Describe and define volume as the measure of how much space something takes up in three dimensions. Contrast volume with area, which measures the space a shape takes up in two dimensions. Discuss which shapes do and don't have volume (such as spheres and circles, respectively). Ask children to tell about a situation in which they've had to think about how much space something took up, such as cooking or packing a suitcase.
Introduce the concept of geometric solids, such as spheres, cubes, rectangular prisms, pyramids and cones. Let children fill containers with marbles and count how many marbles fit in each one. Using numbers of marbles as a conceptual link, describe units used to measure volume, such as cubic centimeters and quarts.
Introduce children to the formulas for calculating the volume of various solids such as a cube or rectangular prism (length times width times height) and a cylinder (pi times the radius squared times height). Draw analogies to children's familiarity with simpler formulas for area. For example, the volume of a cylinder is the area of a circle multiplied by height, which could be thought of as representing the number of circles piled up into a cylinder.
Conclude by letting the children practice calculating the volumes of a few shapes. If there are students who are still having trouble making the conceptual leap, give them a chance to ask questions or keep playing with the marbles and containers.