ZMath Teacher Zhang Free lessons
Free lessons

Short visual lessons, with the full write-up

Every lesson shows why the method works, with a step-by-step write-up and a problem to try.

Fractions, Ratios & Percents ›

Why the rules work — and how fractions lead into ratios, percents and equations.

First lessons coming soon.

Number Sense & Mental Math ›

See why the shortcuts work, using area pictures you can draw yourself.

Multiply 23 × 27 in 3 Seconds

30 s · Number Sense & Mental Math

Multiply 37 × 77 in 3 Seconds

38 s · Number Sense & Mental Math

×11 in 3 Seconds: Pull Apart, Add the Middle

1:38 · Number Sense & Mental Math

49 × 51 in Your Head? Cut One Strip and It's Easy

1:55 · Number Sense & Mental Math

Square Any Number Ending in 5 in Your Head (35², 75²…)

1:58 · Number Sense & Mental Math

Add 1 to 100 in Seconds: Gauss's Trick (With a Picture)

1:47 · Number Sense & Mental Math

Word Problems & Algebra ›

Draw the problem first, then the equation writes itself.

35 Heads, 94 Legs: A 1,500-Year-Old Puzzle, 3 Ways

2:11 · Word Problems & Algebra

Area & Geometry Reasoning ›

Cut, move and compare shapes to see why formulas are true.

Where Do Area Formulas Come From?

2:09 · Area & Geometry Reasoning

The General's Horse: A Famous Chinese Shortest-Path Puzzle

1:29 · Area & Geometry Reasoning

The Bird's Head Model: Find This Area in 10 Seconds

1:32 · Area & Geometry Reasoning

The Butterfly Model: Find the Wings in 10 Seconds

1:41 · Area & Geometry Reasoning

Three Equal Angles on a Line: Find This Side in 10 Seconds

1:23 · Area & Geometry Reasoning

The Swallowtail Model: Two Tails, One Simple Ratio

2:06 · Area & Geometry Reasoning

Why a² + b² = c²: 3 Picture Proofs (Easiest First)

2:55 · Area & Geometry Reasoning

Do These 3 Angles Make 90°? No Protractor Needed

2:59 · Area & Geometry Reasoning