幾何概念 - 夏季訓練營

When students understand the conceptual foundations of Geometry, learning problems, relationships, and formulas becomes logical and students tend to progress at a faster pace.  This class is a preparation course for students planning to enter High School Geometry.  The course teaches the fundamentals of Geometry and relates them to Algebra.  This is also an excellent review for students that have completed Geometry and want to increase their understanding and brush up on their skills.  The class meets for eight 45 minute sessions over 2 weeks.  This boot camp focuses on the “how and why” of Geometry as well as teaching facts and formulas.  Students will spend time in class “proving” formulas to enhance their understanding.  This exercise also helps students discern when to apply a particular formula in everyday life situations.  Proving formulas I geometry helps bridge the gap between abstract ideas and practical application.  When students understand the conceptual foundations of Geometry, learning problems, relationships, and formulas becomes logical and students tend to progress at a faster pace.  


WEEK 1 

Session 1 – BASICS OF GEOMETRY
In the first session students will get an overview of geometry and learn points, lines, planes, line segments, midpoint and distance. Students will learn perimeter and area in the coordinate Plane and be introduced to angles.  

Session 2 – REASONING AND SET NOTATION
In this session, we will discuss the concept of Inductive vs Deductive Reasoning.  Students will learn the symbols for set notation and practice what they learn using a Venn Diagram, Planes, and Lines.

Session 3 – PAIRS OF LINES AND ANGLES
In session 3, students will learn to identify angles and recognize how different pairs of angles can be classified.   To demonstrate the concept and teach the new terms, we will use Parallel Lines, Perpendicular Lines, and Transversals.  We will also look at how geometry and algebra are related.  We will use the concepts learned in classes 1-3 and apply them to various shapes and figures using algebraic equations.

Session 4 - GEOMETRY PROOFS - AXIOMS, POSTULATES, AND THEOREMS
In this session, we will discuss axioms, postulates, and theorems.  Students will learn what a geometry proof is and the steps to construct a proof correctly.  Several new theorems and postulates will be introduced and explained.  A resource sheet will be provided for students to keep in their files and use in their next geometry class.  

WEEK 2 

Session 5 - GEOMETRY PROOFS - PRACTICAL APPLICATION
Week 2 begins by applying the concepts learned in week 1 and constructing geometry proofs using a fill-in-the-blank format.

Session 6 – GEOMETRY PROOFS - PRACTICAL APPLICATION
Session 6 will introduce 2 new postulates and students will practice constructing geometry proofs in class.  

Session 7 – SIMILAR POLYGONS, SIMILARITY STATEMENTS, PRACTICAL APPLICATION
In this session, students will learn the difference between similarity and congruence.  We will look at several common examples of similar polygons and learn to construct a similarity statement.  Toward the end of class, we will explore two real life examples of how similar shapes are used in the real world to measure objects and survey land.

Session 8 – TRIGONOMETRY
Starting with the Pythagorean Theorem, students will explore special and similar right triangles and learn the use of Sine, Cosine, and Tangent

In the last session, students will be given a certificate of completion for the "Geometry Key Concepts Summer Boot Camp" and will be officially ready to enroll in the full year or semester Geometry course!