Expressions & Equations (Classical)

Classical mathematics teaches children to think rigorously about numbers and symbols. This program covers Grade 6 expressions and equations through the classical approach: precise definitions first, then systematic practice, with Latin and Greek etymology woven throughout. No word problems dressed up as stories — just disciplined mathematical reasoning.

Nine weeks cover the Common Core 6.EE standards completely. Week 1 establishes numerical expressions and order of operations as logical convention. Week 2 covers whole-number exponents (from the Latin exponere — to set forth). Week 3 introduces variables and algebraic expressions. Week 4 examines equivalent expressions through the distributive property and combining like terms.

The second half of the program focuses on equations. Week 5 distinguishes expressions from equations (from aequatio — equality). Week 6 covers solving one-step equations with inverse operations. Week 7 applies equation-solving to real-world situations. Week 8 extends to inequalities. Week 9 is a comprehensive review.

Each week includes five worksheets with ten problems each, progressing from definition recall through procedural fluency to analytical reasoning. Problems include formal definition exercises, systematic drill, conceptual questions, and application problems — in the Classical tradition of mastering each foundational skill before building on it.

Every worksheet includes full answer keys with detailed explanations, so parents can guide discussions even if they haven’t done algebra in years.