Please select a Grade Span
Home  Mathematics  Geometry & Measurement

Geometry & Measurement

Overall in the geometry strand, students should "analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; apply transformations and use symmetry to analyze mathematical situations; and use visualization, spatial reasoning, and geometric modeling to solve problems." (NCTM, 2000, p. 41)

Geometry is the study of shape. We can begin by considering, in a sense, the situation of no shape. That is, consider geometric diagrams consisting of vertices and edges in which shape is not essential, only the connections among vertices are essential. This leads to the study of vertex-edge graphs (also called networks or simply graphs). Continuing the study of shape, consider properties of and relationships among shapes, including two- and three-dimensional shapes; location of shapes, leading to coordinate geometry; transformations of shapes, leading to transformation geometry; special shapes, such as circles and triangles, leading to trigonometry; and reasoning about shape, including geometric proof. All these aspects of shape are captured in the essential topics listed and described below.

Technology should be used appropriately to enhance and support the teaching and learning of geometry. This may include the judicious use of graphing calculators, interactive geometry software, and resources on the Internet. Such technology can be used, for example, to facilitate an experimentation and conjecturing approach to teaching and learning geometry.

Essential Topics in Geometry

  • Coordinates
  • Transformations
  • Geometric properties and relationships
  • Trigonometric relationships
  • Vertex-edge graphs

Select a grade span from the dropdown located on the left side of the page.