Geometry+Standard

=Instructional programs should enable all students to=

Grades 6-8 Expectations: In grades 6-8 all students should -

 * precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
 * understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
 * create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Grade 9-12 Expectations: In grades 9-12 all students should -

 * analyze properties and determine attributes of two- and three-dimensional objects
 * 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
 * establish th validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others
 * use trigonometric relationships to determine lengths and angle measures

Grade 6-8 Expectations: In grade 6-8 all students should-

 * use coordinate geometry to represent and examine the properties of geometric shapes
 * use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides

Grade 9-12 Expectations: In grade 9-12 all students should-

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

Grade 6-8 Expectations: In grade 6-8 all students should-

 * describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling
 * examine the congruence, similarity, and line or rotational symmetry of objects using transformations

Grade 9-12 Expectations: In grade 9-12 all students should-

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

Grade 6-8 Expectations: In grade 6-8 all students should-

 * draw geometric objects with specified properties, such as side lengths or angle measures
 * use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume
 * use visual tools such as networks to represent and solve problems
 * use geometric models to represent and explain numerical and algebraic relationships
 * recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

Grade 9-12 Expectations: In grade 9-12 all students should-

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

2011 NCTM