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## Geometry Standard for Grades 3-5

 Expectations
 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.