Our world is defined by space and spatial relationships of geometric shapes and elements. The arguments we use to defend our points of view to others model geometric thinking. The structures and arguments of geometry are one of the oldest, most practical and, to many students, the most relevant studies in mathematics. Skillful teachers in early grades build on students’ innate ability to describe their world by introducing precise geometric vocabulary and basic understandings.
The study of geometry is as extensive as it is fascinating. From the most ancient times, our ancestors have used the tools and truths of geometry to build pyramids for kings, fences for farmers and ships for discovering new worlds. The curiosity and creativity of our students combined with the mathematics made possible by new technologies will certainly grow these ancient truths into amazing new applications. This course limits itself to address only the most fundamental and essential content common to geometry curriculums in grades 8-10.
Component One: Geometric Thinking. This study focuses on developing students’ abilities to present defensible arguments as required for success throughout high school and college studies and in the working world. Application to scientific method and persuasive writing is discussed, as is the need to identify errors in arguments found in the thinking of peers, news media and advertising.
Component Two: The Geometry of Size. The focus of the second component is the use of formulas to describe and compute area, surface area and volume of two and three-dimensional shapes. Examples will emphasize the disciplined and orderly process geometers use to measure the size of shapes in problem solving situations.
Component Three: Geometric Relationships. Seldom are geometric shapes and elements found in isolation in the real world. This component describes the relationships that occur among parallel and perpendicular lines and among congruent and similar figures.
Component Four: Right Triangle. It is doubtful that any other geometric shape is as useful to mankind as is the right triangle. Students of this course will participate in an interactive activity to prove the Pythagorean Theorem and then use it to solve important problems.