Why do this problem?
possibly presents a new way for many pupils to think about the arithmetic they do. The idea of inverse operations is core mathematical concept and this activity offers opportunities to explore them in a meaningful way. The task also presents the chance to allow pupils to have the freedom to be curious and explore all kinds of
mathematics further, as well as persevere in their attempts to "undo" various calculations.
One way would be to start by saying "Here's the number $4$ I'll double it", inviting the pupils then to say what the answer is and then how to get back to the $4$.
You could try some different numbers and repeat the process with doubling each time as the operation.
The operation can then be changed to an addition or subtraction one.
This can now lead to the bigger question about whether same inverse operation works for every starting number.
If your pupils are secure then use the same rule but choose a different, and this time mystery, starting number and tell them the finishing number. Invite them to think about what calculation they'd do to get back to your mystery starting number.
What number do you get?
If you 'undo' the operation what do you get?
What do you have to do to 'undo' adding $6$?
What do you have to do to 'undo' doubling?
Tell me about your ideas.
For those who show fluency in the activity then a further challenge is to say that the starting number has gone through two operations that are done to it. Can the children find out how to undo them each in turn? What order do they have to undo them in?
Children may need to stick to small numbers so that they are not overloaded by trying to remember number facts. It may help to have a 'machine box' and think about the numbers going in and the numbers coming out, and what happens if you undo the action by putting in the numbers backwards.