The Math Trajectory Map™

60 concept nodes.
One connected graph.

Every math concept from PreK through Grade 12, organized into 6 strands, with every prerequisite relationship traced and every dependency made visible.

Strands:
Number & Quantity
Operations & Algebraic Thinking
Algebra & Functions
Geometry & Spatial Reasoning
Measurement & Data
Data, Stats & Probability
ID format: Strand.Domain.Node
PreK
K – 2
Grades 3 – 5
Grades 6 – 8
Grades 9 – 12
1.0 Number & Quantity 10 nodes
1.1.1 Counting & Cardinality PreK → 1.1.2 Number Recognition K → 1.2.1 Place Value (ones/tens) Gr 1–2 → 1.2.2 Place Value (hundreds+) Gr 2–3 → 1.3.1 Fractions (part-whole) Gr 3 → 1.3.2 Fractions (equivalence) Gr 4–5 → 1.4.1 Rational Numbers Gr 6–7 → 1.4.2 Integer & Absolute Value Gr 6 → 1.5.1 Real Number System Gr 8–9 → 1.5.2 Complex Numbers Gr 11–12
2.0 Operations & Algebraic Thinking 10 nodes
2.1.1 Joining & Separating PreK–K → 2.1.2 Addition & Subtraction Gr 1–2 → 2.2.1 Multiplication (arrays) Gr 3 → 2.2.2 Division & Remainders Gr 3–4 → 2.3.1 Fraction Operations Gr 4–5 → 2.3.2 Ratio & Proportional Reasoning Gr 6–7 → 2.4.1 Percent & Rate Gr 7 → 2.4.2 Expressions & Equations Gr 6–8 → 2.5.1 Polynomial Operations Gr 9–10 → 2.5.2 Exponential & Logarithms Gr 11–12
3.0 Algebra & Functions 10 nodes
3.1.1 Patterns & Sorting PreK–K → 3.1.2 Repeating Patterns Gr 1–2 → 3.2.1 Growing Patterns Gr 3–4 → 3.2.2 Input-Output Tables Gr 4–5 → 3.3.1 Variables & Expressions Gr 6 → 3.3.2 Linear Equations Gr 7–8 → 3.4.1 Functions & Domain Gr 8–9 → 3.4.2 Linear & Quadratic Functions Gr 9–10 → 3.5.1 Trigonometric Functions Gr 10–11 → 3.5.2 Calculus Foundations Gr 12
4.0 Geometry & Spatial Reasoning 10 nodes
4.1.1 Shapes & Positions PreK–K → 4.1.2 2D Shape Properties Gr 1–2 → 4.2.1 Perimeter & Area Gr 3–4 → 4.2.2 3D Shapes & Nets Gr 5–6 → 4.3.1 Coordinate Geometry Gr 6–7 → 4.3.2 Transformations Gr 8 → 4.4.1 Congruence & Similarity Gr 8–9 → 4.4.2 Pythagorean Theorem Gr 8 → 4.5.1 Triangle Trigonometry Gr 10 → 4.5.2 Circles & Conic Sections Gr 11–12
5.0 Measurement & Data 10 nodes
5.1.1 Comparing Length PreK–K → 5.1.2 Standard Units Gr 1–2 → 5.2.1 Time & Money Gr 2–3 → 5.2.2 Area & Volume (formulas) Gr 4–6 → 5.3.1 Unit Conversions Gr 5–6 → 5.3.2 Scale & Proportion Gr 7 → 5.4.1 Rates of Change Gr 8 → 5.4.2 Dimensional Analysis Gr 9–10 → 5.5.1 Limits & Continuity Gr 12 → 5.5.2 Integration (area under curve) Gr 12
6.0 Data, Stats & Probability 10 nodes
6.1.1 Sorting & Classifying PreK–K → 6.1.2 Picture & Bar Graphs Gr 1–3 → 6.2.1 Line Plots & Tables Gr 4–5 → 6.2.2 Mean, Median, Mode Gr 6 → 6.3.1 Probability Basics Gr 7 → 6.3.2 Sampling & Inference Gr 8 → 6.4.1 Distributions & Spread Gr 9 → 6.4.2 Linear Regression Gr 9–10 → 6.5.1 Combinatorics Gr 11 → 6.5.2 Statistical Inference Gr 12
Traceability ID
S.D.N = Strand · Domain · Node 1 = Strand (6 total) 1.2 = Domain within strand 1.2.3 = Specific concept node → solid arrow = prerequisite dependency

Math Trajectory Map™ v1.0 — 60 nodes across 6 strands — expanding to 400+ nodes  ·  © 2026 Cultivate Collective LLC

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