K12MATH010: Geometry

Course Syllabus for "K12MATH010: Geometry"

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Geometry comes from the Greek roots geo-, meaning Earth, and –metron, meaning measure. Thus, geometry literally means the process of measuring the Earth. In a more mathematical sense, this course looks at geometric figures that we see in everyday life to understand the patterns in their attributes and how their measures relate to these patterns. It expands on the basic geometric concepts learned in previous math courses, through the applications of these concepts in new contexts. You will learn to develop formal proofs that support patterns and rules of geometric figures previously investigated, including congruent and similar figures, triangles, quadrilaterals, and circles. From here, the course expands on your knowledge about triangles and the Pythagorean theorem, introducing trigonometry of both right triangles and general triangles. The course will help you develop links between the attributes of two-dimensional and three-dimensional figures; help you develop formulas for calculating the volume of prisms, cylinders, pyramids, cones, and spheres; and assist you in using geometric modeling to solve problems involving three-dimensional figures. Toward the end of the course, you will use your algebra skills and the coordinate plane to further investigate and prove the attributes of geometric figures and their relationships with each other. The last unit continues to develop your knowledge of probability, using geometric probability models where appropriate. While this is a geometry course, it assumes prior knowledge of foundational geometry concepts from previous math courses and mastery of algebra. Therefore, to successfully progress through this course, you should arrive with a strong foundation in algebra and familiarity with some basic geometric concepts. You should enter into this course having studied a variety of geometric figures and their distinguishing attributes. You should be able to draw and describe geometrical figures and the relationships between figures. Additionally, you should be comfortable with the concepts of area, perimeter, surface area, and volume, and you should be able to apply these concepts to problem solving. Furthermore, you should be comfortable graphing points on the coordinate plane. Finally, you should have a working definition of congruence and similarity, as this is the starting point for this course and it takes off from there. In addition to learning geometry, this course will work on developing mathematical practice skills that will help you to be successful in future courses. Therefore, in addition to developing geometric reasoning and an understanding of the physical patterns that exist in the world around us, this course will enable you to continue developing your skills of mathematical practice, including problem solving, critical thinking, mathematical modeling, and the ability to use a variety of tools to effectively tackle problems. Completion of this course will provide you with the foundation necessary to successfully progress to Algebra 2. Additionally, this content should prove helpful in developing a solid foundation for science courses, specifically physics, where knowledge of geometric figures and their attributes is critical.

Learning Outcomes

Upon successful completion of this course, you will be able to:

  • Connect the concepts of congruence and similarity to transformations.
  • Write proofs in a variety formats to prove geometric theorems involving congruence, similarity, and other geometric attributes of figures.
  • Make geometric constructions using a compass and straightedge.
  • Use trigonometry to solve problems involving right triangles and general triangles.
  • Express geometric properties using equations.
  • Use algebra and coordinates to prove a simple geometric theorem.
  • Solve linear and quadratic equations to find the intersections of figures on the coordinate plane.
  • Apply theorems about circles to the solution of problems.
  • Explain volume and solve problems using developed formulas.
  • Apply geometric concepts in modeling situations in order to solve problems.

Course Requirements

In order to take this course, you must:

√    Have access to a computer.

√    Have continuous broadband Internet access.

√    Have the ability/permission to install plug-ins or software (e.g., Adobe Reader or Flash).

√    Have the ability to download and save files and documents to a computer.

√    Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.).

√    Have competency in the English language.

√    Have read the Saylor Student Handbook.

√    Have the ability to download the Java applet that is required to view some activities and GeoGebra simulations.

√    Have completed Algebra 1.

Course Information

Welcome to Geometry. General information on this course and its requirements can be found below.
Course Designer: Ms. Kate Cottrell
Primary Resources: This course is comprised of a range of different free, online materials. However, the course makes primary use of the following:

Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials. You will also need to complete the final exam.
Please note that you will only receive an official grade on your final exam. However, in order to adequately prepare for this exam, you will need to work through all of the resources in each unit.
In order to pass this course, you will need to earn a 70% or higher on the final exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take a total of approximately 66 hours to complete. Each unit includes a “time advisory” that lists the amount of time you are expected to spend on each subunit. It may be useful to take a look at these time advisories and determine how much time you have over the next few weeks to complete each unit and then set goals for yourself. For example, unit 1 should take approximately 12 hours to complete. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 3 hours, 30 minutes) on Monday and Tuesday nights, subunit 1.2 (a total of 3 hours) on Wednesday and Thursday nights, and so forth.

Table of Contents: You can find the course's units at the links below.