Ross MackellUK-qualified primary teacher · 9 min read

Your child's homework says "Partition 347." Underneath there's a circle with three little circles hanging off it, like a bunch of cherries. You never did this at school. You're not sure what the teacher wants, and your child isn't sure either.

Here's the good news. Partitioning is one of the simplest ideas in primary maths, and once it clicks, an awful lot of other maths suddenly makes sense. Mental addition, column subtraction, multiplication, even decimals: they all lean on it.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll explain what partitioning is, the two kinds your child will meet, the pictures schools use to teach it, why it matters so much, and a 10-minute routine you can do at the kitchen table.

What is partitioning?

Partitioning is breaking a number into smaller parts. That's it. The parts always add back up to the number you started with.

The most common way to partition is by place value. Each digit in a number has a value depending on where it sits. In 347, the 3 is worth 300, the 4 is worth 40 and the 7 is worth 7. So:

347 = 300 + 40 + 7

If your child isn't sure why the 3 is worth 300, partitioning isn't really the problem. Place value is. Start with my guide on what place value is, then come back here.

You'll also see this written as "3 hundreds, 4 tens and 7 ones". Same thing, different words. Most schools now say ones rather than units, which is one of those small changes that confuses parents. (I explain a few more in why maths is taught differently now.)

Standard and non-standard partitioning

This is the bit that catches parents out. Children don't just learn one way to partition a number. They learn lots.

Standard partitioning splits a number into hundreds, tens and ones: 347 = 300 + 40 + 7. There's only one way to do it.

Non-standard partitioning splits it any other way that still adds up to the same total. The national curriculum asks Year 2 pupils to "partition numbers in different ways", and it keeps coming back in Year 3 and beyond.

Why bother with the strange ones? Because non-standard partitioning is exactly what is happening when your child "borrows" in a subtraction. More on that in a moment.

The pictures schools use

Schools rarely start with the numbers. They start with something your child can see, then move to a picture, then to the digits. You'll probably come across these:

• Part-whole model (the "cherry" diagram). The whole number goes in the big circle. The parts go in the smaller circles underneath. It's a picture of "these parts make this whole".
• Base 10 blocks (sometimes called Dienes). Little cubes for ones, sticks of ten, flat squares of a hundred. 347 is three flats, four sticks and seven cubes.
• Place value counters. Counters labelled 100, 10 and 1 that sit in a place value chart.
• Place value chart. A simple grid with H, T and O at the top. Each digit goes in its own column.

You don't need any special kit at home. Coins work brilliantly: £1 coins, 10p coins and 1p coins. Ask your child to make £3.47 and then tell you how many of each coin they used. That's partitioning, and it's real life.

Watch me explain it

If it helps to see it, here's a short video where I explain partitioning and place value from scratch. It's the same way I'd teach it in class.

And if your child is in Year 4, this lesson from my Year 4 place value series takes partitioning up to four-digit numbers:

Why partitioning matters so much

Partitioning isn't a topic you tick off and forget. It's a tool your child will use every single day in maths. Here's where it shows up.

1. Mental addition

Ask a confident child to work out 46 + 37 in their head and they'll often partition without even knowing it:

• 40 + 30 = 70
• 6 + 7 = 13
• 70 + 13 = 83

Big numbers become small, friendly ones. That's the whole idea.

2. Exchanging in column subtraction

Here's the one I most want parents to understand. Take 52 − 27. You can't do 2 − 7 in the ones column, so your child exchanges a ten. What they're really doing is partitioning 52 in a non-standard way:

Now 12 − 7 = 5 and 40 − 20 = 20, so the answer is 25. When children cross out the 5 and write a little 1 next to the 2, this is what it means. A child who understands this rarely makes the classic subtraction mistakes. I go through the full method in column addition and subtraction.

3. Multiplication

23 × 4 looks hard. Partition the 23 and it isn't:

• 20 × 4 = 80
• 3 × 4 = 12
• 80 + 12 = 92

This is exactly how the grid method works, and it's the thinking hiding inside short multiplication and long multiplication too. Of course, it only works if the times tables are solid, so have a look at how to learn times tables fast if those are wobbly.

Partitioning decimals

The same idea works after the decimal point. In 4.36, the 4 is worth 4 ones, the 3 is worth 3 tenths and the 6 is worth 6 hundredths:

4.36 = 4 + 0.3 + 0.06

Children who can do this find adding and subtracting decimals far easier, because they know a tenth has to line up with a tenth. I've written a full guide on how to add and subtract decimals if your child is at that stage.

3 partitioning mistakes and how to fix them

Mistake 1: Splitting the digits, not the values

Your child writes 347 = 3 + 4 + 7. They've split the digits but forgotten what each one is worth.

The fix: go back to coins or base 10. "Is this 3 worth three pennies or three pounds?" Then write it in a place value chart so they can see the 3 sits in the hundreds column.

Mistake 2: Getting lost when there's a zero

Partition 406. Lots of children write 40 + 6, because the zero "doesn't count".

The fix: explain that the zero is a placeholder. It's holding the tens column open so the 4 stays in the hundreds. 406 is 400 + 0 + 6, which is just 400 + 6. Ask: "How many tens are there?" The answer, none, is important.

Mistake 3: Panicking at non-standard questions

A question says "347 = 200 + ? + 7" and your child freezes because it doesn't look like what they learned.

The fix: show it with coins. Make 347 with three £1s, four 10ps and seven 1ps. Now swap one £1 for ten 10ps. How many 10ps now? Fourteen, so 140. Once they've physically done the swap, the numbers make sense.

A 10-minute partitioning practice routine

Same three steps I use for every skill: watch, copy, practise.

1. Watch: partition one number yourself, out loud. "347. Three hundreds, that's 300. Four tens, that's 40. Seven ones, that's 7."
2. Copy: your child does a very similar one, saying it out loud too.
3. Practise: a few on their own from the table below. Check by adding the parts back together.

Ten minutes, a few times a week, is plenty. Only move on when they're getting three in a row right.

Frequently asked questions

What is partitioning in maths for kids?

Partitioning means splitting a number into smaller parts that add back up to it. For example, 56 can be partitioned into 50 and 6. It helps children understand what each digit is worth and makes adding, subtracting and multiplying easier.

What year do children learn partitioning?

Children start partitioning two-digit numbers into tens and ones in Year 1 and Year 2. They move on to three-digit numbers in Year 3, four-digit numbers in Year 4, and use partitioning with larger numbers and decimals in Years 5 and 6.

What is the difference between standard and non-standard partitioning?

Standard partitioning splits a number by place value, so 347 is 300 + 40 + 7. Non-standard partitioning splits it any other way that gives the same total, such as 200 + 140 + 7. Non-standard partitioning is what happens when children exchange in column subtraction.

What is a part-whole model?

A part-whole model is a diagram with one large circle for the whole number and smaller circles for its parts. Many UK schools use it to show partitioning, because children can see that the parts join together to make the whole.

How can I help my child with partitioning at home?

Use coins. Ask your child to make an amount like £2.35 with £1, 10p and 1p coins, then say how many of each they used. Then ask them to swap one coin for ten smaller ones and say the new partition. Five or ten minutes a few times a week is enough.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (place value in Years 2 to 4, and partitioning "in different ways" in Year 2)
• Oak National Academy, Use known facts to solve problems involving partitioning numbers (free Year 3 lesson resources)
• Ross Mackell, Teacher's Perspective on YouTube