What is BODMAS?

What is BODMAS?
We explain the concept of BODMAS, used to help Year 6 pupils remember what order mathematical calculations should be completed in, and offer examples of how children will be taught to use this mnemonic in the classroom.
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What is BODMAS?

BODMAS is an acronym or mnemonic used to help pupils remember the correct order to complete mathematical calculations in (this called ‘order of operations’).

Other mnemonics children learn in primary school are the rhyme ‘Richard of York Gave Battle in Vain’ (to help remember the colours of the rainbow) and ‘Naughty Elephants Squirt Water’ (to help remember the order of the compass points).

What does BODMAS mean?

Each letter stands for a mathematical operation.

Brackets(      )
Orders/OthersOrders are square roots or indices (sometimes called powers or exponents, square numbers and cube numbers). For example, 2³: the little 3 means that you multiply the number 3 times, 2 x 2 x 2 = 8. A square root is the inverse of a square number, so √25, the square root of 25, is 5 because 5 x 5 or 5² equals 25.
Division: ÷ Splitting into equal groups or parts
Multiplication: x Groups of
Addition: + The total of numbers together
Subtraction: -To take away numbers from other numbers

When you complete a mathematical number sentence involving several different operations then BODMAS helps you to know which order to complete them in. Anything in Brackets should be completed first, then the orders, followed by any division or multiplication and finally addition or subtraction.

Division and Multiplication have been grouped together as they are of the same level; this means that if you have a calculation involving division and multiplication then you complete them as they appear from left to right. This is the same for addition and subtraction; they are completed as they appear from left to right.

Another way of looking at it:

For example:

CalculationOrder of completionAnswer
3 x (7-3) =Complete the subtraction first because it is in brackets3 x 4 =12
2 + 3² =Complete the power first 3² = 3 x 3 = 9 then the addition2 + 9 = 11
3 x 10 ÷ 2 =Multiplication and division have the same level of order so complete from left to right30 ÷ 2 = 15
6 – 2 + 5 =Addition and subtraction have the same level of order so complete from left to right4 + 5 = 9
30 – 2 x 5 =Complete the multiplication first and then the subtraction30 – 10 = 20

When will children be expected to know what BODMAS means and use it? 

Children should be taught the order of operations using all four operations in Year 6, though more able children may be introduced to this concept earlier.

How is BODMAS taught in primary school?

Children will be introduced to the meaning of BODMAS; the teacher will model and talk through examples and then give the children calculations to practise to help them learn and remember the order of operations, applying BODMAS.

Although BODMAS is the most common term it is sometimes also referred to as BIDMAS. In this case the I means Indices which is simply another word for ‘order’ or ‘other’ and the concept is exactly the same.

Most calculators and computers are programmed to complete calculations according to BODMAS, however some very basic calculators may simply calculate in the order the calculations are entered.