Expressions for children

Quick answer

Expressions are mathematical phrases that use numbers, symbols, and letters to show what we want to calculate. For example, n + 5 or 3 × n are expressions. They help us describe patterns, problems, and situations where we don’t know the exact number yet.

Learning outcome

By the end of this page, you will be able to write and read simple expressions using numbers, symbols, and letters – like n + 5 or 3 × n – to describe maths problems where one number is unknown.

• You can use letters to show a missing number in a maths sentence.
• You can read simple expressions like "n + 5" out loud and understand what it means.
• You can create your own expression for a real-life situation.
• You can match expressions to simple word problems.

Why this matters

Expressions are the first step towards learning algebra – which is a way of solving puzzles using letters and symbols. When you use expressions, you’re already thinking like a mathematician. You can describe problems like “I have some apples, and then I get 5 more” using a maths sentence like n + 5. This helps you solve more complex problems later, like when you’re trying to find out how many apples you started with.

Expressions also help you in everyday life – like when you’re planning a party and need to figure out how many snacks you’ll need, or when you're saving money and want to know how much more you need to save.

How it works

Let’s break down what an expression looks like and how to build one:

1. Numbers are the actual values we know, like 3, 10, or 25.
2. Symbols are the signs we use to show what to do: + (add), – (subtract), × (multiply), ÷ (divide).
3. Letters are used to represent unknown numbers. For example, n might stand for the number of apples you have.

An expression is a combination of these – numbers, symbols, and letters – that makes sense mathematically. It doesn’t have an equals sign like an equation. It just shows a situation or pattern.

For example:

• n + 5 means "some number plus 5"
• 3 × n means "3 times some number"
• n – 2 means "some number minus 2"

Examples you can see

Here are some real-life situations turned into expressions:

Try drawing this: You have 5 toy cars. Your sister gives you 3 more. How many cars do you have now?

Write it as an expression: n + 3 where n = 5. So it’s 5 + 3 = 8.

Or imagine you are making a pattern with blocks. You start with 2 blocks and add 3 more each time. Your pattern is:

• 2 blocks
• 2 + 3 = 5 blocks
• 5 + 3 = 8 blocks

You can write this pattern as an expression: 2 + 3n where n is the number of times you add 3.

Try it as a mini adventure

Adventure: The Mystery Box

You are on a treasure hunt! You find a box with a note that says:

"I have some coins. If I add 10 more, I will have 25 coins. How many coins did I start with?"

Let’s solve this together:

1. Let n be the number of coins you started with.
2. You add 10 more coins: n + 10.
3. You end up with 25 coins: n + 10 = 25.
4. This is an equation, but the expression part is n + 10.

So the expression is n + 10. You can use this expression for any number of coins you start with!

Mini challenge: If you started with 15 coins, how many would you have after adding 10? Use the expression n + 10.

Answer: 15 + 10 = 25 coins.

Common mistakes

• Mistake: Thinking that n + 5 means “5 more than n” but forgetting that the order doesn’t matter in addition.
  Why it happens: Children sometimes mix up which number comes first.
  Fix: Remind them that n + 5 is the same as 5 + n.
• Mistake: Writing n = 5 instead of n + 5 when describing a situation.
  Why it happens: Confusing expressions with equations.
  Fix: Explain that expressions don’t have an equals sign – they show a situation.
• Mistake: Using more than one letter for one unknown.
  Why it happens: Thinking that each unknown needs its own symbol.
  Fix: Use one letter like n for one unknown number.

Parent and carer guide

As a parent or carer, you can help your child by:

1. Using everyday situations: Ask questions like, “If you had 5 cookies and ate some, how many would be left?” Encourage them to write this as an expression like 5 – n.
2. Reading expressions aloud: Say “n plus 5” or “3 times n” instead of “n + 5” or “3 × n”.
3. Playing with letters: Use letter tiles or blocks to build expressions together.
4. Encouraging creativity: Let your child create their own expressions for stories or games.
5. Not pressuring: Expressions are new – it’s okay if they don’t get it straight away. Keep it fun and exploratory!

Watch out for confusion between expressions and equations. Expressions are like a sentence – they show a situation. Equations are like a puzzle – they have an answer!

Practice questions

1. Write an expression for: "You have 8 pencils and give some to your friend."
   Answer: 8 – n
2. Write an expression for: "You buy 4 boxes of crayons, and each box has 12 crayons."
   Answer: 4 × 12
3. What does n + 7 mean?
   Answer: A number plus 7
4. Write an expression for: "You have 3 times as many toys as your sister."
   Answer: 3 × n
5. Which is an expression?
   Answer: n + 5 (not n + 5 = 10)

FAQ

What is the difference between an expression and an equation?

An expression is like a sentence that describes a situation using numbers, symbols, and letters. An equation is like a puzzle that has an equals sign and is asking for an answer.

Can I use any letter for n?

Yes! You can use any letter like n, x, or y to represent a number you don’t know yet.

Why do we use letters in maths?

Letters help us write maths problems when we don’t know the exact number yet. It makes it easier to solve puzzles and describe patterns.

Are expressions only for older kids?

No! You can start using expressions as early as 5 or 6 years old. They are a fun way to think about maths problems.

Can I use expressions in games?

Absolutely! When you’re playing a game and need to figure out how many points you’ll have after scoring some more, you can write it as an expression.