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Archived Information

Mathematics Curriculum Framework - November 2000

Learning Standards by Strand

for Grades 5-6

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

Learning Standards

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

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. cross symbol
Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces. cross symbol
Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular. cross symbol
Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). solid circle symbol
Find the distance between two points on horizontal or vertical number lines. solid circle symbol
Predict, describe, and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections. solid triangle symbol
Identify types of symmetry, including line and rotational. solid triangle symbol
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. solid triangle symbol
Match three-dimensional objects and their two-dimensional representations, e.g., nets, projections, and perspective drawings. solid square symbol


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.


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Learning Standards for Grades 3-4
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Learning Standards for Grades 7-8

Last Updated: November 1, 2000
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