Geometry

Placement Information

Placement Process
One critical factor for restful learning is the proper placement of students. If you are unsure which level is the best fit for your student, reach out to the instructor you are considering. Once registered, anticipate contact regarding placement evaluations from instructors by May 15th and throughout the summer. Students must be registered to enter the placement process. Early placement exams may allow time for tutoring or additional review based on the outcomes. See more about placement evaluations in our Student-Parent Handbook.

Math Placement Process
For registered students, please anticipate contact regarding placement evaluations from instructors by May 15th and throughout the summer. Students must be registered in a math course to receive a placement assessment. Math classes have a detailed and specific placement process.
Read more about the math placement process here.

Watch the math placement process video with our department chair, Dr. Fransell Riley, here.

See the Math Scope and Sequence here.

The objective of this Geometry course is to serve as a study of Geometry from both a classical and modern perspective, exploring parallels and contrasts between the two. The course will follow the path set by Euclid of studying definitions, postulates, theorems, and constructions. They will develop logical and spatial reasoning as they work on writing proofs weekly. This study will serve as a backdrop as we utilize the theorems to solve modern geometric problems. Students will study angles, lines, triangles, polygons, circles, area and volume, coordinate geometry, and trigonometry. Students will explore connections between math and everyday applications through problem-solving and hands-on activities. They will study Greek Geometry, Euclid and Descartes, the history of geometry, and what led to its merger with Algebra. Thus, they will understand geometry from a classical viewpoint and both modern viewpoints (proof-driven versus Algebra-driven).

Students will develop and practice problem-solving skills by working on sample SAT Geometry problems and some competition-level problems. They will complete portfolio projects that deepen their understanding of the concepts, appreciate the role of mathematics in God’s creation, and lead them to explore real-world applications of mathematics. Throughout the course, students will be led to see mathematics as a tool to solve real-world problems.

Experience
The teaching of a new concept opens with a brief review of previously covered content. This review connects the previous lesson to the current lesson. The premise of the current lesson is presented via a question or idea. The students now have a puzzle or idea that they want to explore. As we delve deeper into answering the question at hand, we begin to discover the new mathematical concept. We use our prior knowledge and intuition to uncover a new truth about mathematics. Once this truth has been uncovered, we begin to work examples; first as a class and then as individuals or in groups. As our understanding of the concept deepens, we extend our knowledge base to include specific cases or situations that lead to minor adjustments in the truth that we have uncovered – thus expanding the truth. We use a variety of methods to uncover new truths. The most frequent method is a Socratic-style discussion that the entire class participates in. A discussion takes place that reveals the relevance of this truth in our mathematical studies or our daily lives (real-life application).

Delivery
Each teacher has a unique presentation style in delivering the aforementioned experience. Sometimes the teacher leads the discussion using questions; following the example set by Socrates. Sometimes a problem is presented and the students take the lead in finding a solution based on extending previous knowledge. Sometimes students participate in a hands-on activity to discover new truths. Sometimes a short lecture or presentation is required, however, we aim to minimize lecturing, especially before high school.

Methodology
Students continue to study the new truth and deepen their understanding of it via homework, classwork, projects, and assessments. Since our classes do not meet 5 days per week, students must spend time studying the concepts outside of class. This also helps students grow in their ability to think and work math concepts independently which is required for future math classes. For this reason, we ask that parents minimize the assistance that students are given on assignments. If a student receives an A on an assignment, it should be a true indication of their independent ability as the teacher interprets this A as independent mastery.

Review assignments or classroom review activities are utilized to assist students with opportunities to retain or improve their mastery. Assessments are directly or indirectly cumulative and serve as an opportunity to deepen their learning. Assessments are not meant to be a regurgitation of previous homework assignments.

Preparedness
Students who are adequately prepared to take this course will have mastered (can work independently without prompting):

Students are expected to have, successfully, completed a comparable Algebra 1 course
Completion of one Logic course would be helpful

Required Materials:
Books and supplies are not included in the purchase of the course.

