Why do this problem?
is a good one to play with young children once they are familiar with the basic number operations. They will like the idea of their number being "secret", and of course being able to work out someone else's "secret" number! Looking for a ''secret'' number is the basis for algebra and solving unknowns in
equations. So as well as enjoying what they are doing, your class will be engaging with some important mathematical ideas.
A good way to start might be for you either to enter your own secret number and invite the class to suggest what to add, or perhaps ask two children to come to the front to demonstrate. This activity will create a great opportunity for rich discussion amongst the class about how they can work out the secret number. You could ask the children to think for themselves first, then share their
ideas with a partner and finally with the whole group. (Think-pair-share.)
Playing this game is a good lead-in to talking about inverse operations. You could also introduce some element of recording, perhaps by asking the children to record what they do each time in their own way - this can help to reveal a lot about their thinking processes.
What number added to $4$ makes $10$?
What number multiplied by $5$ makes $35$?
How could you check your answer?
The best extension for this is for children to play the game with a partner as they are invited to do in the original problem. For some, there need be no limit to the numbers or operations involved. However, it would be a good idea to get all "secret" numbers and working out recorded!
Use a calculator openly with the children so that they can see exactly what is happening. When they understand the mechanism of the game then start using a "secret" number with very simple numbers. Learners could also use a number line or multiplication square to help.