Mathematical Curriculum Map™

Numbers and operations — computing with structure.

Expressions — arithmetic generalized with variables.

Equations — solving for unknowns by undoing operations.

Functions — processes mapping inputs to outputs.

Advanced functions — behavior, limits, and change.

Calculus — the derivative as instantaneous rate.

Ratio — comparing quantities multiplicatively.

Proportional relationships — constant multiplicative structure.

Slope — constant rate of change between variables.

Rate of change — in exponential and other families.

Instantaneous rate — the limit of average rates.

Derivative — the slope concept perfected.

Area — counting unit squares in regions.

Circle area — πr² and proportional reasoning.

Formulas — derived areas of polygons and circles.

Coordinate geometry — area computed from coordinates.

Accumulation — summing infinitely many thin slices.

Integral — the area concept perfected.

Patterns — noticing and extending structure.

Sequences — ordered lists with rules.

Functions — rules mapping every input.

Recursive relationships — each term from the last.

Series — summing sequences, finite and infinite.

Angle relationships — vertical, supplementary, parallel lines.

Transformations — angles preserved under motion.

Proof — angle theorems established rigorously.

Right triangles — ratios of sides within angles.

Unit circle — angles as circular motion.

Trigonometric functions — periodic change modeled.

Statistics — describing data with center and spread.

Sampling — why representative data matters.

Scatter plots — two-variable data and trends.

Trend lines — modeling data with functions.

Normal distribution — the model of natural variation.

Inference — confidence intervals and justified conclusions.