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Concept Taxonomy for Algebra I

This taxonomy organizes the 200 Algebra I concepts into 12 categories, designed for balanced distribution and clear visualization in the learning graph.

1. Foundation Concepts

TaxonomyID: FOUND

Fundamental building blocks of algebra including numbers, variables, constants, and basic algebraic terminology. These are the prerequisite concepts that students must understand before progressing to more advanced topics.

Examples: Number, Variable, Constant, Coefficient, Term, Expression, Equation

2. Properties and Operations

TaxonomyID: PROP

Mathematical properties and order of operations that govern algebraic manipulation, including commutative, associative, distributive, identity, and inverse properties.

Examples: Order of Operations, Commutative Property, Associative Property, Distributive Property

3. Number Systems

TaxonomyID: NUMS

Different types of numbers and their relationships, including integers, rational numbers, real numbers, and number representations.

Examples: Integers, Rational Numbers, Real Numbers, Absolute Value, Number Line

4. Exponents and Radicals

TaxonomyID: EXP

Concepts related to powers, exponents (integer, rational, negative, zero), exponent rules, and radical expressions including square roots and cube roots.

Examples: Exponent, Base, Power, Product Rule for Exponents, Scientific Notation, Square Root

5. Polynomials

TaxonomyID: POLY

Polynomial expressions including monomials, binomials, trinomials, polynomial operations (adding, subtracting, multiplying), and special products.

Examples: Monomial, Binomial, Polynomial, Multiplying Polynomials, FOIL Method, Difference of Squares

6. Factoring

TaxonomyID: FACT

All concepts related to factoring polynomials including GCF, factoring trinomials, difference of squares, perfect squares, and factoring techniques.

Examples: Factoring, Greatest Common Factor, Factoring Trinomials, Zero Product Property, Solving by Factoring

7. Linear Equations and Inequalities

TaxonomyID: LIN

Solving and applying linear equations and inequalities in one variable, including multi-step equations, literal equations, and absolute value equations/inequalities.

Examples: Solving Equations, Multi-Step Equations, Literal Equations, Linear Inequality, Absolute Value Equations

8. Functions and Relations

TaxonomyID: FUNC

Function concepts including definition, notation, domain, range, function types (piecewise, step, absolute value), and function transformations.

Examples: Function, Domain, Range, Function Notation, Piecewise Function, Function Transformation

9. Graphing and Coordinate Geometry

TaxonomyID: GRAPH

Coordinate plane, plotting points, graphing lines, slope concepts, intercepts, and different forms of linear equations.

Examples: Coordinate Plane, Slope, Y-Intercept, Slope-Intercept Form, Plotting Points, Graphing Inequalities

10. Systems

TaxonomyID: SYS

Systems of linear equations and inequalities, solution methods (graphing, substitution, elimination), and applications of systems.

Examples: System of Equations, Substitution Method, Elimination Method, System of Inequalities, Solution Region

11. Quadratic and Exponential Functions

TaxonomyID: QUAD

Quadratic functions, parabolas, solving quadratic equations (multiple methods), exponential functions, growth/decay, and comparing function types.

Examples: Quadratic Function, Parabola, Vertex, Quadratic Formula, Exponential Function, Exponential Growth

12. Data Analysis and Applications

TaxonomyID: DATA

Statistics, data analysis, scatterplots, correlation, regression, sequences, and real-world applications of algebraic concepts.

Examples: Scatterplot, Correlation, Line of Best Fit, Arithmetic Sequence, Applications of Linear Equations

Taxonomy Design Notes

  • Target Distribution: ~16-17 concepts per category (200 ÷ 12 ≈ 16.7)
  • Maximum per Category: <30% of total concepts (<60 concepts)
  • Color Coding: Each category will receive a distinct color in the visualization
  • Pedagogical Progression: Categories generally flow from foundational to advanced topics
  • Balanced Coverage: No single category dominates the learning graph

Category Abbreviation Guidelines

  • All TaxonomyIDs are 3-5 uppercase letters
  • IDs are intuitive and related to category name
  • IDs are unique and used as keys in the learning graph JSON