3D Geometry
3-D Geometry

What are students expected to know?  (from the Ontario curriculum)
– compare and sort prisms and pyramids by geometric properties (i.e., number and shape of faces, number of edges, number of vertices), using concrete materials;
– identify and describe the two-dimensional shapes that can be found in a three dimensional figure (Sample problem: Build a structure from blocks, toothpicks, or other concrete materials, and describe it using geometric terms, so that your partner will be able to build your structure without seeing it.);
– describe and name prisms and pyramids by the shape of their base (e.g., rectangular prism, square-based pyramid);

DIMENSIONS

Students often know what "3D" looks like, though some have difficulty explaining it.  The D in 3D stands for dimension.  The first dimension is length (as seen with the image of the straight line).  The second dimension is width.  The rectangle shown below demonstrates the 2 dimensions as it has a length and a width appearing flat.  The third dimension is height (or depth).  The rectangular prism below demonstrates the third dimension, adding depth.
13107_110532_0.png
Sample question:  using pictures, words, and numbers, explain what 2D and 3D mean and how 2D shapes and 3D solids are related.
SOLIDS
13107_12411_7.png


FACES, EDGES, AND VERTICES (VERTEX) OF 3D SOLIDS

As illustrated below, 3D solids can have many attributes such as, faces, edges, and vertices.  A face is a flat surface of a 3D solid.  An edge is where 2 faces meet.  A vertex is where 2 or more edges meet.  Look at the examples below and see if you can identify where the faces, edges, and vertices of each 3D solid are.

                    Face                                           Edge                                Vertex (Vertice)
        13107_30531_0.png                             13107_30715_2.png                   13107_30809_3.png
13107_110754_1.png       13107_110842_2.png      13107_110925_3.png

Sample question:  using pictures, words, and numbers, explain how many faces, edges, and vertices are on a hexagonal prism.

PRISMS AND PYRAMIDS

A prism has 2 congruent (same size and shape) bases.  The shape of the base tells the name of the prism.  A prism has at least 3 rectangular faces.

A pyramid has 1 base.  The base is a face.  The shape of the base tells the name of the pyramid.  A pyramid has at least 3 triangular faces.

                           13107_111750_6.png                                   13107_111211_5.png

Sample question:  explain the similarities and differences between a triangular based pyramid and triangular prism.





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