Taxonomy Distribution Report

Overview

• Total Concepts: 200
• Number of Taxonomies: 12
• Average Concepts per Taxonomy: 16.7

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
QUAD	QUAD	27	13.5%	✅
GRAPH	GRAPH	26	13.0%	✅
LIN	LIN	25	12.5%	✅
FUNC	FUNC	20	10.0%	✅
POLY	POLY	18	9.0%	✅
DATA	DATA	18	9.0%	✅
EXP	EXP	15	7.5%	✅
FACT	FACT	15	7.5%	✅
SYS	SYS	14	7.0%	✅
Foundation Concepts - Prerequisites	FOUND	10	5.0%	✅
PROP	PROP	6	3.0%	✅
NUMS	NUMS	6	3.0%	✅

Visual Distribution

QUAD   ██████  27 ( 13.5%)
GRAPH  ██████  26 ( 13.0%)
LIN    ██████  25 ( 12.5%)
FUNC   █████  20 ( 10.0%)
POLY   ████  18 (  9.0%)
DATA   ████  18 (  9.0%)
EXP    ███  15 (  7.5%)
FACT   ███  15 (  7.5%)
SYS    ███  14 (  7.0%)
FOUND  ██  10 (  5.0%)
PROP   █   6 (  3.0%)
NUMS   █   6 (  3.0%)

Balance Analysis

✅ No Over-Represented Categories

All categories are under the 30% threshold. Good balance!

Category Details

QUAD (QUAD)

Count: 27 concepts (13.5%)

Concepts:

• 1. Quadratic Function
• 1. Parabola
• 1. Vertex
• 1. Axis of Symmetry
• 1. Maximum Value
• 1. Minimum Value
• 1. Standard Form of Quadratic
• 1. Vertex Form
• 1. Graphing Quadratics
• 1. Quadratic Equation
• 1. Solving Quadratics by Graphing
• 1. Solving by Square Roots
• 1. Completing the Square
• 1. Quadratic Formula
• 1. Discriminant
• ...and 12 more

GRAPH (GRAPH)

Count: 26 concepts (13.0%)

Concepts:

• 1. Graphing Inequalities
• 1. Coordinate Plane
• 1. Ordered Pair
• 1. X-Coordinate
• 1. Y-Coordinate
• 1. Origin
• 1. Quadrants
• 1. Plotting Points
• 1. Linear Function
• 1. Graph of a Line
• 1. X-Intercept
• 1. Y-Intercept
• 1. Slope
• 1. Rise
• 1. Run
• ...and 11 more

LIN (LIN)

Count: 25 concepts (12.5%)

Concepts:

• 1. Solving Equations
• 1. One-Step Equations
• 1. Two-Step Equations
• 1. Multi-Step Equations
• 1. Variables on Both Sides
• 1. Equations with Fractions
• 1. Equations with Decimals
• 1. Literal Equations
• 1. Solving for a Variable
• 1. Formula Manipulation
• 1. Linear Equation in One Variable
• 1. Solution Set
• 1. Identity Equation
• 1. Contradiction
• 1. Conditional Equation
• ...and 10 more

FUNC (FUNC)

Count: 20 concepts (10.0%)

Concepts:

• 1. Relation
• 1. Function
• 1. Domain
• 1. Range
• 1. Input
• 1. Output
• 1. Function Notation
• 1. Evaluating Functions
• 1. Independent Variable
• 1. Dependent Variable
• 1. Vertical Line Test
• 1. Discrete Function
• 1. Continuous Function
• 1. Piecewise Function
• 1. Step Function
• ...and 5 more

POLY (POLY)

Count: 18 concepts (9.0%)

Concepts:

• 1. Like Terms
• 1. Combining Like Terms
• 1. Simplifying Expressions
• 1. Expanding Expressions
• 1. Monomial
• 1. Binomial
• 1. Trinomial
• 1. Polynomial
• 1. Degree of Polynomial
• 1. Leading Coefficient
• 1. Standard Form of Polynomial
• 1. Adding Polynomials
• 1. Subtracting Polynomials
• 1. Multiplying Polynomials
• 1. FOIL Method
• ...and 3 more

DATA (DATA)

Count: 18 concepts (9.0%)

Concepts:

• 1. Applications of Linear Equations
• 1. Consecutive Integers
• 1. Perimeter Problems
• 1. Distance Rate Time Problems
• 1. Applications of Systems
• 1. Applications of Quadratics
• 1. Projectile Motion
• 1. Compound Interest
• 1. Data Set
• 1. Scatterplot
• 1. Correlation
• 1. Positive Correlation
• 1. Negative Correlation
• 1. No Correlation
• 1. Line of Best Fit
• ...and 3 more

EXP (EXP)

Count: 15 concepts (7.5%)

Concepts:

• 1. Exponent
• 1. Base
• 1. Power
• 1. Integer Exponents
• 1. Rational Exponents
• 1. Negative Exponents
• 1. Zero Exponent
• 1. Product Rule for Exponents
• 1. Quotient Rule for Exponents
• 1. Power Rule for Exponents
• 1. Scientific Notation
• 1. Square Root
• 1. Cube Root
• 1. Radical Expression
• 1. Simplifying Radicals

FACT (FACT)

Count: 15 concepts (7.5%)

Concepts:

• 1. Factoring
• 1. Greatest Common Factor
• 1. Factoring by GCF
• 1. Factoring Trinomials
• 1. Factoring Difference of Squares
• 1. Factoring Perfect Squares
• 1. Factoring by Grouping
• 1. Prime Factorization
• 1. Prime Polynomial
• 1. Zero Product Property
• 1. Solving by Factoring
• 1. Factoring Completely
• 1. Sum of Cubes
• 1. Difference of Cubes
• 1. Factoring Quadratic Form

SYS (SYS)

Count: 14 concepts (7.0%)

Concepts:

• 1. System of Equations
• 1. Solution of a System
• 1. Consistent System
• 1. Inconsistent System
• 1. Independent System
• 1. Dependent System
• 1. Graphing Method
• 1. Substitution Method
• 1. Elimination Method
• 1. Linear Combination
• 1. System of Inequalities
• 1. Graphing Systems
• 1. Solution Region
• 1. Boundary Line

Foundation Concepts - Prerequisites (FOUND)

Count: 10 concepts (5.0%)

Concepts:

• 1. Number
• 1. Variable
• 1. Constant
• 1. Coefficient
• 1. Term
• 1. Expression
• 1. Equation
• 1. Inequality
• 1. Evaluating Expressions
• 1. Substitution

PROP (PROP)

Count: 6 concepts (3.0%)

Concepts:

• 1. Order of Operations
• 1. Commutative Property
• 1. Associative Property
• 1. Distributive Property
• 1. Identity Property
• 1. Inverse Property

NUMS (NUMS)

Count: 6 concepts (3.0%)

Concepts:

• 1. Integers
• 1. Rational Numbers
• 1. Real Numbers
• 1. Absolute Value
• 1. Number Line
• 1. Coordinate System

Recommendations

• ✅ Excellent balance: Categories are evenly distributed (spread: 10.5%)
• ✅ MISC category minimal: Good categorization specificity

Educational Use Recommendations

• Use taxonomy categories for color-coding in graph visualizations
• Design curriculum modules based on taxonomy groupings
• Create filtered views for focused learning paths
• Use categories for assessment organization
• Enable navigation by topic area in interactive tools

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Report generated by learning-graph-reports/taxonomy_distribution.py