KS3

Algebra Basics

A parent's guide to algebra — what it is, how schools teach it, and how to help.

What Your Child Is Learning

Algebra uses letters to represent numbers we don't know yet. That's it. There's nothing more mysterious to it than that. When your child sees \(x\), it just means "some number we haven't figured out yet." When they see \(3x\), it means "3 times that unknown number" — not "thirty-something."

The letter \(x\) is the most common, but they'll see \(a\), \(n\), \(y\) and others. The choice of letter doesn't change the maths — it's just a label. Your child will learn to write expressions (like \(3x + 2\)), simplify them by collecting like terms, and eventually solve equations to find the value of the unknown.

This is where maths shifts from "doing sums" to "thinking logically." It's a big moment, and it can feel abstract at first. The good news is that the core ideas are straightforward once you see them clearly.

Quick translations

\(3x\) = "3 times x" (not thirty-x)

\(x^2\) = "x times x" (not 2x)

\(3x + 2x = 5x\) = collecting like terms

\(3x + 2\) = you can't simplify this (the terms are different)

How Schools Teach It Now

Schools start with collecting like terms — simplifying expressions by grouping the things that match. Here's how they'd simplify \(3x + 4 + 2x - 1\):

Identify the like terms. The \(x\)-terms are \(3x\) and \(2x\). The number terms (constants) are \(4\) and \(-1\).
Collect the \(x\)-terms. \(3x + 2x = 5x\). Think of it as "3 apples plus 2 apples = 5 apples."
Collect the constants. \(4 - 1 = 3\).
Write the simplified expression. \(5x + 3\). You can't simplify any further because \(x\)-terms and number terms are not like terms.

Schools also teach forming expressions from word problems. For example: "A plumber charges a £30 call-out fee plus £20 per hour." If the number of hours is \(h\), the total cost is \(20h + 30\). Translating real life into algebra is a key skill at KS3.

Common Mistakes to Watch For

Thinking \(x\) always means multiply. In primary school, \(x\) was the multiplication symbol. In algebra, it's a letter. If your child sees \(3x\) and thinks "3 multiplied by... wait, by what?", remind them that \(x\) is now an unknown number, and the multiplication sign is written differently (a dot or just putting things next to each other).
Adding unlike terms. Writing \(3x + 2 = 5x\) is very common. The \(3x\) and the \(2\) are not the same kind of thing. You can't add apples and oranges. \(3x + 2\) is already as simple as it gets.
Confusing expressions and equations. An expression (like \(3x + 2\)) doesn't have an equals sign. An equation (like \(3x + 2 = 14\)) does. You simplify expressions. You solve equations.
Forgetting invisible multiplication. When your child sees \(3(x + 4)\), the number next to the bracket means multiply. So \(3(x + 4) = 3x + 12\). Schools call this "expanding brackets."

Try It Together

The Problem

I think of a number, double it, add 5, and I get 17. What was my number?

Step 1: Call the mystery number \(x\).

Step 2: Double it: \(2x\).

Step 3: Add 5: \(2x + 5\).

Step 4: We know the answer is 17, so: \(2x + 5 = 17\).

Step 5: Subtract 5 from both sides: \(2x = 12\).

Step 6: Divide both sides by 2: \(x = 6\).

Check: Think of 6, double it (12), add 5 (17). Correct.

Try another one: I think of a number, multiply by 3, subtract 4, and I get 11. What was my number? (Answer: 5.)

Let Them Practise

These free games let your child practise algebra skills.

Play Like Terms Collector → Play Think of a Number →

MaffsGames needs no account and no sign-up; what it records while your child plays is set out on the privacy page.

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