Balance scale equations

Quick answer

Balance scale equations help you find the missing number in a maths problem by making both sides equal, just like a real balance scale.

Learning outcome

By the end of this page, you will understand how to use a balance scale to find missing numbers in equations, and you'll know that both sides of an equation must always be equal.

• You can see that both sides of an equation must be the same
• You can solve simple equations by adding or removing the same amount from both sides
• You can use balance scale thinking to find unknown values
• You can apply this idea to real-life problems like sharing snacks or comparing weights

Why this matters

Balance scale equations are a fun and visual way to learn algebra. You already use this idea when you share snacks equally, or when you compare weights of things. Understanding how to keep both sides equal helps you solve more complex maths problems later. It's like learning to play a game before you can win it!

How it works

Think of a balance scale like a seesaw. If both sides are the same weight, it stays balanced. In maths, if both sides of an equation are equal, it's balanced. To find the missing number, you need to make sure both sides stay equal while you work out what the unknown number is.

1. Look at the equation and find the missing number
2. Think about what you need to do to keep both sides equal
3. Add or take away the same amount from both sides
4. Work out what the missing number is

Examples you can see

Let's look at some balance scale examples to understand how it works.

Here's a simple example you can imagine:

You have a balance scale. On the left side, you put 4 apples. On the right side, you put 6 apples. The scale is not balanced. To make it balanced, you need to add 2 more apples to the left side. Now both sides have 6 apples. The equation is: 4 + 2 = 6.

Try it as a mini adventure

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

"The weight of a box is 12 kg. If you take away 5 kg, the remaining weight is the same as the weight of a bag. What is the weight of the bag?"

Let's solve this like a detective:

1. Start with the scale: 12 kg - 5 kg = ? kg
2. Think: What number minus 5 equals the weight of the bag?
3. Work it out: 12 - 5 = 7
4. So the bag weighs 7 kg

Great detective work! You found the weight of the bag. Try this challenge:

1. Draw a balance scale with 8 on one side
2. On the other side, draw a box with a question mark
3. How much weight should be in the box to make it balanced?

Common mistakes

• Mistake: Thinking that adding something to one side without adding it to the other side keeps the equation balanced.
• Why it happens: You might forget that a balanced scale needs both sides to be equal.
• Fix: Always add or take away the same amount from both sides.

• Mistake: Not checking if both sides are equal after solving.
• Why it happens: You might be in a hurry to get the answer.
• Fix: After solving, put the answer back into the equation to check.

• Mistake: Thinking that the missing number can be any number.
• Why it happens: You might not understand that equations have only one correct answer.
• Fix: Remember that both sides must be equal, so there's only one right answer.

Parent and carer guide

Helping your child with balance scale equations is easy and fun!

1. Start with physical examples: Use a real balance scale or draw one on paper. Place small objects on each side and ask your child to make it balance.
2. Ask questions: "What do you need to add to make it equal?" or "What number makes both sides the same?"
3. Use everyday situations: When sharing snacks, talk about how to make it fair. "If you have 5 cookies and I have 3, how many more do you need to have the same?"
4. Keep it light: Don't worry if they get it wrong at first. Mistakes help you learn!
5. Practice together: Try simple equations like 3 + ? = 8 or 10 - ? = 4. Solve them together and check the answers.

Practice questions

1. What number makes this equation balanced? 5 + ? = 9
2. Find the missing number: 12 - ? = 7
3. Solve: ? + 4 = 11
4. What number balances this? 6 + 3 = ?
5. Complete the equation: 15 - ? = 9
6. Find the missing number: 8 + ? = 13
7. Solve: ? - 5 = 6
8. What number makes both sides equal? 7 + 2 = ?
9. Complete: 10 - ? = 3
10. What number goes in the box? ? + 5 = 12

Answers:

1. 4
2. 5
3. 7
4. 9
5. 6
6. 5
7. 11
8. 9
9. 7
10. 7

FAQ

What is a balance scale equation?

A balance scale equation is a maths problem where you need to find a missing number to make both sides of an equation equal, just like a balance scale that stays level when both sides have the same weight.

Why do we need to learn about balance scales?

Learning about balance scales helps you understand how equations work. It's a fun way to think about making things equal, which is important in many real-life situations like sharing food or comparing weights.

Can I use balance scale thinking in games?

Yes! You can use balance scale thinking when you're playing games that involve sharing, comparing, or balancing. For example, in a board game, if you have more points than your friend, you might need to give some away to make it fair.

How can I practice balance scale equations?

You can practice by drawing balance scales, using real objects like toys or food, or solving simple equations like 5 + ? = 10. Try to always make sure both sides are equal!

Is this the same as algebra?

Yes! Balance scale equations are a simple version of algebra. They teach the same idea: finding unknown values by keeping equations balanced. As you grow up, you'll use this same thinking in more complex algebra problems.