Cube-n-ometry

We studied cube-n-ometry from a number of different perspectives. First, we looked at professions that utilize top views, front views and side views to educate. Some of these professions included cartographers or map makers who generally use aerial, top or birds eye views. The take these photos from satellites, airplanes, helicopters, or unmanned drones. From these pictures they can develop very accurate maps.

Second, we looked at architecture and building. Architects use top views, side views and front views to communicate blue prints for builders. Finally, we looked at front and side views of the human body used by scientists and doctors. We then looked at isometric drawings of cube structures and had the children draw a front, top and side view. This is not easy to do so I built actual structures of the isometric drawings so they could see each of the views in actual three dimensions.

This brought us to a discussion of dimensions of a cube. We looked at the building blocks of a cube: square faces, edges, and vertices, each a face, edge and vertex. The cube itself or any solid is three dimensions (we can use any three of the words “base, length, width, height, depth, or breadth” as long as they are on different planes. All solids are three dimensional (like the cube). The face of a solid is two dimensional (like the square face of a cube; this is the surface area). The edge or length from one vertex to another is one dimensional (like the segment of one edge of a cube; this is distance). Finally, a vertex or point has no dimension or zero dimensions (like the vertex of a cube; this is location).

Below, I attached a Cube-n-ometry powerpoint that I shared with the children on an iPad.

Everyone likes to build solid structures so we explored several different origami cube constructions. I showed them a traditional origami cube which required 18 pieces of paper and was not very stable. Even less stable is the Jackson Cube formed with six square modules. A beautiful construction is the Cube with Windows which require 12: 1 x 2  dimension modules (I included these directions in their packets and worked with a few of our veteran mathletes on its construction). 

The easiest, most reliable, and incredibly stable cube construction is the Sonobe Cube invented by Mitsunobu Sonobe. This requires six square pieces of paper and the steps are easy to replicate.

I created two approximately 8 minute videos to show the children how to put them together. The first is called Sonobe Cube Construct Modules.MOV and the second is called Sonobe Cube Connect Modules.MOV. When you click on this link, the second video appears first so be sure to watch them in the proper order. It may take a minute to download each video so give it some time before you watch them. The children will need six square pieces of paper before they begin.

https://drive.google.com/folderview?id=0B4YjCwrdiMO1bzQ1dFk0SkZlZW8&usp=sharing

Have fun and build as many Sonobe Cubes as possible, put your name on each, and bring them into class next week.