3D 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 twodimensional 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, squarebased 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.
Sample question: using pictures, words, and numbers, explain what 2D and 3D mean and how 2D shapes and 3D solids are related.
SOLIDS
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)
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.
Sample question: explain the similarities and differences between a triangular based pyramid and triangular prism.
