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Maths History

The equal sign adventure

Show how the equals sign means balance, not just 'write the answer here'.

Quick answer

The equal sign (=) means "the same as" or "balanced", not just "write the answer here". You can think of it like a seesaw – both sides must be equal to stay balanced.

Learning outcome

By the end of this page, you will understand that the equal sign shows balance between two sides, just like a seesaw, and that both sides must be the same amount. Success signs:
  • You can explain that 5 + 3 = 8 means the same as 8
  • You can complete equations like 4 + ? = 9
  • You can use the word "balanced" when talking about equations
  • You can spot when equations are balanced or unbalanced

Why this matters

Understanding that the equal sign means balance is important because it helps you solve maths problems correctly. Many children think the equal sign just means "write the answer", but that's not true! If you think of it like a seesaw, you'll do better in maths. This idea helps you work with more complex problems later, like algebra.

How it works

Think of the equal sign like a seesaw. If you have 3 apples on one side and 3 apples on the other side, the seesaw is balanced. That's the same as saying 3 = 3. If you add more apples to one side, the seesaw goes down. To make it balanced again, you need to add the same number to the other side. We can also use the equal sign to show that two things are the same amount even if they look different. For example, 2 + 3 = 5 and 4 + 1 = 5. Both sides equal 5, so they're balanced.

Examples you can see

Let's look at some examples of balanced equations:
Equation Balance Check
5 + 2 = 7 5 + 2 = 7, so both sides are balanced
10 = 4 + 6 10 = 10, so both sides are balanced
3 + 4 = 2 + 5 7 = 7, so both sides are balanced
9 - 3 = 5 6 ≠ 5, so this is not balanced
Here's a real-world example: imagine you have 4 toy cars and your friend has 4 toy cars. You both have the same amount, so 4 = 4. That's balanced! Another example: if you have 6 stickers and your sister has 6 stickers, you both have the same number. So 6 = 6.

Try it as a mini adventure

Adventure: The Balanced Scale Challenge You are a detective solving a mystery. You have a magical scale that only works if both sides are perfectly balanced. 1st time: You put 3 apples on one side and 3 apples on the other side. The scale balances. What equation shows this? 3 = 3 2nd time: You put 5 bananas on one side and 2 bananas + 3 bananas on the other side. The scale balances. What equation shows this? 5 = 2 + 3 3rd time: You put 8 cookies on one side and 4 cookies + ? cookies on the other side. The scale balances. How many cookies go in the box? 4 4th time: You put 10 blocks on one side and 3 blocks + ? blocks on the other side. The scale balances. How many blocks go in the box? 7 5th time: You put 12 crayons on one side and 6 crayons + ? crayons on the other side. The scale balances. How many crayons go in the box? 6

Common mistakes

  • Mistake: Thinking that the equal sign means "write the answer here"
    Why it happens: Many children learn early that after an equals sign comes an answer, so they think it's just a command to write a number.
    Fix: Practice with balance examples. Show that both sides must be equal, not just one side with an answer.
  • Mistake: Writing 5 + 3 = 8 + 2 = 10
    Why it happens: Children think the equals sign means "do this operation" and just keep writing numbers.
    Fix: Explain that each equals sign should connect two balanced sides. 5 + 3 = 8 and 8 = 8, so 5 + 3 = 8 is correct.
  • Mistake: Not understanding that 10 = 5 + 5 is the same as 5 + 5 = 10
    Why it happens: Children think the order matters, but the equal sign shows balance.
    Fix: Show that 10 = 5 + 5 and 5 + 5 = 10 both work because both sides are equal.

Parent and carer guide

To help your child understand the equal sign, try these 5-10 minute activities: What to say:
  • Ask your child: "What does the equal sign mean?"
  • Use everyday examples like "I have 3 apples, and you have 3 apples. We have the same amount, so 3 = 3."
  • Try balance games with toys or food items.
What not to worry about:
  • Your child might think 5 + 3 = 8 + 2 = 10 is correct – that's just a misunderstanding of how to use equals signs
  • It's normal for children to think the equals sign means "go to the next line"
  • Don't rush to correct – let them discover the idea through play
How to help:
  • Use visual aids like blocks or counters to show balance
  • Ask questions like "How can we make both sides equal?"
  • Practice with simple problems like 4 + ? = 7

Practice questions

  1. Complete the equation: 6 + 2 = ?
  2. Complete the equation: 9 = 4 + ?
  3. Complete the equation: 5 + 3 = ? + 1
  4. Is this equation balanced: 7 + 2 = 9? Why or why not?
  5. Complete the equation: 10 = ? + 3
Answers:
  1. 8
  2. 5
  3. 7
  4. Yes, because 7 + 2 = 9
  5. 7

FAQ

What does the equal sign really mean?

The equal sign means "the same as" or "balanced". It shows that both sides of the equation have the same value.

Why is it important to understand this?

It helps you solve more complex maths problems later, like algebra. It also helps you understand that maths is about balance, not just writing answers.

Can the equal sign be used in different ways?

Yes! The equal sign shows that two things are equal. It can be used with numbers, shapes, or even words. For example, 2 + 2 = 4 and 4 = 2 + 2 are both true.

What if I see 5 = 3 + 2?

This is balanced because 3 + 2 = 5, so both sides equal 5.

How can I make this easier for my child?

Use balance examples, like toys or food items. Ask questions like "How can we make both sides equal?" and practice with simple problems.