Math Department

High School Resources

High School Math Content Standards

Geometry

Number Sense

• Use estimation skills when sketching diagrams, including relative sizes of angles and segments.
• Determine limitations and boundaries of variables representing angles and lengths.
• Eliminate unreasonable solutions.
• Understand the number "Pi" and its relationship to circles, cylinders, and spheres.

Computation

• Simplify expressions involving radicals and exponents.
• Simplify complex fractions when they appear in proportions and formulas.
• Evaluate formulas, including distance, midpoint, area, perimeter, volume, Pythagorean theorem, and quadratic formula.
• Set up and solve proportions related to similar figures.
• Use trigonometric ratios to compute measures of unknown parts of a right triangle.

Measurement

• Measure angles using a protractor.
• Use a variety of methods for basic constructions and models (e.g. paper folding, compass, straight edge, protractor, technology).
• Use appropriate unit labels in solutions of application problems.

Theory

• Develop the language and vocabulary of geometry.
• Understand the parts and structure of Euclidean Geometry (i.e. undefined terms, definitions, postulates/axioms, and theorems).
• Explore the importance of logical reasoning, justification and formal proof.
• Distinguish between Euclidean geometry and non-Euclidean geometry.
• Recognize and use coordinate geometry and transformational geometry.
• Understand the difference between inductive and deductive reasoning.

Deduction

• Develop the language and vocabulary of geometry.
• Understand the parts and structure of Euclidean Geometry (i.e. undefined terms, definitions, postulates/axioms, and theorems).
• Explore the importance of logical reasoning, justification and formal proof.
• Distinguish between Euclidean geometry and non-Euclidean geometry.
• Recognize and use coordinate geometry and transformational geometry.
• Understand the difference between inductive and deductive reasoning.

Diagrams and Models

• Identify, classify, and draw two-dimensional and three- dimensional geometric figures.
• Develop spatial relationships and concepts using models
• Investigate properties of triangles, quadrilaterals, and other polygons
• Investigate properties of circles
• Investigate properties of three-dimensional figures
• Investigate properties of geometric figures using appropriate technology and software

Probability

• Construct a sample space illustrating all outcomes of a particular event
• Solve probability problems involving geometric models

Patterns

• Understand the inequality relationships between the sides and angles of a triangle
• Identify and apply patterns from right triangles, including 30¡-60¡-90¡, 45¡-45¡-90¡, and Pythagorean triples, to application problems
• Identify and describe patterns that emerge from two-dimensional and three-dimensional geometric figures (e.g. Euler's formula for vertices, edges, and faces; altitudes and slant height of solids, etc.)
• Describe and apply transformations of geometric figures

Algebra

• Develop and solve equations that model geometric relationships.
• Simplify and solve equations generated by formulas including distance, midpoint, and the Pythagorean Theorem.

Optional/Enrichment

• History of Mathematics.
• Non-Euclidean Geometries.
• Mapping/Cartography.
• Tessellations, Escher-type designs, and fractals.