Prior to teaching this lesson, familiarize yourself with the Cubes applet.
Introduce the lesson by holding up a familiar household prism such as a clear plastic storage container. Use the object to review vocabulary including rectangular prism, length, width, height, surface area, and volume. Ask students to identify the three linear measurements: length, width, and height. Start by labeling the bottom face and its length and width. The height is the perpendicular distance between the top and bottom faces. Explain to students that length or width is sometimes called depth. The applet that students will explore uses the terms width, depth, and height.
To illustrate the concept of volume, drop some inch or centimeter cubes into the box. Let students know that in today's lesson they will explore volume by interacting with virtual boxes and by making origami boxes. Project the Cubes applet, and show students how to navigate it. Explain to students that there is a minor glitch that can be solved by hitting "clear" before dropping cubes into a virtual box.
Distribute the Fill 'Er Up activity sheet to each student. Have students work with partners and explore prisms. Then, have them complete Questions 1–6.
Distribute two sheets of paper and some centimeter cubes to each student. Be sure to place enough centimeter cubes that students can measure the length, width, and height of their prisms, but not so many that they can completely fill their prisms. Have students work in larger groups of 3–4, providing peer support during the origami. Each student will use the Folding Directions to create a physical model of a rectangular prism. Some students will experience difficulty following the written and pictorial directions. Try to assign a student with strong spatial reasoning to guide their group members through the folding. As an instructional accommodation, consider providing completed models for students who have difficulty.
Discuss with students how the volume can be determined without completely filling the prism with cubes. Some students may need to fill their prism completely.
Summarize key concepts of the lesson at the end of class. Ask volunteers to explain how they approximated the volume of the box using centimeter cubes. The first two rows from the table in Question 2 will reinforce the concept that doubling all three dimensions will result in a box with a volume that is eight times as large. Show symbolically that when the dimensions of a prism are doubled, the volume of the new box will be eight times as large as the original box.
- Voriginal = lwh
- Vnew = (2l)(2w)(2h) = 8lwh
Reinforce this idea by showing a box that was made using paper with double the dimensions. Verify using visual estimation that the volume of this box is 8 times as large as the original box. You might also want to go over the last row from the table in Question 2 because it involves algebraic reasoning.
Showcase a well-made origami model. This is a good opportunity to highlight the accomplishment of a student who does not participate in class often or applaud the efforts of a low achiever.
