Variables for children

Quick answer

Variables are letters or symbols that stand for numbers that can change or are unknown. They help us write maths problems more clearly and solve puzzles where we don’t know all the numbers yet.

Learning outcome

By the end of this page, you will understand that variables are letters or symbols that can stand for different numbers, and you will be able to use simple variables in maths problems.

• You can spot when a letter is being used as a variable in a maths sentence.
• You can use a variable to represent an unknown number in a problem.
• You can solve simple problems where one number is missing.
• You can explain how variables make maths easier to write and understand.

Why this matters

Variables are a big step towards algebra, which is a way of solving puzzles with numbers. You already use variables in your everyday life without realising it! When you say "I have some apples" or "I need a few more coins", you are using a kind of variable. Variables help us write maths problems more clearly and solve puzzles where we don’t know all the numbers yet.

Learning about variables helps you think more like a mathematician. It shows you that maths isn’t just about adding and subtracting, but also about patterns, relationships, and problem-solving. Variables are used in games, science, cooking, and even in sports!

How it works

Think of a variable like a box that can hold different numbers. The box has a label on it, like x, y, or ?. We don’t know what number is inside the box yet, but we can use it in our maths problems.

Here’s how it works:

1. Choose a letter or symbol to represent a number that we don’t know yet.
2. Write a maths sentence using that letter.
3. When we get more information, we can find out what number goes in the box.

Let’s explore this with some examples.

Examples you can see

Imagine you are at a party and you want to share some cookies equally between your friends. You don’t know how many friends are coming, so you use a variable to show that number.

Let’s say f is the number of friends.

If you have 12 cookies, you can write:

12 ÷ f = number of cookies per friend

So if f = 3, then each friend gets 4 cookies. If f = 4, then each friend gets 3 cookies.

Another example:

You have some money in your pocket. Let’s say m is the amount of money you have. You want to buy a toy that costs £5. So you can write:

m – 5 = amount left after buying the toy

If you had £10, then you’d have £5 left. If you had £15, then you’d have £10 left.

Variables are also used in simple puzzles:

5 + ? = 12

We can write this as:

5 + x = 12

Here, x is the variable. It stands for the number that makes the sentence true. In this case, x = 7.

Let’s try another one:

3 × y = 18

Here, y is the variable. It stands for the number that makes the sentence true. In this case, y = 6.

Try it as a mini adventure

Imagine you are a detective trying to solve a mystery! You find a note that says:

"I had some stickers. I gave 5 to my friend. Now I have 8 stickers left."

Let’s use a variable to find out how many stickers you started with.

Let’s say s is the number of stickers you started with.

You gave 5 away, so you had:

s – 5 = 8

Now you need to find s. How many stickers did you start with?

Step 1: s – 5 = 8

Step 2: Add 5 to both sides to find s

Step 3: s = 8 + 5

Step 4: s = 13

You started with 13 stickers!

Let’s do another one:

"I bought some pencils. I used 3 and now I have 9 left."

Let’s say p is the number of pencils you bought.

p – 3 = 9

Step 1: p – 3 = 9

Step 2: Add 3 to both sides

Step 3: p = 9 + 3

Step 4: p = 12

You bought 12 pencils!

Common mistakes

• Mistake: Thinking that a variable always means the same number.
  Why it happens: Children often think that if a letter is used in a sentence, it must be a fixed number.
  Fix: Explain that a variable is like a box that can hold different numbers. It changes depending on the situation.
• Mistake: Not understanding that variables are just symbols for numbers.
  Why it happens: Some children think variables are special or magical.
  Fix: Use real-life examples like a box labeled "x" that can hold different things (cookies, toys, stickers).
• Mistake: Confusing variables with letters in words.
  Why it happens: When children see letters in maths, they might think they are part of words.
  Fix: Make it clear that in maths, letters like x and y are just symbols for numbers.
• Mistake: Writing the wrong symbol for a variable.
  Why it happens: Sometimes children pick a symbol that looks like a number or a word.
  Fix: Encourage using simple letters like x, y, or z for variables.

Parent and carer guide

Helping your child understand variables doesn’t need to be hard! Here’s how you can support them in just 5–10 minutes:

1. Use everyday situations: Talk about things like "I have some coins in my pocket" or "We need to share 12 cookies". Use variables to show unknown numbers.
2. Play a game: Create a simple game where you say "I have some stickers, I gave 3 away and now I have 5 left. How many did I start with?" Let your child solve it using a variable.
3. Ask questions: Ask your child to explain what a variable is. If they say it's a letter that stands for a number, they’re on the right track!
4. Don’t rush: Variables are new, so don’t expect your child to get it right away. Practice makes progress!
5. Keep it fun: Use drawings, toys, or snacks to make it more engaging. The more fun it is, the more they’ll remember.

Remember: Variables are just a way to write maths problems more clearly. Don’t worry if your child doesn’t get it all at once. It’s a big idea that takes time to grow into.

Practice questions

1. Write a sentence using the variable n to show that you had 10 sweets and ate some. You now have 4 left. What is the sentence?
2. If y + 7 = 15, what is y?
3. Write a sentence using the variable z to show that you had some pencils, you gave 6 away, and now you have 9 left.
4. If 8 + x = 14, what is x?
5. Write a sentence using the variable m to show that you had 15 cookies, you gave some to your friend, and now you have 6 left.

Answers:

1. 10 – n = 4
2. y = 8
3. z – 6 = 9
4. x = 6
5. 15 – m = 6

FAQ

What is a variable?

A variable is a letter or symbol that stands for a number that can change or is unknown.

Why do we use variables?

We use variables to make maths problems easier to write and understand. They help us solve puzzles where we don’t know all the numbers yet.

Can variables be any letter?

Yes, variables can be any letter of the alphabet. Common ones are x, y, and z.

Do variables always have to be numbers?

Yes, variables always stand for numbers in maths. They can be different numbers in different situations.

How are variables used in real life?

Variables are used in many ways, like planning a party, cooking recipes, or sharing snacks. They help us solve problems by showing what we don’t know yet.