What Is Algebra? Letters for Numbers

A1What Is Algebra?

Letters standing in for numbers.

Algebra uses a letter for a number we don't know yet — that's the whole idea.

The mystery box.

? + 3 = 10

n + 3 = 10 → n = 7

The letter n is just the mystery box with a name.

A letter holds the place of a number until we work it out.

Learn the Idea

1Start with a mystery box.

‘Box + 3 = 10’ — children already solve this in Year 2. What's in the box? 7.

☐ + 3 = 10

2Swap the box for a letter.

Algebra just renames the box: n + 3 = 10. Nothing else changed.

n + 3 = 10

3Any letter works.

n, x, y, a — the letter is a label, not a value. n + 3 = 10 and x + 3 = 10 mean the same.

n · x · y

💡 Key IdeaA letter is not an abbreviation — n doesn't stand for ‘number of nuts’, it IS the unknown number itself.

Worked Example

What number is each letter?

m + 5 = 12

m = 7

10 − k = 6

k = 4

3 × w = 18

w = 6

Watch Out! Common Mistakes

Thinking letters are abbreviations.

Careful! In ‘3a’, the a is a NUMBER we don’t know — not ‘apples’. ‘3 apples’ thinking breaks algebra later.

A letter always equals the same thing.

Wrong! n was 7 in one puzzle, but n can be anything in the next. Each problem gives the letter a fresh value.

Panic at the letters.

Reassure! Every algebra question is a mystery-box question wearing a suit. Swap the letter back to ☐ and it looks like Year 2 again.

⬇ Cheat Sheet

WHAT IS ALGEBRA?

A letter = an unknown number (a named mystery box).
Any letter works: n, x, y, a…
The letter's value can change between problems.
Swap letter ↔ box whenever it helps.

Example: n + 3 = 10 → n = 7 (same as ☐ + 3 = 10).

📖 Continue Your Journey

A1 What Is Algebra?A2 Function Machines A3 Writing Expressions A4 Substitution A5 Simplifying Expressions A6 One-Step Equations A7 Two-Step Equations A8 Sequences A9 The nth Term A10 Formulae A11 Bar Models for Unknowns A12 Algebra Problem Solving

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Next Lesson: A2 Function MachinesIn goes a number, out comes another.

📄 Free printable: Download the What Is Algebra? cheat sheet (PDF) — keep it by your child's desk.

Quick summary

A letter stands for an unknown number — a named mystery box.
n + 3 = 10 is exactly ☐ + 3 = 10; the answer is 7 either way.
Any letter can be used and its value is fresh in each problem.
Letters are numbers in disguise, not abbreviations for words.

Frequently asked questions

What is algebra in simple terms?

Working with unknown numbers by giving them letter names. 'Box + 3 = 10' becomes 'n + 3 = 10' — same puzzle, grown-up notation.

Why do children find algebra scary?

The letters look like a new subject, but the thinking is familiar missing-number work. Connecting n back to the mystery box removes the fear.

When is algebra taught in primary school?

Formally in Year 6 in England — simple formulae, sequences and missing-number equations — and it's a favourite 11+ stretch area.

Start here

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