finding the volume of each shape, encourage students to refer to their Power Solids for reference. You also may wish to distribute copies of the table on page 2 for reference. Once you have finished your discussion, students can mathematically calculate the volume of each Power Solid to confirm the accuracy of their initial estimations.
Explain to students that the thickness of the plastic takes away from the volume each shape can hold. Therefore, students must measure from inside edge to inside edge rather than from outside edge to outside edge when computing what the shape can hold. Also, explain that the shapes are slightly larger at the opening so they can slip out of the mold during manufacturing. This will cause slight variations in the measurements. Tell them that the standard height is 4.6 cm, and the other measurements are derived from this to keep the shapes in relationship to each other.
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