# What is place value?

The first couple of weeks of school are underway. Your child is settling into their new class and getting to know their teacher. And then the homework lands in the book bag / inbox and it’s all about place value.

What is place value?

Simply put, it’s the value of each digit in a number depending on its position. For example, in 325 we say that there are 3 hundreds, 2 tens and 5 ones. In the number 3250, the 3 represents 3 thousands, the 2 represents 2 hundreds and the 5 represents 5 tens.

If you were born in the 80s you may remember the “ones” being called “units”!

How will children learn about place value?

In the UK, year 1 and 2 children might start using a place value grid and real life objects/cubes to investigate the place value of numbers.

As children progress, they may be asked to use or draw “place value columns”.

Once children understand the value of each digit in a number, they will be asked to apply their knowledge to solve problems and reason mathematically.

What is a placeholder in maths?

When a zero is used in a number, teachers often call it a placeholder.

We teach children that zero is not worth anything on its own – its job is to “hold the place” (not a technical term!) in a number. Without it, the value of each digit would be different.

We read numbers from left to right so in a 3 digit numbers we know there will be hundreds, tens and ones. In 804, we know that the value of the 8 is “8 hundreds” and the the value of the 4 is “4 ones”. The zero tells us there are no tens in the number and – crucially – without it being there, anyone reading the number would assume it was eighty four.

In writing, apostrophes for contraction do a similar job to the placeholder in maths, holding the place for letters that they replace, for example can’t / cannot.

What is partitioning/decomposing in maths?

Your child might be asked to partition or decompose some numbers. Simply put, with a 3 digit number, this means splitting up the number into hundreds, tens and ones. Once you’ve done so, this is called showing the number in “expanded form”. See below:

Eg. Partition (or decompose) 764 using digits

Answer: 764 = 700 + 60 + 4

Eg. Write 764 in expanded form

Answer: 764 = 700 + 60 + 4

Eg. Partition 764 using words

Answer: 764 = 7 hundreds plus 6 tens plus 4 ones

What are Dienes blocks / Base 10 blocks?

These are plastic or wooden blocks that children use to help visualise and understand numbers. They are often used in the classroom for children to handle to help them understand place value.

What does this place value maths question mean?

“When a number is one more or one less than a given number, the tens digit in the number always stays the same. True or false?”

Here is an example of the what your child’s teacher might be looking for in response to this question.

“This statement is false because, for example, when you add one to 39, the answer is 40. The tens digit changes to a 4. When you find one less than 50, the answer is 49 and the tens digit has changed to 4.