Mastering Algebraic Proofs with Two-Column Tables

Miacademy & MiaPrep Learning Channel

This video introduces students to the concept of algebraic proofs, shifting the focus from simply solving equations to justifying each step of the process using properties of equality. The lesson uses the standard two-column proof format (Statements and Reasons) to organize logical arguments. The narrator, Justin, guides viewers through transforming a standard algebraic equation solution into a formal proof, explaining how to cite specific properties like the Subtraction, Multiplication, and Additive Properties of Equality. The video walks through two distinct examples in detail. The first example converts a multi-step linear equation into a proof, establishing the basic structure. The second example demonstrates that there can be multiple valid ways to prove the same conclusion (e.g., distributing versus dividing first) and introduces the Symmetric Property of Equality for formatting the final answer. The importance of efficiency and logical ordering is highlighted through a side-by-side comparison of methods. Ideally suited for Algebra I students, this resource bridges the gap between computational algebra and the logical reasoning required for geometry and advanced math. It reinforces the vocabulary of mathematical properties (Distributive, Symmetric, etc.) and emphasizes that mathematical work requires rigorous justification, not just a correct final answer.