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Algebra 1

Scholé Academy Placement Process
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.

Algebra I serves as the foundation for all future mathematics and science courses. Students begin to formulate abstract algebraic generalizations from their concrete understanding of mathematics. Students will learn to solve problems using equations, inequalities, and graphs. Students will in-vestigate linear relationships, translating those relationships into mathematical equations and then functions. Students will explore: simplifying algebraic and radical expressions, linear and nonlinear functions, exponents, polynomials, solving quadratic equations, data analysis, and prob-ability. Students will begin learning to write proofs and will work challenging problem sets from math competition books, college algebra books, and other resources. Students will also learn the history of Algebra and participate in philosophical discussions of the course content.

Classes involve Socratic discussions, interactive lectures, interactive computer activities, peer problem presentations, collaborative group assignments, competitions, and games. The content of the course extends beyond the book. Throughout the course, we begin lessons with a study of math as a subject. We learn about the history of math and the people who discovered the methods we are studying. We discuss how early mathematicians were led to developing the concepts, and why they are relevant to us. We study math the way the first mathematicians did; studying some of the same problems and reconstructing their methods in uncovering mathematical truths. With this framework in place, now having discovered the truth, we turn our attention to practicing the truth. We work on examples and problems which help us deepen our understanding of the concept. Lastly, we learn how to use math; how to use and recognize it in real-life applications, how to use the concept to extend our understanding to new math concepts, or use the concept to extend our knowledge in other fields.

The course also includes an element of problem-solving. It is my goal to convey to students that mathematics is about much more than numbers and computation. It encompasses analytical, logical, and creative thinking. Therefore, we spend time working on our problem-solving ability. Students are presented with open-ended problems that do not lend themselves to a prescribed formula or algorithm. Such problems require them to develop and employ problem-solving strategies.

Student output consists of completing homework, classwork, labs, projects, and assessments. In all cases, student work is graded for taking an appropriate approach, providing an accurate answer, and utilizing clear communication in the form of supporting their work by showing their thinking.

Algebra is a foundational course for all future mathematics courses and several future science and business courses; additionally, algebraic thinking is a skill that permeates daily life. Thus, the course is designed to develop algebraic thinking, in lieu of simply presenting steps and tricks to solve problems. The pace of the course averages one lesson per day; depending on difficulty. The mathematical ability of the students varies and they do not all struggle with the same content. Therefore, lab work is provided to differentiate learning based on student needs. Students who have mastered the content are provided with challenging problems that require synthesis and analysis while students who would benefit from more review are provided that opportunity.

Placement: Please read about our new process above.

  • This course is designed for students who have successfully completed pre-algebra.
  • Mathematical acumen is an important component of placement in this course, however, the student should also be prepared to exhibit a minimal level of executive functioning skills. Such skills would include the ability to focus during the class, avoid distracting behavior, take notes, monitor and submit assignments, navigate web-based technology including downloading, saving, and uploading files, respond to teacher feedback on graded assignments, communicate with the teacher when they do not understand, and participate in-class activities.

High School Credit: This course is the equivalent of one high school credit in mathematics.

Time Commitment: The average student should plan to study mathematics for 60-90 minutes on each (of the two days) that we do not meet for classes. Additionally, they should spend 10-20 minutes on class days reviewing or summarizing their notes. The difficulty of mathematics varies with content, therefore, there may be times when less or more time is required to obtain mastery. This could include (sometimes) studying on Saturdays.

Parental Involvement: Parents’ expectations are simply to ensure that the student has all of the required materials needed for the course, a stable internet connection, a distraction-free environment during class, and adequate time to study outside of class hours. Parent assistance with assignments is not expected and should not be required. However, if your student is accustomed to having your assistance with math, there will likely be a transition period as they build their level of tolerance and confidence in working math independently.

A Typical Class: A typical class 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 delve deeper into. As we delve deeper into answering the question at hand, we begin to discover the new mathematical concept. We are using 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. A discussion takes place that reveals the relevance of this truth in our mathematical studies or our daily lives (real-life application). Students continue to study the new truth and deepen their understanding of it via homework assignments. In subsequent classes, students will continue to study the concept and its relationship to new truths that will be revealed.

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. Alternative methods are interactive computer activities, group assignments, class competitions, and games.

