Why the Tricks Work

Algebra as proof

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Following a letter through a trick proves it works for every number.
• Factoring reveals hidden structure, like “always a multiple of 5”.
• (n + 1)² − n² = 2n + 1: consecutive squares differ by odd numbers.

Steps

1. A mind-reading trick
2. Design your own trick
3. Five in a row
4. Odd numbers between squares
5. Without squaring
6. Next-door neighbours
7. Reversed digits