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Geometry materials developed for the Special School District. These materials can be used for high school students, and possibly for some middle school students depending on their developmental level.

NCTM Standards

The materials were developed to adhere as much as possible with the NCTM Standards. The materials were developed with a student in mind who had one semester of algebra. The materials covered there include some coordinate geometry, thereby leaving more time to focus on the other standards.

In grades 9–12 all students should [1]:

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

  • 1. analyze properties and determine attributes of two- and three-dimensional objects;
  • 2. explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them;
  • 3. establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;
  • 4. use trigonometric relationships to determine lengths and angle measures.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

  • 5. use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations;
  • 6. investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates.

Apply transformations and use symmetry to analyze mathematical situations

  • 7. understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;
  • 8. use various representations to help understand the effects of simple transformations and their compositions.

Use visualization, spatial reasoning, and geometric modeling to solve problems

  • 9. draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;
  • 10. visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections;
  • 11. use vertex-edge graphs to model and solve problems;
  • 12. use geometric models to gain insights into, and answer questions in, other areas of mathematics;
  • 13. use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.

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