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 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.
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.
Fill 'Er Up Activity Sheet
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.
Higginson, William and Lynda Colgan. "Algebraic Thinking Through Origami." Mathematics Teaching in Middle School 6: 343.