Partitioning numbers

Quick answer

Partitioning numbers means splitting a number into smaller parts in different ways, which helps you add, subtract, and multiply more easily.

Learning outcome

By the end of this page, you will be able to split numbers into parts in different ways to make calculations easier.

• You can break down bigger numbers into smaller parts.
• You can use these parts to add or subtract quickly in your head.
• You can understand how numbers are made up of tens and ones (or hundreds, tens, and ones).
• You can use partitioning to solve maths problems more confidently.

Why this matters

Partitioning numbers is a powerful maths skill that helps you think about numbers in flexible ways. When you break a number into parts, it makes mental maths easier. This skill is used in everyday life, like when you’re sharing snacks, calculating how much money you have, or working out how many steps you’ve walked.

Partitioning is also important for understanding how numbers work. It helps you build a strong number sense, which is the ability to understand how numbers relate to each other. This skill will help you in more advanced maths later, like working with decimals, fractions, and larger numbers.

How it works

Partitioning means splitting a number into smaller parts. For example, the number 27 can be split into 20 and 7, or 25 and 2, or even 10 and 17. You can split it any way you like, as long as the parts add up to the original number.

Here’s how you can partition numbers:

1. Look at the number. For example, 36.
2. Think of different ways to split it. You could split 36 into 30 and 6, or 20 and 16, or 10 and 26.
3. Choose the way that makes your calculation easier. If you're adding 36 + 15, splitting 36 into 30 and 6 might help you add 30 + 15 = 45, then add 6 = 51.

Examples you can see

Let’s look at how we can partition some numbers in different ways.

Partitioning numbers is especially helpful when adding or subtracting mentally. Let’s try an example:

Problem: 34 + 27

Step 1: Partition 34 into 30 and 4.

Step 2: Partition 27 into 20 and 7.

Step 3: Add the tens first: 30 + 20 = 50.

Step 4: Add the ones: 4 + 7 = 11.

Step 5: Add the totals: 50 + 11 = 61.

This way, you’re not trying to add 34 + 27 all at once. Instead, you're adding smaller parts that are easier to work with.

Try it as a mini adventure

The Great Number Hunt

You are on a treasure hunt! You’ve found a map that says “To find the treasure, split the number 63 into parts that are easier to add.”

First stop: Split 63 into 60 and 3.

Second stop: Now, add 63 + 19. Partition 19 into 10 and 9.

Third stop: Add 60 + 10 = 70.

Fourth stop: Add 3 + 9 = 12.

Fifth stop: Add 70 + 12 = 82.

Congratulations! You’ve found the treasure!

Try this again with other numbers like 45 + 38 or 76 + 24. Each time, choose how to split the numbers to make the maths easier.

Common mistakes

• Mistake: Thinking that partitioning means breaking numbers into equal parts only.
• Why it happens: Children may think that 10 can only be split as 5 + 5, but it can be 6 + 4, 7 + 3, or even 1 + 9.
• Fix: Show that there are many ways to split a number, and any split that adds up to the original is correct.
• Mistake: Forgetting to check that the parts add up to the original number.
• Why it happens: When children are excited about splitting numbers, they might make a mistake and not double-check.
• Fix: Always add your parts back together to make sure they equal the original number.
• Mistake: Using partitioning only for addition, not for subtraction.
• Why it happens: Children often see partitioning as just for adding, not for taking away.
• Fix: Practice partitioning for subtraction too. For example, 56 – 23 can be split into 56 – 20 = 36, then 36 – 3 = 33.

Parent and carer guide

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

1. Practising partitioning at home. Use everyday items like coins, blocks, or counters to split numbers into parts.
2. Playing games. Try a game where you ask your child to split a number into two parts, or challenge them to find as many ways as possible.
3. Encouraging mental maths. Let them split numbers in their head to solve simple sums like 43 + 27.
4. Using real-life examples. When shopping, ask your child to split the price of an item into parts, like £3.50 into £3 and 50p.
5. Not rushing. Let your child explore different ways to split numbers without pressure.

Remember, the goal is not to memorise, but to understand how numbers work. Celebrate their thinking and ask questions like, “How did you split that?” or “Can you think of another way?”

Practice questions

1. Partition 45 into two parts. What are two possible ways?
2. Split 72 into tens and ones. What is one way to do this?
3. Partition 89 into two parts. What are two ways you can do this?
4. Use partitioning to solve: 54 + 28.
5. Use partitioning to solve: 67 – 39.

Answers:

1. 40 + 5 or 30 + 15
2. 70 + 2
3. 80 + 9 or 40 + 49
4. 54 + 28 = 82 (split 54 into 50 + 4 and 28 into 20 + 8, then add 50 + 20 = 70, 4 + 8 = 12, then 70 + 12 = 82)
5. 67 – 39 = 28 (split 39 into 30 + 9, then 67 – 30 = 37, then 37 – 9 = 28)

FAQ

What is partitioning in maths?

Partitioning means splitting a number into smaller parts. These parts can be added together to make the original number.

Why is partitioning useful?

It helps you solve addition and subtraction problems more easily by breaking them into smaller, manageable parts.

Can I partition any number?

Yes, any number can be partitioned in many different ways. For example, 10 can be split as 5 + 5, 6 + 4, or 1 + 9.

How can I practice partitioning at home?

You can use objects like blocks, coins, or counters to split numbers into parts. Try asking, “How can we split 25 into two parts?”

Is partitioning the same as rounding?

No. Partitioning splits a number into parts that add up to the original number, while rounding changes a number to the nearest ten, hundred, etc.