Sections with Amy Sherman and Matthew Davenport

Euclid Elements, Heath Translation (choose one option below)
- Free web version: Clark University, org
- Free PDF: Wilbour Hall, Univ Texas with Greek
- Purchase Print Book: Amazon (this should not be necessary unless it is your preference)
- This book will provide our classical viewpoint of geometry, including writing proofs. We will discuss Euclid’s proofs, compare them to modern textbook proofs, and write our own
Digital Textbook: Reveal Geometry with ALEKS**
- The instructor does not teach from the book but uses it for example problems, class work problems, student reference, and course structure. The book represents the modern viewpoint of geometry; solving geometric problems using algebra, which students need to learn to prepare for future courses, real world applications, and future exams. Notwithstanding, this book also covers logical reasoning and writing
- ALEKS delivers practice problems to students in a manner that promotes mastery and retention. Students work problems on paper and turn them in to the instructor for review. Students are required to correct their work using ALEKS’ step-by-step solution; thus, they learn from their errors before trying another similar problem. This provides students the opportunity to learn to solve geometry on paper and digitally, which is a 21st century
- Purchased via instructor ($40) by 5/31. Info. will be sent via email in
Mathematics for the Nonmathematician (used print or digital is ok)
- This text will be used to learn some of the related history and philosophy of the concepts covered.
Digital tablet. Choose from: Wacom Intuos, Huion, XP-Pen, or other.
Three-ring notebook with five dividers or 5 subject spiral
Binder Pencil Pouch with multiple sharpened pencils, erasers, protractor, and a drawing com- pass or bullseye compass, square patty paper (we do not need this much patty paper, so you can opt to use typing paper or similar) — these are examples only, less expensive items are acceptable
Scientific Calculator Examples: TI, Sharp, other
Notebook Paper and Graph paper
Free web accounts: desmos.com, ziteboard.com, desmos.calculator,
- Ziteboard is used often as a virtual classroom chalkboard, the others are used sparingly

In addition, the instructor will provide pdf files or problems from various sources.

OPTIONAL MATERIALS:

Paper versions of the digital textbook (this would be in addition to the digital text, not instead of): Textbook Vol 1 and Textbook Vol 2. Used from Amazon: Textbook Volume 1 and Textbook Volume 2

Sections with Eric Robinson

Khan Academy (free account)
IXL ($20)

Amy Sherman is an experienced Secondary Math teacher. She has spent the past 16 years teaching grades 6-12 in public and private schools, and as a private tutor. She holds a B.S. in Organization Communication from Oklahoma Christian University, and holds Texas Educator Certifications in grades 4-8 and grades 8-12 Mathematics. As an educator she works to create opportunities for students to succeed and grow in confidence, as well as opportunities to struggle without being defeated. Her goal for her class is to have a learning environment that encourages contemplation and a genuine appreciation for the subject matter. She has a desire for her students to see the whole in every part, and to recognize the beauty and patterns in mathematics.

Amy lives in Houston with her husband and 3 children. They are active parishioners at St. Anthony the Great Orthodox Church, where Amy teaches Church School and serves on the Church School Leadership Committee. In her spare time, she enjoys cheering on her kids at their sporting events, and watching old movies with her family and their orange cat, Todd. [email protected]

Eric Robinson has a MFA (Master of Fine Arts) degree in printmaking from Iowa State University and a BS in secondary math education from Western Governors University. Eric and his wife homeschool, so he has taught math from number recognition through Calculus 2. Having taught in private Christian (protestant and Catholic) schools and in public schools as well as tutoring in person and online, he is excited to teach courses in the Great Hall of Scholé Academy so that learning can be the true focus.

Eric was attracted to Scholé Academy for the commitment to restful learning. Eric loves the beauty of mathematical reasoning. He loves the feeling of accomplishment and confidence that comes from learning math. He loves the lightbulb moments, and he loves the real skills math builds--skills that make so many things doable and possible.

