Algebra Foundations

Algebraic Expressions Preserve Structure

Learn how variables, terms, factors, and equivalent transformations encode quantitative relationships.

Linear Equations Express Balance

Solve one-variable linear equations by preserving equality and interpreting each transformation.

Requires: Algebraic Expressions Preserve Structure

Graphs Turn Relationships into Geometry

Build and interpret coordinate graphs, slope, intercepts, and linear equations as representations of change.

Requires: Linear Equations Express Balance

Functions Organize Input and Output

Understand function notation, domains, tables, graphs, composition, and inverse relationships in algebra.

Requires: Graphs Turn Relationships into Geometry

Sequences Use Position to Organize Values

Understand indexed terms, explicit and recursive rules, and arithmetic and geometric sequence structure.

Requires: Functions Organize Input and Output

Summation Notation Makes Repeated Addition Precise

Read, expand, transform, and evaluate sigma notation—the compact language behind finite sums and Riemann sums.

Requires: Sequences Use Position to Organize Values

Factoring Reveals Polynomial Structure

Reverse distribution, recognize common patterns, and use factors to expose zeros and solve equations.

Requires: Algebraic Expressions Preserve Structure

Quadratic Functions Model Curved Change

Connect standard, factored, and vertex forms to the geometry and behavior of parabolas.

Requires: Factoring Reveals Polynomial Structure · Functions Organize Input and Output

The Quadratic Formula Solves Every Quadratic Equation

Derive the formula by completing the square and interpret its discriminant, roots, and numerical meaning.

Requires: Quadratic Functions Model Curved Change

Systems of Linear Equations Find Shared Constraints

Solve intersections by substitution and elimination, then classify unique, absent, and infinite solutions.

Requires: Linear Equations Express Balance · Graphs Turn Relationships into Geometry