A word from course instructor, Dr. Fransell Riley, on teaching math classically:
When teaching mathematics, my main goal is to infuse students with a passion and eagerness to excel in their study of math. I attempt to connect math to everyday applications, putting math into context with the world around them, taking their learning beyond simply memorizing steps and tricks. I focus on developing the ability to think algebraically. We discover the concepts and while uncovering truths about the concept, we discover the steps or patterns that become an algorithm for solving such problems. I encourage students to learn to embrace the challenge and frustration presented by mathematics. I believe that mathematics is suited perfectly for a classical teaching approach. It provides the perfect forum for the students to develop the virtues of patience and perseverance: patience in accepting the struggle that they encounter while learning a new concept, and perseverance to endure the mistakes and uncertainty that take place while mastering a concept. Mathematics also serves as a constant reminder that sloth and pride (represented by attempting to skip steps while working a problem, failing to work in a neat and orderly fashion, or failing to seek appropriate assistance when needed) will surely lead to failure. Algebra represents a precarious stage of their mathematics development as mathematics begins its transition from the concrete to the abstract. The foundation, upon which the remainder of their mathematics success will depend, is being laid. My passion is fueled by joining students in establishing this foundation during this precarious transition. When they leave my class, I hope that I have helped them to build the resilience, work ethic, algebraic thinking, problem-solving skills, and confidence that they will need to face the challenges awaiting them in the future.



Mrs. Bartko’s Syllabus

Mrs. Terral’s Syllabus

For each skill instructors have determined whether it is a prerequisite skill or a skill to be developed throughout the course. For lower school, instructors indicate where parent support is expected.

  • With Parent Support: Skills that most lower school students will need help with.
  • Developing: Skills that the instructor will help develop and emphasize throughout the year.
  • Mastered: Prerequisite skills that the instructor is expecting students to possess.


  • All Pre-Algebra Course prerequisite skills
  • Integer Operations (Fluent from -10 to 10)
  • Operations with Negative Fractions and Mixed Numbers
  • Laws of Exponents (Fluent at about 1 every 10 seconds)
  • Scientific Notation (Fluent in Converting)
  • Compare and Order Rational Numbers
  • Understand Roots
  • Classify Numbers
  • Identify Proportional Relationships and Direct Variation
  • Solve Multi-Step Equations
  • Proportional Relationships
  • Solve One Step and Two Step Inequalities
  • Probability of Simple and Compound Events
  • Vertical, Adjacent, Complementary, and Supplementary Angles
  • Pythagorean Theorem, Distance Formula
  • Transformations, Congruence, and Similarity
  • Area, Surface Area, Volume of 2D, 3D, and Composite Figures
  • Dimensional Analysis (Conversion Factors)


  • Developing
    • Be able to manage Canvas assignments and submissions (view assignments, check for teacher messages, submit homework as pdf file, submit revisions if necessary, set Canvas notifications for the class, view class notifications when posted, etc.).
    • Be able to review notifications ongoing throughout the year; notifications which include: class announcements, homework assignments, due dates, instructor comments made on assignments, instructor comments made on individual student submissions, instructor comments made on graded items, etc.
    • Be able to set notifications settings to alert the student of class announcements, homework assignments, due dates, instructor comments made on assignments, instructor comments made on individual student submissions, instructor comments made on graded items, etc.
  • Mastered
    • Be able to respectfully and wisely engage with other students and the instructor on Canvas discussion boards.
    • Be able to respectfully, wisely and formally engage with instructor through private Canvas messaging.
    • Be responsible for reviewing teacher feedback, suggestions and comments about student work and employing that feedback as necessary.


  • Developing
    • Be able to build a logical, well-reasoned argument through a written essay providing sound reasoning (i.e. true premises, valid arguments, sound conclusions).
    • Be able to hand-write answers in complete sentences.
  • Mastered
    • Be able to write sentences with basic sentence syntax (i.e. capitalization of first word in a sentence, punctuation at the end of each sentence, space between sentences, capitalization of proper nouns, each sentence having a subject and predicate, etc.).


  • Developing
    • Be able to read material independently and identify questions which require clarification or further explanation from the instructor.
    • Be able to read material independently and identify the information which might be relevant to course discussions and objectives (even if the student doesn’t fully understand all of what’s being read).


  • Mastered
    • Be able to type short answers in complete sentences.


  • Developing
    • Follow class discussions and seminar conversations to record notes without the instructor identifying specifics.
    • Be prepared to generate thoughtful questions to enhance the class discussion, to identify areas needing clarification, and to make valuable connections with other course content.
  • Mastered
    • Follow along with instructor-led note-taking and record notes during class.
    • Be prepared to thoughtfully answer questions when called on in a group setting, during class.
    • Be prepared to volunteer thoughtful comments, answers and ideas in a group setting, during class.


