What is expanded notation?

What is expanded notation?
We explain what expanded notation means, how it is taught in primary school and how it can help children with addition and multiplication calculations.
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What is expanded notation?

Children are encouraged to use arrow cards in Key Stage 1 to help them understand that two-digit numbers are made up of tens and ones.

This is also referred to as understanding place value.  This is the foundation to then being able to understand how to add and multiply two-digit numbers using expanded methods.

Expanded notation in primary school

Sometimes teachers will talk about an 'expanded method' for working out a number sentence. This means partitioning a number before carrying out an addition or multiplication. For example:

59 + 38 =

Using the expanded method, you would partition the numbers, then complete the calculations:

50 + 30 = 80

9 + 8 = 17

80 + 17 = 97

Expanded notation for multiplication

The expanded method for multiplication could be writing the calculation out like this:

63 x 45 =

60 x 40 = 2400
60 x 5 = 300

3 x 40 = 120

3 x 5 = 15

2400 + 300 + 120 + 15 = 2835

Alternatively, you could use the grid method, which many people find easier:


Expanded methods are often used by primary school teachers for addition and multiplication, because they allow children to see clearly what they are adding and multiplying, that is: 60 x 40, rather than 6 x 4. With the shorter methods like the column method, children are not encouraged to think about the fact that the numbers are tens and units and subsequently get no practice in multiplying and adding tens numbers.