Mathematics: Geometry

• Standard 1: Problem Solving
• Standard 2: Communication
• Standard 3: Reasoning
• Standard 4: Connections
• Standard 5: Estimation & Computation
• Standard 6: Numeration & Number Theory
• Standard 8: Measurement
• Standard 9: Statistics
• Standard 10: Probability
• Standard 11: Algebra
• Standard 12: Patterns, Relations, Functions
• Introduction to Mathematics
• Table of Contents - All Standards

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Content Standard: Geometry

Students will demonstrate knowledge of geometric structure as an integral part of the real world.

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Fourth Grade Performance Standards: Geometry

By the end of grade Four, students will:

Describe two-and three-dimensional figures (e.g., circles, polygons, trapezoids, prisms, spheres) by

• naming them
• comparing, sorting, and classifying them
• drawing and constructing physical models to specifications
• identifying their properties (e.g., number of sides or faces, two- or three-dimensionality, equal sides, number of right angles)
• predicting the results of combining or subdividing two-dimensional figures
• explaining how these figures are related to objects in the environment

Use physical materials and motion geometry (such as slides, flips, and turns) to identify properties and relationships, including but not limited to

• symmetry
• congruence
• similarity

Identify and use relationships among figures, including but not limited to

• location (e.g., between, adjacent to, interior of)
• position (e.g., parallel, perpendicular)
• intersection (of two-dimensional figures)

Use simple two-dimensional coordinate systems to find locations on maps and to represent points and simple figures

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Eighth Grade Performance Standards: Geometry

By the end of grade Eight, students will:

Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) by

• naming, defining, and giving examples
• comparing, sorting, and classifying them
• identifying and contrasting their properties (e.g., symmetrical, isosceles, regular)
• drawing and constructing physical models to specifications
• explaining how these figures are related to objects in the environment

Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent faces).

Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features

Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures

Locate objects using the rectangular coordinate system

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Grade Level Performance Standards: Grade Six: Geometry

The student will:

Construct, measure and bisect geometric figures.

Construct various solid and plane figures; explore relationships between perimeter, area, volume and surface area.

Investigate and construct various tessellations.

Classify and compare the symmetries of geometric figures.

Investigate area and perimeter of geometric and irregular shapes; record conjectures.

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Grade Level Performance Standards: Grade Seven: Geometry

The student will:

Construct three-dimensional geometric models; investigate methods for finding volume and surface area.

Use technology to test conjectures about geometric figures.

Analyze geometric patterns in tessellations and shape sequences.

Investigate how changes in area affect perimeter and changes in perimeter affect area; report results.

Draw combinations of two-dimensional geometric figures from verbal or written instructions.

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Grade Level Performance Standards: Grade Eight: Geometry

The student will:

Construct three-dimensional geometric models; analyze methods for finding volume and surface area; generate formulas.

Use technology to construct two- and three-dimensional geometric figures.

Analyze and generalize geometric patterns of regular and semi-regular tessellations and shape sequences.

Draw representations of three-dimensional figures using isometric grids.

Generalize formulas for area and perimeter of geometric and irregular shapes; present results.

Draw combinations of two-dimensional geometric figures accurately from verbal or written instructions.

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Twelfth Grade Performance Standards: Geometry

By the end of grade Twelve, students will:

Identify, describe, and analyze properties of figures, relationships among figures, and relationships among their parts by

• constructing physical models
• drawing precisely with paper-and-pencil, hand calculators, and computer software
• using appropriate transformations (e.g., translations, rotations, reflections, enlargements)
• using reason and logic

Use geometric models to solve mathematical and real-world problems

Present convincing arguments by means of demonstration, informal proof, counter-examples, or any other logical means to show the truth of

• statements (e.g., these two triangles are not congruent)
• generalizations (e.g., the Pythagorean theorem holds for all right triangles)

Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity

Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent)

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