Patterns and Algebra Thinking

A pattern is a rule wearing a disguise. The sequence 3, 6, 9, 12 looks like a list of numbers, but underneath it hides a rule: add 3 each time. Finding the rule is the real work of mathematics - once you have it, you can predict the hundredth number without writing all ninety-nine before it.

Algebra begins the moment a pattern gets a name. Instead of saying add 3 each time, mathematicians write a rule with a letter, like 3 times n, where n stands for which position you want. The letter is not scary - it is just a box that holds whatever number you choose.

This way of thinking shows up far beyond math class. Saving five dollars every week is a pattern. A song with a repeating chorus is a pattern. Once your brain learns to hunt for the rule underneath, you start seeing the hidden structure of things everywhere you look.