Pre-Algebra (Accelerated)

Content
Pre-Algebra Accelerated is a one-year course that covers all of the pre-algebra concepts taught in Foundations VII and VIII; two-courses in one year. This course is designed for two groups of students:

Those who would thrive from the challenge of an accelerated course due to their joy of math, keen desire to learn math, ability to grasp concepts more quickly than average, or motivation to pursue a STEM field in the future. These are typically 7th grade students who aim to complete Algebra I in 8th grade and advanced math (such as Calculus) before high school graduation.

This course is also suited for those who have already learned most of the concepts but would greatly benefit from another year of study in order to cover gaps and deepen their understanding before starting Algebra I. These are typically 8th/9th grade students.

If neither of these describes your student, then they are likely better suited for the traditional two-year sequence of taking Foundations VII (Pre-Algebra Part 1) followed by Foundations VIII (Pre-Algebra Part 2).

This course is a bridge between Arithmetic and Algebra. Students begin their transition from concrete thinking to abstract thinking by learning how to handle variables in algebraic expressions (combining like terms) and in solving multi-step equations and 2-step inequalities. They will develop fluency in the laws of exponents, and in rational and irrational number operations. Students will expand their understanding of percentages and ratios to include the probability of simple and compound events, learn to identify proportional relationships, and understand the slope of a line. They take their first steps towards understanding relations and functions, domain and range, and solving systems of equations.

Expanding on their geometry foundation, students will learn the Pythagorean Theorem and its uses as well as transformations, congruence, and similarity of shapes. They will study angle relationships, angles in triangles, area, surface area, and volume. They will develop 21st-century skills in analyzing data 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 and understand God’s creation. They will practice different problem-solving strategies: Solve an Easier Problem and Solve a Subproblem.

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):

• Can add, subtract, multiply, and divide integers.
• Determine the Absolute Value of a Number
• Divide Fractions and Mixed Numbers
• Convert between Percent, Fraction, and Decimal
• Find the percent of a number and unit rates
• Graph on the Coordinate Plane
• Solve two-step equations, 
• Calculate mean, median, and mode
• Calculate Surface Area
• Solve percent problems (taxes, tips, interest, etc…)
• Classify Angles
• Calculate Area of Polygons, Circles, and Composite Figures
• Translate verbal phrases into expressions or equations