Algebra I

Algebra I serves as the foundation for all future mathematics and science courses. Students continue to study equations, but the focus shifts to solving nonlinear equations (exponential and quadratic). Students begin their study of functions and understand them to be an abstract, algebraic generalization of the relationship between variables. Students will learn about function families and algebraic transformations. They will student the following function families: linear, absolute value, piece-wise, exponential, and quadratic. They will develop 21st-century skills in analyzing data by studying measures of spread and various ways to summarize data.

Students will develop and practice problem-solving skills by working on challenging problems, including competition-level problems. Students will delve into the history of Algebra and participate in philosophical discussions of the course content. 

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. They will practice problem-solving through their study of HOT (Higher-Order-Thinking) 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). 

Watch a sample of Scholé Academy Math instruction with Dr. Fransell Riley

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):

• Solve equations with variables and distribution on both sides of equal sign
• Fluent using the Laws of Exponents
• Calculate Square and Cube Roots
• Converting, Add, Subtract, Multiply Scientific Notation
• Dimensional Analysis (using a Conversion Factor)
• Can Identify a Function
• Write and Solve a System of Equations Using Substitution
• Graph a line using slope and intercept
• Angle Relationships with Parallel Lines
• Pythagorean Theorem and Distance Formula
• Congruence, Similarity, and Transformations on the Coordinate Plane
• Volume of Cylinders, Cones, and Spheres
• Can solve multi-step word problems

Quarter 1

1. Evaluate Numerical and Algebraic Expressions
2. Review Properties of Real Numbers
3. Evaluate Expressions Involving Absolute Value
4. Review Solving Multistep Equations and Proportions
5. Solve Equations with Absolute Value
6. Identify Functions
7. Properties of Graphs
8. Writing Equations of Lines

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

Quarter 2

1. Transformations of Linear Functions
2. Arithmetic and Geometric Sequences
3. Special Functions: Piecewise, Step, Absolute Value
4. Scatterplots, Lines of Fit, Regression
5. Correlation and Causation
6. Solve Two-Step, Multi-Step, and Compound Inequalities
7. Solve Absolute Value Inequalities
8. Graph Inequalities
9. Solve Systems of Equations and Inequalities

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

Quarter 3

1. Rational Exponents
2. Simplifying and Operations with Radical Expressions
3. Exponential Equations and Functions
4. Adding, Subtracting, Multiplying Polynomials
5. Factoring Binomials and Trinomials
6. Graphing and Transforming the Quadratic Equation

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

Quarter 4

1. Solving the Quadratic Equation
2. Combining Functions
3. Solving Systems of Equations with Quadratic and Linear Functions
4. Measures of Central Tendency
5. Measures of Spread: Variance, Standard Deviation
6. Representing and Using Data
7. Distribution of Data
8. Compare and Summarize Data

• 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:
  1. Visit zoom.us/download.
  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.
• 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.