6th Grade Math: Menger Sponge Project
The 6th Grade Math class has been working on building a Menger Sponge using Origami techniques. You can view the final product in the first floor hallway of the McIntosh Center for the Arts & Sciences.
The description of creating a Menger Sponge is as follows: (written by the 6th Grade)
A. Start with a cube.
B. Divide all sides into thirds.
C. Then, remove the middle cube on each face, and the one left in the center. This is called Stage One.
We have taken seven small cubes out of the original. The volume has gone down, but the surface area has increased.
D. Now divide each of the remaining cubes into thirds on each face, and remove the middle cube on each face, and the one left in the middle. This is Stage Two.
This time, we removed 140 smaller cubes, reducing the volume even more, while increasing
the surface area.
We can continue this forever. The volume keeps getting smaller, but the surface area keeps growing.
To build this in class, we really went the opposite way. We built a cube that was 27 inches on a side, with holes to make it look like a Stage Two Menger Sponge.
6th grade math is tiered at Powhatan. Visit our website to learn more: www.powhatanmain.wpengine.com
Established in 1948, Powhatan School is a Kindergarten-8th grade private school accredited by the Virginia Association of Independent Schools and is a member of both the National Association of Independent Schools and Independent Education. Powhatan serves families in Clarke County, Frederick County, Western Loudoun County, Warren County, Winchester City and the panhandle of West Virginia. Powhatan is a private school located near Purcellville VA. Powhatan is a private school near Round Hill VA. Powhatan is a private school near Waterford VA. Powhatan is a private school near Upperville VA. Powhatan is a private school near Winchester VA. Powhatan is a private school near Stephens City VA. Powhatan is a private school near Charles Town WV. Powhatan is a private school near Kearneysville WV. Powhatan is a private school near Front Royal VA. Powhatan is a private school near Berryville VA.
