Most people think of arithmetic and algebra as completely separate worlds. Arithmetic is often seen as the “basic maths” of adding, subtracting, multiplying, and dividing numbers, while algebra is thought of as a more abstract subject involving mysterious letters and symbols. But here’s the secret: algebra is not a different language altogether – it’s simply arithmetic written in patterns. Once you learn how to see those patterns, the leap from numbers to letters becomes far less daunting, and even exciting.
Arithmetic is essentially the study of number patterns. When you add 2 + 2, you are recognising a very simple pattern: “two, repeated twice, makes four.” Multiplication is just a faster way to see a repeated addition pattern: 3 × 4 means “three added four times.”
These simple operations might not seem connected to algebra at first, but they’re the foundation of algebraic thinking. Algebra takes these repeated number patterns and generalises them. Instead of saying “2 + 2 = 4,” algebra allows us to say, “n + n = 2n.” Suddenly, the story isn’t about one single number – it’s about any number.
Let’s look at an example:
The algebraic version is nothing more than a generalised version of the arithmetic one. The letters don’t make the problem harder – they make the idea bigger. Instead of being about just one pair of numbers (5 and 7), it becomes a rule that applies to every possible pair of numbers.
Here’s another example with multiplication:
The second version is the same pattern, expressed in a way that covers all numbers, not just one. Algebra is simply pattern-spotting taken to the next level.
Pattern recognition is at the heart of human intelligence. From music to art, from architecture to science, patterns are what allow us to make predictions, to learn rules, and to understand the world around us. In maths, pattern recognition is the bridge between arithmetic and algebra.
When learners train themselves to spot the repeated steps in arithmetic – such as “every odd number ends with 1, 3, 5, 7, or 9,” or “adding two even numbers always produces an even number” — they are laying the groundwork for algebra. These observations can then be expressed in algebraic form, which makes them universally true, not just true for a handful of examples.
For instance:
What begins as a small observation in arithmetic becomes a general rule in algebra – a law of numbers that works every time.
So how do you get better at spotting patterns? Here are some practical tips:
The key idea is not to memorise, but to notice. Every time you find yourself saying, “Hey, that’s interesting,” you’re already thinking algebraically.
The leap from arithmetic to algebra often feels intimidating, but in reality, it’s a natural next step. Arithmetic gives us individual examples; algebra gives us the general rules. When you learn to see patterns in the numbers you already know, algebra stops being abstract and starts feeling like a natural extension of your everyday arithmetic.
So, the next time you work out a sum, pause and ask yourself: “What pattern is hiding here? How could I write this for any number instead of just one?” That little shift in thinking is the secret link between arithmetic and algebra – and once you see it, you can’t unsee it.
