Online Class: ABCs of Geometry

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Course Description

This course will provide the learner with a better understanding of the underlying concepts of geometry. Through readings, lessons, quizzes and independent explorations, the learner will leave the course with more complete understanding of geometry and begin to be able to think in a geometrical fashion.  Websites are also provided to help the learner further explore the topics on his/her own. At the end of this unit, the learner will be able to describe some of the basic premises behind geometric thinking, reasoning and study. They will also be able to demonstrate the following learning objectives:

Objectives (based on the Van Hiele levels of geometric thought):

  1. Students will be able to demonstrate the ability identify the ways geometry is used by people in their daily lives (i.e. professions, synthetic universe, natural universe, in the home, etc...)
  2. Students will be able to recognize and name figures (triangle, square, rectangle, rhombus, parellelogram, polygon, pentagon, hexagon, octagon, kite, rectangular and triangular pyramids, prisms, cone, sphere) [Level 0 Visualization]
  3. Students will be able to analyze various properties of shapes (i.e. right angles, parallel sides, number of sides, number of corners, etc...) [Level 1 Analysis]
  4. Students will be able to construct relationships between classes of figures (i.e. rectangles are parallelograms with a right angle, etc…) [Level 2 Informal Deduction]
  5. Students will be able to think deductively in regards to geometrical concepts. [Level 3 and 4 Deduction/Rigorous Proof]

Course Requirements

There are no pre requisites. Anyone over the age of 13 is welcome to join this course. It is recommended though that individuals have obtained a ninth grade education in order to grasp the Math information presented.

Course Topics


Lesson 1 - Geometry in Our World

Lesson 2 - Learning All About Shapes

Lesson 3 – Tessellations

Lesson 4 - Symmetry

Lesson 5 - Pentominoes

Lesson 6 - Three Dimensional Shapes

Lesson 7 - Perimeter

Lesson 8 - Area

Lesson 9 - If... Then Statements

Lesson 10 - Area of Three Dimension Objects

Lesson 11 - Translations, Reflections, Rotations

Lesson 12 - Classifying Shapes by Properties

Lesson 13 - Proofs and Abstract thinking in Geometry

Lesson 14 - Geometry in Our Universe

Lesson 15 - Geometry in Professions

Course Materials

No additional course materials required to complete this course.

Grading Policy

Each lesson will include a written and practice assignment that will directly apply what you have learned. A brief 10 pt. quiz will follow each lesson. Students will successfully complete this course by mastering all learning outcomes with 70% or higher overall grade.


This class does not qualify a student for credit in other universities or educational systems.

Learning Outcomes

By successfully completing this course, students will be able to:
  • Recognize the role of Geometry in the real world.
  • Recognize geometric shapes.
  • Understand tessellations.
  • Apply the concept of symmetry in geometry.
  • Recognize pentominoes.
  • Solve geometry problems of three dimensional shapes.
  • Calculate the perimeter or any shape.
  • Calculate the area of any shape.
  • Calculate the area of three dimensional objects.
  • Understand translations, reflections, and rotations in geometry.
  • Classify shapes by properties.
  • Create proofs in Geometry.
  • Understand how Geometry is prevalent in our universe, and
  • Demonstrate mastery of lesson content at levels of 70% or higher.

Assessment Guide

Assessment Points
Lesson 1 - Geometry in Our World9
Lesson 2 - Learning All About Shapes9
Lesson 3 - Tessellations9
Lesson 4 - Symmetry9
Lesson 5 - Pentominoes10
Lesson 6 - Three dimensional shapes10
Lesson 7 - Perimeter10
Lesson 8 - Area10
Lesson 9 - If… Then Statements10
Lesson 10 - Area of Three Dimension Objects10
Lesson 11 - Translations, Reflections, Rotations5
Lesson 12 - Classifying Shapes by Properties9
Lesson 13 - Proofs and Abstract thinking in Geometry9
Lesson 14 - Geometry in Our Universe9
Lesson 15 - Geometry in professions9
The Final Exam135
Total Points:272

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