Mastering the Foundations of Geometry

Mastering the Foundations of Geometry (ages 14 - 18) 
Mastering the Foundations of Geometry is a class designed to support students interested in learning more about Geometry topics taught at the high school level. This is a weekly class that meets to discuss the most important topics in Geometry. Each class meeting is independent and does not build upon the previous sessions. While each session has a guided topic and objective, students will have opportunities each week to ask  ANY questions about Geometry and discuss their knowledge about related topics with myself and other students. 



1. Week of September 6th: Introduction to Geometry – A Review of the Geometry notation used to describe Points, Lines, Planes, Angles, and bisectors, segment and angle Relationships.
2. Week of September 13th: Parallel Lines and Transversal Angles – This lesson will discuss how parallel and perpendicular lines built the modern world! We will explore their transversal properties, as well as how learn about how to use a protractor.
3. Week of September 20th: Polygons and Interior/Exterior Angle Sums – We will discuss polygon vocabulary up to a dodecagon, as well as learning the Interior Angle Sums and how to find the  Exterior Angle of any n-gon
4. Week of September 27th: Triangle Properties – Students will discuss common words to describe triangles based on their side and angle measures. all about Scalene, Isosceles and Equilateral triangles, with a focus on the Triangle Inequality Theorem 
5. Week of October 4th: Geometric Transformations – We will learn about the 4 types of 2-D Transformations: Translation, Reflection, Rotation, and Dilation 
6. Week of October 11th: Congruence – Students will discuss if two figures are Congruent, as well as Congruent Triangle theorems (such as SSS, ASA, SAS, AAS, HL, and CPCTC) and the vocabulary needed to begin writing proofs. 
7. Week of October 18th: Geometry Proofs – This class will discuss proof writing, learning how to construct logical arguments to prove various geometry concepts. 
8. Week of October 25th Similarity  – Students will begin to distinguish between Similar and Congruent figures, and learn 3 new theorems for identifying Similar Triangles.
9. Week of November 1st: Right Triangles – Students will discuss Right Triangles, beginning with the Pythagorean Theorem with a focus on simplifying radicals. e will discuss  how to solve problems involving 45-45-90 and 30-60-90 triangles using radical proportions.  
10. Week of November 8th: Similar Right Triangles – Students will discuss similar right triangles that exist infinitely in every right triangle and how the geometric mean can help us solve problems.  
11. Week of November 15th: Introduction to Trigonometry – We will explore the world of trigonometry with an intro into SOHCAHTOA and how this discovery led humankind to so many wonderful innovations we use daily. Students will begin to use trigonometry to solve for missing sides and angles as well as begin to apply their knowledge of trigonometry to solve word problems. 
12. Week of November 22nd: Quadrilaterals – This lesson will provide an introduction to the world of quadrilaterals. We will discuss the properties of Squares, Rectangles, Parallelograms, Trapezoids, and Kites
13. Week of November 29th: Circles – Students will learn about Circumference and Area of a circle, as well as how to write the equation of a circle using an algebra skill called completing the square. 
14. Week of December 6th: Circle Properties– We will explore circle properties of measures, such as arc measure, central angles, inscribed angles, arc length and the area of a sector.
15. Week of December 13th: Chords Secants and Tangents of Circles – This lesson will help students master the vocabulary of lines that intersect a circle, and the theorems that help mathematicians solve problems. 
16. Week of December 20th: Area vs. Volume – Students will learn the differences between area and volume, as well as formulas associated with Prisms, Cylinders, Cones, Spheres, and Pyramids 

In each of these lessons, I will …
1.	… utilize my accessibility to professional educational software and free websites available to all learners on the internet. 
2.	… provide the class with scaffold learning opportunities, where each student can be successful and grow at their pace.
3.	… give students opportunities to ask questions and interact with the lesson in ways that are purposeful and meaningful towards developing long-term, concrete understanding of the concepts presented. 
4.	… inspire students to understand the deeper meaning and purpose of mathematics and all its importance to the progress of humankind. 
5.	… show students free resources they can use to improve the skills presents.