Geometry Standard
Instructional programs from pre-K through grade 12 should enable all students
to --
Standard Component | Grades 6-8 Expectations |
analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about geometric relationships;
Length, Perimeter and Area
Lines, Rays, Line Segments, and Planes
Angles
Quadrilaterals
Surface Area and Volume
Geometry in Tessellations
Symmetry in Tessellations
Visual Patterns in Tessellations
Introduction to Fractals: Infinity, Self-Similarity and Recursion
Geometric Fractals
Fractals and the Chaos Game
Properties of Fractals
Chaos
Pascal's Triangle
Irregular Fractals
The Mandelbrot Set
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precisely describe, classify, and understand relationships among types of
two- and three-dimensional objects using their defining properties;
understand relationships among the angles, side lengths, perimeters,
areas, and volumes of similar objects;
create and critique inductive and deductive arguments concerning geometric
ideas and relationships, such as congruence, similarity, and the Pythagorean
relationship.
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specify locations and describe spatial relationships using
coordinate geometry and other representational systems;
Length, Perimeter and Area
Translations, Reflections, and Rotations
Fractals and the Chaos Game
Properties of Fractals
Chaos
The Mandelbrot Set
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use coordinate geometry to represent and examine the properties
of geometric shapes;
use coordinate geometry to examine special geometric shapes, such as
regular polygons or those with pairs of parallel or perpendicular sides.
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apply transformations and use symmetry to analyze mathematical
situations;
Quadrilaterals
Translations, Reflections, and Rotations
Geometry in Tessellations
Symmetry in Tessellations
Visual Patterns in Tessellations
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describe sizes, positions, and orientations of shapes under informal
transformations such as flips, turns, slides, and scaling;
examine the congruence, similarity, and line or rotational symmetry of
objects using transformations.
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use visualization, spatial reasoning, and geometric modeling to
solve problems.
Geometry in Tessellations
Symmetry in Tessellations
Visual Patterns in Tessellations
Introduction to Fractals: Infinity, Self-Similarity and Recursion
Geometric Fractals
Fractals and the Chaos Game
Properties of Fractals
Chaos
Pascal's Triangle
Irregular Fractals
The Mandelbrot Set
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draw geometric objects with specified properties, such as side lengths or angle
measures;
use two-dimensional representations of three-dimensional objects to
visualize and solve problems such as those involving surface area and volume;
use visual tools such as networks to represent and solve problems;
use geometric models to represent and explain numerical and algebraic
relationships;
recognize and apply geometric ideas and relationships in areas outside the
mathematics classroom, such as art, science, and everyday life.
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