Algebra misconceptions

Quick answer

Algebra misconceptions happen when children think that equations can be changed on only one side, or that the equals sign means "the answer is here" instead of "both sides are the same". Understanding that both sides of an equation must stay balanced is the key to algebra readiness.

Learning outcome

By the end of this page, you will understand that equations must stay balanced, and you will know how to solve simple equations by keeping both sides equal.

• You can spot when someone makes a mistake in an equation
• You can solve simple equations by doing the same thing to both sides
• You can explain why the equals sign means "the same as"
• You can use real-life examples to understand balancing equations

Why this matters

Algebra is all about finding the missing number, and that starts with understanding that both sides of an equation must be the same. When you know how to keep equations balanced, you're ready for more advanced maths like solving for unknowns. It helps in everyday life too – like sharing snacks, splitting a bill, or working out how many toys you can buy with your pocket money.

How it works

Think of an equation like a seesaw. If one side goes up, the other side must go down to stay balanced. If you add something to one side, you must add the same thing to the other side. If you take something away, you must take it away from both sides.

1. Look at the equation and identify what you want to find
2. Find out what you need to do to get that number by itself
3. Do the same thing to both sides of the equation
4. Check your answer by putting it back into the original equation

Examples you can see

Let's look at some examples that show how equations must stay balanced:

Here’s a story to help you imagine this:

Imagine you and your friend are sharing 12 cookies. You each get the same number. So, you write the equation:

2 × ? = 12

You know that 2 times 6 equals 12, so each of you gets 6 cookies. But if someone said, "2 × 6 = 12, so 2 × 6 + 3 = 12 + 3", that would be wrong because it’s not balanced anymore. The new equation would be 12 = 15, which is not true!

Try it as a mini adventure

Let’s go on a maths treasure hunt! You are looking for a secret number in a magical equation. The clue says:

3 + ? = 10

You need to find what number makes the equation true. You can think of it like this:

1. You know 3 + ? = 10
2. To find the missing number, you can take away 3 from both sides
3. 3 + ? - 3 = 10 - 3
4. ? = 7

Check your answer: 3 + 7 = 10. That’s right!

Now try another one:

5 × ? = 20

1. 5 × ? = 20
2. Divide both sides by 5
3. 5 × ? ÷ 5 = 20 ÷ 5
4. ? = 4

Check: 5 × 4 = 20. Yes!

Common mistakes

• Mistake: Changing only one side of an equation

  Why it happens: Children often think the equals sign means "the answer is here" instead of "both sides are the same".

  How to fix it: Always remember to do the same thing to both sides of the equation.

• Mistake: Thinking that equations are like a sentence with an answer at the end

  Why it happens: Children are used to seeing "5 + 3 = 8" and think that's the end of the story.

  How to fix it: Explain that the equals sign means "the same as", not "the answer is here".

• Mistake: Adding or subtracting on only one side

  Why it happens: It's easier to just change one side quickly.

  How to fix it: Always add or subtract the same number to both sides.

Parent and carer guide

As a parent or carer, you can help by:

• Using everyday situations to talk about balance, like sharing snacks or splitting a bill
• Reinforcing that the equals sign means "the same as" and not "the answer is here"
• Practising with simple equations like 5 + ? = 10 or 3 × ? = 12
• Checking that your child does the same thing to both sides of an equation
• Encouraging your child to explain their thinking, not just give an answer

Remember, it's okay to make mistakes – that's how we learn. Be patient and supportive, and keep making maths fun!

Practice questions

1. What number makes this equation true? 4 + ? = 12
2. What number makes this equation true? 7 × ? = 21
3. What number makes this equation true? 10 - ? = 3
4. What number makes this equation true? 6 ÷ ? = 2
5. What number makes this equation true? 5 + 5 = ?

Answers:

1. 8
2. 3
3. 7
4. 3
5. 10

FAQ

What is an algebra misconception?

An algebra misconception is a misunderstanding about how equations work, like thinking that you can change only one side or that the equals sign means "the answer is here".

Why is it important to keep equations balanced?

Keeping equations balanced helps us find the correct answer. If one side changes without the other side changing too, the equation is no longer true.

How can I help my child with algebra misconceptions?

You can help by using real-life examples, talking about balance, and encouraging your child to do the same thing to both sides of an equation.

What comes after learning about balancing equations?

After learning to balance equations, children will move on to solving for unknown numbers, working with variables, and eventually solving more complex algebra problems.

Can I use games to teach balancing equations?

Yes! Games like balancing a seesaw, sharing toys, or playing with weights can help children understand that both sides must be equal.