  • Developing
    • Understand the difference between assignments given by an instructor and the necessary and independently initiated need for private study of material.
    • Be able to schedule and manage multiple projects from multiple instructors and courses.
    • Be able to schedule time outside of class to complete independent review of materials.
    • Be able to determine the best places and ways to study at home (i.e. quiet, undistracted, utilizing various methods of review (auditory, written, visual, practice tests, flashcards, etc.).
    • Be responsible to study at home for quizzes, tests and other assessments

*Required Materials:

1. Digital Textbook: Reveal Math Algebra  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 re- view. 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
2. 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 con-cepts covered. Provides students with interesting and challenging
  • 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
  • Scientific Calculator Examples: TI, Sharp, other
  • Notebook Paper and Graph paper
  • Free web accounts:,, 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.


Paper versions of the digital textbook (this would be in addition to the digital text, not instead of): Textbook Vol 1 & Textbook Vol 2 or you can buy used from Amazon: Used Vol 1 and Vol 2 Used

*Required materials are not included in the purchase of the course.

Dr. Fransell Riley spent most of her career working as a quantitative analyst. She earned her PhD in mathematics from the University of Texas at Arlington with every intention of remaining in corporate America. Though she enjoyed her work, she ultimately responded to an internal call to pursue a passion for educating students, including her own children. Fransell has taught math and science to students of all ages from elementary school to college. While teaching, she noticed that her natural teaching style aligned almost perfectly with the concepts of classical education. She takes a holistic approach to teaching and involves her students in discussions aimed at developing a deeper understanding of the concept being taught with the desire that student learning extend beyond memorizing algorithms. Fransell has a passion for mathematics and seeks to share that passion with the next generation. Beyond math, Fransell enjoys spending time with her husband and two sons. They are all athletes and nature lovers; they enjoy participating in sports, hiking, exploring nature, and traveling. When they aren’t enjoying God’s creation, you can find them indoors reading or watching reruns from the Star Trek series.


Danielle Bartko is an experienced Math and Science teacher, and Orthodox Church Cantor and Choir Director. She taught in public schools and a Montessori based Orthodox private school. She has served the American Carpatho-Russian Orthodox Diocese as a Cantor and Choir Director, and the Orthodox Church in America as a Choir Director. She spent countless summers at Camp Nazareth, first as a camper, and later as a counselor and chant teacher.

She holds degrees in Biology and Music from Lafayette College, and Secondary Teacher Certification from DeSales University. She has taught grades 5-12, and currently homeschools her children. She has experience in a variety of teaching methods, and has taught students with diverse academic needs. She is a lifelong learner, and has enjoyed growing and changing as an educator over the years. Her goal is to inspire her students to become lifelong learners as well.

Her Liturgical music education comes from a variety of coursework in Orthodox Music and Choral Directing. She has taken classes through Christ the Saviour Seminary and the OCA Liturgical Music Department, and independent study with Very Rev. Protopresbyter Michael Rosco and Professors Paul Hilko, George Hanas, Andrew Talarovich, and Jerry Jumba. Whenever she travels and visits a church, she will sneak into the choir loft, wait for an invitation to sing with the choir, and then ask for copies of good music to keep as a souvenir.

She grew up in New Jersey, but now lives in Pittsburgh PA with her husband and two young daughters. When she is not homeschooling her children or teaching classes, she enjoys gardening, jigsaw puzzles, SRS Iconography classes, visiting with friends and family, and going to the beach.


Jamie Terral has been teaching math and science in variety of settings including private christian education, online tutoring, community college, and homeschool for the past 20 years. She holds a Bachelor of Science in Biomedical Engineering from Texas A&M University and a Masters of Education from Concordia University Texas. She currently lives with her husband and four children in North Texas. Her husband serves as the pastor of Faith Lutheran Church and together they homeschool their children. Her journey in homeschooling has lead to the discovery of Classical Christian education and the nurturing of restful learning.

Jamie strives to engage her students in the learning process by making her classes enjoyable and creative. When not in the classroom or teaching her own children, Jamie enjoys studying nutrition, growing food, paddle boarding and getting her Vitamin D outside in God’s creation.

Red checkmarkComputer: 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.

Red checkmarkHigh-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.

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

Red checkmarkHeadset: 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

Red checkmarkZoom: 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. unnamed-e1455142229376 To download Zoom:

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

Red checkmarkDigital Tablet: Using a digital tablet in class allows students to more fully engage the course content by working out math problems on the digital whiteboard. We recommend using a Wacom Intuos tablet like this one, though similar products may be used.


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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.