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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):
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...)
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]
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]
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]
Students will be able to think deductively in regards to geometrical concepts. [Level 3 and 4 Deduction/Rigorous Proof]
Course Lessons
Lesson 1 - Geometry in Our World
Geometry surrounds all of us, making it a safer and more productive place.
Lesson 2 - Learning All About Shapes
At the beginning of any study of geometry, one must be able to identify shapes. Many of the names of shapes are derived from how many sides, angles or how the sides relate to each other.
Lesson 3 - Tessellations
A tessellation is defined as a pattern of shapes which are all closed and totally cover a surface.
Lesson 4 - Symmetry
Symmetry refers to both parts of a shape or figure as having equal or matching points.
Lesson 5 - Pentominoes
To create a pentomino one must connect five of the blocks on the grid together where they only touch on one side.
Lesson 6 - Three Dimensional Shapes
Shapes which have length, width and thickness are known as three-dimensional shapes.
Lesson 7 - Perimeter
In two-dimensional shapes, the perimeter is the distance around the shapes.
Lesson 8 - Area
The area of an object is how much space it takes up
Lesson 9 - If... Then Statements
An if...then statement is a statement where each part is contingent on the other.
Lesson 10 - Area of Three Dimension Objects
There are two different types of area which can be calculated for three-dimensional shapes, surface area and volume.
Lesson 11 - Translations, Reflections, Rotations
There are four types of isometries which are: translations, rotations, reflections and glide reflections.
Lesson 12 - Classifying Shapes by Properties
The process of drawing conclusions about shapes and theories is an important aspect of geometry.
Lesson 13 - Proofs and Abstract thinking in Geometry
A proof is the process of drawing as many true conclusions about the information provided as possible to gain the narrowest viewpoint about what is presented.
Lesson 14 - Geometry in Our Universe
Geometric patterns can be found in the nonsynthetic universe and in the synthetic or man-made universe.
Lesson 15 - Geometry in Professions
There are numerous professions which need to have a basic understanding of the principles of geometry in order for success within the profession.
Optional Certificates Awarded
Certificate of Merit
Certificate of Academic Excellence
Certificates may be awarded by the instructor at his/her own discretion and are based on student merit.
To save your award and have a hard-copy delivered, there is a $30.00 processing fee that covers the customization, printing, and delivery of the award, as well as access to the UniversalClass™ Portfolio Service that documents your achievements online.
Official awards have a serial number that verifies the authenticity of the award (great for employers
to verify your achievement).
This is a non-credit course, and is provided for your personal enrichment.
This course is not intended to be a substitute for any state, government, licensing, or educational requirements.
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