幾何学 - 第 2 学期 (通年コース)

This course provides in-depth instruction of Geometry topics to prepare students for higher level math to include Trigonometry, Pre-Calculus and beyond.  The class is offered in the Outschool on-going format to offer more flexibility for parents.  The on-going format allows students to enroll for sessions as needed without committing to a full year.  Students may enroll to learn a specific topic, for additional support and practice with an existing class, or for the complete Geometry curriculum.  Students enrolling in this class should have a strong understanding of basic mathematical operations and have completed an Algebra 1 level course.  

Throughout this course, students will focus on abstract concepts applied to geometry and geometry proofs.  We will spend time each class discussing the reasoning behind different abstract geometry concepts and practicing the application of logic and deductive reasoning.  Time will be allocated to understanding the “why” of geometry and geometry proofs in addition to simply “proving” them.  Geometry is about changing the way students “think” about math.  I’ve found that once students understand conceptually, geometry is not quite as perplexing and students are now able to identify what a specific problem is asking and solve for the correct answer.  My teaching style combines lectures with examples and exercises completed both independently and with other students in the course.  Word problems are integrated throughout the sessions to teach logic, reasoning, and critical thinking.  Word problems also demonstrate a student’s ability to apply what they’ve learned to everyday, real life situations.  The class meets for two 45-minute sessions each week through the fall and spring semesters.  

Week beginning:

Sept 9        Introduction to Geometry and Geometry Proofs
Sept 16      Points, Lines, Rays, Line Segments
Sept 23      Planes and Sets
Sept 30      Angles
Oct 7          Types of Angles
Oct 14.       Parallel and Perpendicular Lines
Oct 21.       Supplementary and Complementary Angles
Oct 28.      Transversals
Nov 4         Perimeter and Interior Angles
Nov 11        Area
Nov 18       Constructing and Identifying Triangles
Nov 25       BREAK - NO CLASS
Dec 2         Regular Polygons
Dec 9         Geometry of a Circle, Sphere, and Ellipse
Dec 16       Practical Application with Real Life Examples and Word Problems

Dec 23.      BREAK - NO CLASSES

Jan 6          Introduction to Geometry Proofs - deductive and inductive reasoning
Jan 13        Area of a Circle and Ellipse
Jan 27        Volume of a Rectangular Solid and Cylinder
Feb 3         Volume of a Pyramid, Cone, Prism, and Sphere
Feb 10       Surface Area of a Solid
Feb 17       Radicals
Feb 24      Pythagorean Theorem
Mar 3        More on Radicals
Mar 10      BREAK - NO CLASS
Mar 17       Special Triangles: 45 - 45 - 90  
Mar 24      Special Triangles: 30 - 60 - 90
Mar 31       Axioms, Postulates, and Theorems
Apr 7         Corresponding Parts of a Triangle
Apr 14       Proving Triangles Congruent: SSS and SAS
Apr 21       Proving Triangles Congruent: ASA and AAS
Apr 28      Proving Right Triangles Congruent
May 5       Proving Triangles Similar with AA
May 12      Transformational Geometry

BONUS MATERIAL (as time permits) 
Trigonometric Functions
Reciprocal Trigonometric Functions