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Mathematics Curriculum Framework
November 2000

Learning Standards by Strand

Geometry
for Grades 5-6

	Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
	Specify locations and describe spatial relationships using coordinate geometry and other representational systems
	Apply transformations and use symmetry to analyze mathematical situations
	Use visualization, spatial reasoning, and geometric modeling to solve problems

Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

6.G.1	Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides, e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral, and right triangles.
6.G.2	Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.
6.G.3	Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular.
6.G.4	Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).
6.G.5	Find the distance between two points on horizontal or vertical number lines.
6.G.6	Predict, describe, and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections.
6.G.7	Identify types of symmetry, including line and rotational.
6.G.8	Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g., translations, rotations, and reflections.
6.G.9	Match three-dimensional objects and their two-dimensional representations, e.g., nets, projections, and perspective drawings.

Exploratory Concepts and Skills

• Use manipulatives and technology to model geometric shapes.
• Investigate tessellations (tilings).
• Explore the angles formed by intersecting lines.
• Identify and draw shapes and figures from different views/perspectives.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Selected Problems or Classroom Activities
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