Eric also loves the Word of God. God is a God of truth and order, and so we find in scripture truth and logical arguments that help us to understand creation--God, ourselves, one another, redemptive history, and our hope in Christ Jesus. Eric loves sharing the Word of God to start every course session. Eric does that for the same reason he learns and teaches math: because doing so enriches us and helps us to discover the truths God has made. As Proverbs 25:2 says, "It is the glory of God to conceal a matter, but the glory of kings is to search out a matter." [email protected]

Matthew Davenport earned his B.S. in Mechanical Engineering at Tufts University with a second major in Philosophy. After working five years with the US Army as a project engineer, he left to study the philosophy of Soren Kierkegaard at St. Olaf College and renewed his faith at the English L’Abri Fellowship. Afterwards, he found his calling as a Classical Christian educator at Samuel Fuller School, where he taught math, science and logic and helped to launch their high school expansion. He currently works for Massachusetts General Hospital as a project manager in the Cancer Center.
Matthew lives in Worcester, MA with his wife and son, where he enjoys hiking, disc-golfing, gardening, playing piano, and learning more each day about the truth, goodness, and beauty of God’s creation. [email protected]

Quarter 1

Construct Logical Arguments (statements, conditionals)
Conjectures and counterexamples
Deductive vs Inductive Reasoning
Introduce Writing direct proofs
Constructions or Excerpts of Euclid Elements Book
Points, Lines, and Planes
Angle Relationships
2D and 3D Figures
Transformations and Symmetry
Triangles and Congruence (SAS, ASA, etc...)

The order in which topics are presented may vary according to instructor and course section.

Quarter 2

Introduce writing indirect proofs
Relationships in Triangles (points of concurrency, inequalities)
Quadrilaterals (conditions for each shape)
Similarity (AA, SSS, SAS, Triangle Proportionality)
Right Triangles (Py. Thm, & converse, Special Right Tri, Geometric Mean)

The order in which topics are presented may vary according to instructor and course section.

Quarter 3

Intro to Sin, Cos, Tan
Applications of Trig
Law of Sines and Cosines
Circles (angles, arcs, chords, inscribed, tangents, secants)

The order in which topics are presented may vary according to instructor and course section.

Quarter 4

Equations of Circles and Parabolas
Area, Surface Area, and Volume (using Trig to calculate)
Sample Spaces
Probability and Counting
Permutations and Combinations
Conditional Probability
Two-Way Frequency Tables

The order in which topics are presented may vary according to instructor and course section.

Computer: You will need a stable, reliable computer, running with a processor with a speed of 1 GHz or better on one of the following operating systems: Mac OS X with Mac OS 10.7 or later; Windows 8, 7, Vista (with SP1 or later), or XP (with SP3 or later). We do not recommend using an iPad or other tablet for joining classes. An inexpensive laptop or netbook would be much better solutions, as they enable you to plug an Ethernet cable directly into your computer. Please note that Chromebooks are allowed but not preferred, as they do not support certain features of the Zoom video conference software such as breakout sessions and annotation, which may be used by our teachers for class activities.

High-Speed Internet Connection: You will also need access to high-speed Internet, preferably accessible via Ethernet cable right into your computer. Using Wi-Fi may work, but will not guarantee you the optimal use of your bandwidth. The faster your Internet, the better. We recommend using a connection with a download/upload speed of 5/1 Mbps or better. You can test your Internet connection here.

Webcam: You may use an external webcam or one that is built in to the computer. Webcam Recommendations: Good (PC only) | Best (Mac and PC)

Headset: We recommend using a headset rather than a built-in microphone and speakers. Using a headset reduces the level of background noise heard by the entire class. Headset Recommendations: USB | 3.5mm

Zoom: We use a web conferencing software called Zoom for our classes, which enables students and teachers to gather from around the globe face to face in real time. Zoom is free to download and easy to use. To download Zoom:

Visit zoom.us/download.
Click to download the first option listed, Zoom Client for Meetings.
Open and run the installer on your computer.
In August, students will be provided with instructions and a link for joining their particular class.

Scanner: In this class, students frequently submit homework assignments by scanning pages from their workbooks. Students and/or their parents should have easy access to a scanner and the ability to use it.

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First, read the available course descriptions, noting prerequisites, target grades, and course objectives. If you think your student is prepared for the course, go ahead and register. After registration, a placement assessment may be provided to students, depending on the course and the student’s previous enrollment with Scholé Academy. Registration is finalized when the student’s placement assessment has been returned by the course instructor with placement confirmation.

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Our Assistant to the Principal will be in touch with you after your enrollment to help you with next steps, including any placement evaluations that may be required for your course selections.

This registration will be finalized when the student's placement assessment has been returned by the course instructor with placement confirmation.