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Subject: Mathematics

Course Description:

One day in 2580 B.C., a very serious architect stood on a dusty desert with a set of plans. His plans called for creating a structure 480 feet, with a square base and triangular sides, using stone blocks weighing two tons each. The Pharaoh wanted the job done right. The better our architect understood geometry, the better were his chances for staying alive.

Geometry is everywhere, not just in pyramids. Engineers use geometry to bank highways and build bridges. Artists use geometry to create perspective in their paintings, and mapmakers help travelers find things using the points located on a geometric grid. Throughout this course, we’ll take you on a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem solving.

This course is all about points, lines and planes. Just as importantly, this course is about acquiring a basic tool for understanding and manipulating the real world around you.

Major Topics:

Segment 1

  • Undefined Terms of Geometry
  • Mathematical Language
  • Segments
  • Segments and the Coordinate Plane
  • Exploring Angles
  • Angle Addition Postulate
  • Angle Bisectors
  • Angle Relationships
  • How to Use a Compass
  • How to Use a Protractor
  • Dimensionality
  • Lines and Angle Pairs
  • Properties of Parallel Lines
  • Slope
  • Linear Equations
  • Writing Equations of Lines
  • Logical Reasoning
  • Algebraic Properties
  • Algebraic Proofs
  • Proving Lines Parallel
  • Perspective Drawing
  • Introduction to Geometer’s Sketchpad
  • Classifying Triangles
  • Interior and Exterior Angles in a Triangle
  • Properties of Isosceles and Equilateral Triangles
  • Triangle Inequalities
  • Proofs in Geometry
  • Exploring Triangle Congruence
  • Congruence in Right Triangles
  • Pythagorean Theorem
  • Midsegments of Triangles
  • Perpendicular Bisectors
  • Medians and Altitudes
  • Angle Bisectors
  • Similar Polygons
  • Similarity in Right Triangles
  • Proportions
  • Applications of the Pythagorean Theorem
  • Trigonometric Ratios
  • Scale Drawing

Segment 2

  • Polygons and Quadrilaterals
  • Parallelograms
  • Proving Quadrilaterals are Parallelograms
  • Rectangles, Rhombi, and Squares
  • Investigating Rectangles, Rhombi and Squares
  • Trapezoids
  • Kites
  • Golden Ratio
  • Angle Measures of Polygons
  • Perimeter
  • Areas of Rectangles and Squares
  • Areas of Parallelograms and Rhombi
  • Areas of Triangles, Trapezoids and Kites
  • Areas of Regular Polygons
  • Three Dimensional Figures
  • Surface Area of Prisms
  • Surface Area of Pyramids
  • Volume of Pyramids
  • Parts of Circles
  • Equations of Circles
  • Circumference and Area of Circles
  • Sectors and Segments
  • Geometric Probability
  • Arcs and Angles
  • Arcs and Chords
  • Inscribed Angles
  • Secants, Tangents and Angle Measures
  • Segments in a Circle
  • Surface Area of Cylinders and Cones
  • Volume of Cylinders and Cones
  • Volume of a Sphere
  • Transformations
  • Symmetry
  • Reflections
  • Translations
  • Rotations
  • Dilations
  • Matrices
  • Glide Reflection
  • Composites of Reflections
  • Tesselations

Participation Requirements:

Besides engaging students in challenging curriculum, INVS guides students to reflect on their learning and to evaluate their progress through a variety of assessments. Assessments can be in the form of self-checks, practice lessons, multiple choice questions, projects, oral assessments and discussions. Instructors evaluate progress and provide interventions through the variety of assessments built into a course, as well as through contact with the student in other venues.

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Course Details

  • Course Code: 1206310
  • Course Credits: 2.0

Algebra I or its equivalent.

Estimated Completion:
2 segments / 32-36 weeks