Grades 4–10
Area & Geometry Reasoning
Area models, cut-and-move proofs, similar triangles and rotations — the picture-first reasoning that leads into high school Geometry.
Where Do Area Formulas Come From?
The General's Horse: A Famous Chinese Shortest-Path Puzzle
The Bird's Head Model: Find This Area in 10 Seconds
The Butterfly Model: Find the Wings in 10 Seconds
Three Equal Angles on a Line: Find This Side in 10 Seconds
The Swallowtail Model: Two Tails, One Simple Ratio
Why a² + b² = c²: 3 Picture Proofs (Easiest First)
Do These 3 Angles Make 90°? No Protractor Needed
Which Triangle Is Biggest? Your Eyes Will Lie to You
Why Do a Triangle's Angles Add Up to 180°? (Picture Proof)
Why Is This Triangle ALWAYS Half the Rectangle?
