Children learn that addition and multiplication can be done in any order, using handy pairings to add several numbers easily while seeing that subtraction and division cannot be swapped.
In Year 2, children discover that numbers can be added or multiplied in any order to get the same answer, while subtraction and division cannot be flipped. When working with addition, such as adding three one-digit numbers, children learn to reorder the calculation to make mental arithmetic simpler, grouping numbers into convenient pairs like bonds to 10.
A common mistake is overapplying this rule to other operations, leading children to think that subtraction can also be reversed (believing 7 − 2 is the same as 2 − 7). Children also frequently calculate strictly from left to right, missing obvious, friendly pairs that would prevent counting errors.
Practice tasks visually reinforce these relationships. Children solve balance problems like The same total, sides swapped — what is hidden and What is missing on the other side to make it equal. In exercises such as Choose the convenient order and Four terms, two convenient pairs, they look at several numbers, pick the easiest sequence to add, and explain why that order makes the calculation simpler.