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Geometry Standard for Grades 3-5




Instructional programs from prekindergarten through grade 12 should enable all students to—  In grades 3–5 all students should— 
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
  • identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;
  • classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;
  • investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
  • explore congruence and similarity;
  • make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
  • describe location and movement using common language and geometric vocabulary;
  • make and use coordinate systems to specify locations and to describe paths;
  • find the distance between points along horizontal and vertical lines of a coordinate system.
Apply transformations and use symmetry to analyze mathematical situations
  • predict and describe the results of sliding, flipping, and turning two-dimensional shapes;
  • describe a motion or a series of motions that will show that two shapes are congruent;
  • identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs.
Use visualization, spatial reasoning, and geometric modeling to solve problems
  • build and draw geometric objects;
  • create and describe mental images of objects, patterns, and paths;
  • identify and build a three-dimensional object from two-dimensional representations of that object;
  • identify and draw a two-dimensional representation of a three-dimensional object;
  • use geometric models to solve problems in other areas of mathematics, such as number and measurement;
  • recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.

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