Pre-Algebra Syllabus

Set your child up for success in Algebra and beyond with our Pre-Algebra program! This engaging course thoroughly prepares students for the challenges of advanced math by teaching essential problem-solving techniques and commonly used algorithms. Students will master core concepts, including properties of arithmetic, fractions, decimals, percents, ratios, rates, proportions, complex unit conversions, number theory, geometry, and statistics. Perfect for middle school students who are comfortable with all arithmetic operations across rational numbers and skilled in using variables in expressions and equations, this program ensures they’re ready for the rigor of Algebra.

Aligned with the Common Core State Standards for Pre-Algebra, our curriculum is enhanced with logic puzzles, competition-style challenges, and hands-on problem-solving exercises—delivering a math experience that goes far beyond traditional programs.

Required Textbook: Art of Problem Solving: Pre-Algebra

Required for: Algebra A

Concepts, skills, and learning tools students see in this course include, but are not limited to:

• Solidifying understanding of Arithmetic, Counting, Exponents, Square Roots, Number Theory, Decimals, Percents, and Fractions
• Expressing and Solving Equations and Inequalities, Ratios and Proportions and analyzing Data and Statistics
• Foundational knowledge of Angles, Perimeter and Area, Right Triangles and Quadrilaterals
• Problem-solving skills, logic puzzles, algebraic and geometric thinking, competition-style problems

Upon completing the course, students will be able to:

• Numbers: Understand properties of arithmetic (e.g., commutative and distributive), evaluate expressions with exponents and roots, explore number theory (real numbers, fractions, decimals, percents), and apply counting principles.
• Number Relationships: Solve equations and inequalities, work with ratios, proportions, and rates, and analyze data from graphs and datasets.
• Geometric Concepts: Identify and work with different types of angles, polygon relationships, and parallel lines, and calculate perimeters and areas of polygons.
• Right Triangles and Quadrilaterals: Apply properties like the Pythagorean theorem to right triangles and understand quadrilateral properties.

Students registering for this course should be comfortable with the following Math:‍

• Identifying numbers up to 1 billion
• Able to perform arithmetic operations with all rational numbers, including addition, subtraction, multiplication, & division of fractions, decimals, including both positive and negative numbers
• Drawing and labeling a Cartesian plane
• Translating word problems into mathematical expressions
• Using variables in expressions and equations

• Foundations of Algebra (9 weeks): Explore variables, expressions, properties of operations, and multi-step equations, including work with inequalities and graphing.
• Fractions, Decimals, and Percents (6 weeks): Master operations with fractions and decimals, convert between fractions and decimals, and understand percentages, including percentage change.
• Ratios, Rates, and Proportions (6 weeks): Dive into ratios, proportions, unit conversions, speed, and practical applications of percentages.
• Statistics and Probability (6 weeks): Learn common statistical measures, represent data, explore counting techniques, and calculate basic probabilities.
• Geometry and Measurement (11 weeks): Study angles, parallel lines, polygons, area, and perimeter; calculate with circles and special triangles, including the Pythagorean theorem.