Geometry Standard

 

NCTM Principles and Standards for School Mathematics

 

 

ÒInstructional programs from prekindergarten through grade 12 should enable all students to –Ó

                                                                                                                                                                  NCTM p. 41

 

 

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

 

 

Pre-K – 2

á recognize, name, build, draw, compare, and sort two- and three-dimensional shapes

á describe attributes and parts of two- and three-dimensional shapes

á investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.

 

3 – 5

á identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes

á classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids

á investigate, describe, and reason about the results of subdividing, combining, and transforming shapes

á explore congruence and similarity

á make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions

 

6 – 8

á precisely describe, classify and understand relationships among types of two- and three-dimensional objects using their defining properties

á understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

á create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship

 

9 – 12

á analyze properties and determine attributes of two- and three-dimensional objects

á 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

á establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others

á use trigonometric relationships to determine lengths and angle measures

 

 

 

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

 

 

 

á      Apply transformations and use symmetry to analyze mathematical situations.

 

 

 

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

 

 

 

 

 

 

 

 

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