Place value misconceptions

Quick answer

Place value misconceptions happen when children think that each digit in a number stands alone, rather than understanding that each digit's value depends on its position in the number.

Learning outcome

By the end of this page, you will understand how place value works and be able to correctly read and write numbers up to 1000, knowing that each digit's value changes depending on where it is placed.

• You can explain why the number 345 is different from 543
• You can use base ten blocks or drawings to show the value of each digit
• You can correctly say numbers like 708 as "seven hundred and eight"
• You can identify which digit is in the hundreds, tens, and ones place

Why this matters

Understanding place value helps you count, add, subtract, and compare numbers. It's like knowing how to read a book – if you don't understand the letters, you can't read the words. If you don't understand place value, it's harder to do maths later on. Place value is used in everyday life when you count money, tell time, read your school grades, or even when you're playing games and scoring points.

How it works

Place value means that each digit in a number has a different value depending on where it is. Think of it like a house with rooms. The rightmost room is the "ones" room, the next room is the "tens" room, and the next is the "hundreds" room.

1. Start with the ones place – this is the rightmost digit
2. Move left to the tens place – this is the second digit from the right
3. Move left again to the hundreds place – this is the third digit from the right
4. Each place is ten times bigger than the one to its right

Examples you can see

Let's look at the number 427:

This means:

• 4 hundreds = 400
• 2 tens = 20
• 7>

So 427 = 400 + 20 + 7

Another example: 603

This means:

• 6 hundreds = 600
• 0 tens = 0
• 3>

So 603 = 600 + 0 + 3 = 603

Try it as a mini adventure

Imagine you are a treasure hunter on a secret island! You found a chest with a riddle: "I am a number with 5 in the hundreds place, 0 in the tens place, and 9 in the ones place. What number am I?"

Let's solve this together:

1. Start with the hundreds place – you know it's 5
2. Move to the tens place – it's 0
3. Finally, the ones place – it's 9
4. So the number is 509

Great job! You found a clue that says 509. Now, let's find another clue. What number has 7 in the hundreds place, 3 in the tens place, and 2 in the ones place?

Try to work it out yourself:

1. Hundreds place = 7
2. Tens place = 3
3. Ones place = 2
4. So the number is ?

Answer: 732

Common mistakes

• Mistake: Thinking 345 is the same as 543 because they use the same digits
• Why it happens: Children often treat digits as separate items instead of understanding that each digit's value changes based on position
• Fix: Use base ten blocks or drawings to show that 345 means 3 hundreds, 4 tens, and 5 ones

• Mistake: Saying "four hundred and five" when the number is 405
• Why it happens: Confusion between "and" meaning "plus" and "and" meaning "between hundreds and tens"
• Fix: Practice saying numbers with the correct way: "four hundred and five" for 405

• Mistake: Ignoring zero in numbers like 603
• Why it happens: Zero can be invisible to children, making them think there are no tens
• Fix: Always name the place value for each digit, even if it's zero

Parent and carer guide

Help your child understand place value with these tips:

• Use base ten blocks or everyday items like counters, beans, or pasta to build numbers
• Practice saying numbers aloud, like "345 is three hundreds, four tens, and five ones"
• Play a place value game: you say a number, and your child builds it with blocks or draws it
• Look for numbers in real life: house numbers, prices, clocks, or sports scores
• Don't worry if your child makes mistakes – they're learning!

Remember, this is a big concept, so take your time. Try to make it fun with games or stories.

Practice questions

1. What number is made up of 2 hundreds, 6 tens, and 8 ones?
2. Write the number 407 in words
3. Which digit is in the tens place in the number 539?
4. What is the value of the digit 7 in the number 742?
5. How many hundreds, tens, and ones are in the number 910?

Answers:

1. 268
2. four hundred and seven
3. 3
4. 700
5. 9 hundreds, 1 ten, 0 ones

FAQ

What is place value?

Place value means that each digit in a number has a different value depending on where it is. For example, in 427, the 4 is worth 400 because it's in the hundreds place.

Why is place value important?

Place value helps you understand how numbers work, which makes it easier to add, subtract, and compare numbers. It's the foundation for all other maths you'll learn.

How can I help my child with place value at home?

You can use base ten blocks, count money, look at house numbers, or play games where you build numbers. Practice saying numbers aloud and asking your child to explain what each digit means.

What if my child keeps mixing up the place values?

That's normal! Keep practicing with hands-on activities. Use visual aids like charts or drawings to show the place value of each digit. Be patient and encouraging.

What comes after place value?

After place value, children learn about larger numbers, decimals, and how to use place value in operations like addition and subtraction with regrouping.