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Mobius Strip (1 face, 1edge) and Cylindrical Loops (2 faces, 2 edges)

Building on our exploration of perimeter in one dimension and area in two dimensions, we entered the real world of three dimensions. Starting with a rectangular strip of paper about 1.5” x 11” (by cutting a 1.5” piece the long way from a piece of regular 8.5” X 11” paper), I taped the two short edges together to make a cylindrical loop.

Dimensions, Perimeter, Area, Polygons, Apothem, Isometric Rhombuses, and Functions

Getting carried away with perimeter and area is so much fun! The first page of the pdf was just straight rectangles calculating perimeter in linear units and area in square units. There are so many ways to calculate perimeter (2L + 2W or 2(L+W)) or just use your pencil point to count each linear unit by ones (not very exciting but effective). I prefer, adding the length and the width and then doubling that sum.

Perimeter and Area Dice Game and Function to find dimensions of equal perimeter and area.

Many careers like architecture, aeronautical and graphic design, engineering, farming, sports, painting, construction, manufacturing, military applications, boating, the coast guard, and many others include the use of area and perimeter on a regular basis.  Perimeter is the linear  (one dimensional) distance around the outline of the rectangle.

Dice Squares ADDITION and MULTIPLICATION Game

After creating Sonobe Cubes last week, many of the children started to create dice out of their cubes. 

 

Sonobe Cube Ratios and Construction

Last week’s hexagonal prisms of linear ratio 1:2:3 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).