Ross MackellUK-qualified primary teacher · 9 min read

Try this tonight. Write 4,762 on a piece of paper and ask your child one question: "What is the 7 worth?"

If they say "seven hundred" straight away, brilliant. If they say "seven", or they hesitate, you've just found something important. Because almost every written method they'll learn in primary school depends on getting that answer right.

That idea is called place value. It's taught from Year 1, it sounds simple, and it quietly causes more maths problems than anything else I see in Key Stage 2.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll explain what place value is, what your child should know in each year group, why it matters for everything else, and the mistakes to look out for. You'll also get a short routine and some questions to try at home.

What is place value?

We only use ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Yet we can write any number in the world with them. Place value is the reason that works.

The same digit can be worth completely different amounts depending on its position. Look at these two numbers:

• In 352, the 5 is worth 50 (5 tens).
• In 532, the 5 is worth 500 (5 hundreds).

Same digits, very different numbers. Teachers talk about the difference between the digit (the 5) and its value (50 or 500). If your child can tell you both, they understand place value.

You'll also hear the word partitioning. That just means splitting a number by its place value: 352 = 300 + 50 + 2. Children use it all the time in mental maths and in written methods.

The place value chart

Schools use a place value chart to show which column each digit is in. Here's 4,762 in a chart, plus a decimal example underneath.

Th is thousands, H hundreds, T tens, O ones. After the decimal point come tenths (t) and hundredths (h). Notice that schools now say "ones", not "units", so your child may correct you on that one.

The key rule: each column is ten times bigger than the one to its right. Ten ones make a ten. Ten tens make a hundred. Ten tenths make a one. Once a child really gets this, carrying and exchanging stop being magic tricks and start making sense.

Zero: the placeholder

Zero is the most important digit in place value, and the one children find hardest.

Compare 42 and 402. The zero in 402 tells you there are no tens. Without it, the 4 slides into the tens column and the number shrinks to 42. Zero is "holding the place", which is why it's called a placeholder.

This is where you'll see one of the most common mistakes. Say "four thousand and six" out loud and ask your child to write it. Lots of children write 40006 or 4006 with the digits in the wrong places, because they write what they hear: "four thousand" then "six". The correct answer is 4,006: four thousands, no hundreds, no tens, six ones.

Place value in each year group

Here's what the national curriculum expects, in plain English.

If your child is in Year 5 and still unsure about four-digit numbers, that's not a reason to panic. It's a reason to go back a step. Place value builds up one column at a time, so it's usually quick to fix once you find the gap.

Why place value matters for every written method

Here's the part most guides skip. Place value isn't a topic your child "does" in September and then moves on from. It's hidden inside every written method they'll learn.

• Column addition: when 7 + 8 makes 15 in the ones column, you carry a ten into the tens column. That's place value.
• Column subtraction: when you "borrow" (schools say exchange), you swap one ten for ten ones. That's place value. My column addition and subtraction guide shows this step by step.
• Long multiplication: the famous zero in the second row is there because you're multiplying by tens. That's place value. I explain it in long multiplication step by step.
• Short division: when you carry a remainder to the next digit, 2 hundreds become 20 tens. That's place value too, as you'll see in my bus stop method guide.
• Decimals and percentages: 0.5 being bigger than 0.45, or 10% being one tenth, are both place value ideas.

This is why I always tell parents that arithmetic comes before reasoning and problem solving. A child can't reason about numbers they don't understand. When a child is struggling across lots of maths topics at once, place value is very often the single root cause. I've written more about that in the real reason your child is struggling in maths.

Multiplying and dividing by 10, 100 and 1,000

This is the Year 5 skill where place value really gets tested, and where an old shortcut causes trouble.

Many of us were taught: "To times by 10, just add a zero." It works for 34 × 10 = 340. But try it on a decimal: 3.4 × 10. "Add a zero" gives 3.40, which is the same as 3.4. Completely wrong. The real answer is 34.

What really happens is that the digits move:

• × 10: every digit moves one place to the left. 3.4 becomes 34.
• × 100: two places to the left. 3.4 becomes 340.
• ÷ 10: one place to the right. 52 becomes 5.2.
• ÷ 100: two places to the right. 5,200 becomes 52.

The decimal point stays still and the digits move past it. If you draw a place value chart and physically slide the digits along, it makes much more sense than any rule. Teach the "digits move" version from the start and your child will never need to unlearn anything.

This skill matters later for working out percentages, where finding 10% is just dividing by 10.

3 place value mistakes and how to fix them

Mistake 1: Reading the digit, not the value

• What it looks like: "What's the 7 worth in 4,762?" "Seven."
• The fix: Ask "which column is it in?" first, then "so what's it worth?" Point to the column on a chart until they don't need it.

Mistake 2: "Just add a zero"

• What it looks like: 3.4 × 10 = 3.40, or 2.5 × 100 = 2.500.
• The fix: Replace the rule with "the digits move". Use a chart and slide the digits. Check with money: 10 lots of £3.40 is clearly not £3.40.

Mistake 3: Thinking a longer decimal is bigger

• What it looks like: "0.45 is bigger than 0.6, because 45 is bigger than 6."
• The fix: Put both in a chart. 0.6 has 6 tenths. 0.45 only has 4 tenths. Compare the biggest column first. Money helps again: 60p is more than 45p.

A 10-minute place value routine

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

1. Watch: draw a place value chart. Write a number in it and say each digit's value out loud. "4 thousands, 7 hundreds, 6 tens, 2 ones."
2. Copy: your child does the same with a similar number, saying it out loud.
3. Practise: three or four questions on their own, like the ones below.

Coins are brilliant for this. 1p, 10p and £1 coins are ones, tens and hundreds of pennies. Ten 10p coins swap for £1, which is exactly how exchanging works. For younger children, bundles of ten straws or lolly sticks do the same job.

Pick questions that match your child's year group, and only move on when they're getting three in a row right. Ten minutes, a few times a week, is plenty.

Frequently asked questions

What is place value in maths?

Place value is the value of a digit based on its position in a number. In 352, the 3 is in the hundreds column so it's worth 300, the 5 is in the tens column so it's worth 50, and the 2 is worth 2. Each column is worth ten times the column to its right.

What year do children learn place value?

All the way through primary school. Children count and write numbers to 100 in Year 1, learn the value of digits in two-digit numbers in Year 2, three-digit in Year 3 and four-digit in Year 4. By Year 6 they work with numbers up to 10,000,000 and three decimal places.

What is a placeholder in maths?

A placeholder is a zero that holds an empty column so the other digits stay in the right place. In 402, the zero shows there are no tens. Without it, the number would be 42.

How do I teach my child place value at home?

Draw a simple place value chart and use real objects. Coins work well: 1p, 10p and £1 show ones, tens and hundreds of pennies, and swapping ten 10p coins for £1 shows how exchanging works. Model one example out loud, let your child copy, then give them a few to try alone.

Why is place value important?

Every written method depends on it. Carrying in addition, exchanging in subtraction, the zero in long multiplication, remainders in short division and comparing decimals are all place value. A child who is unsure about place value will usually find all of these hard.