Why do this problem?
provides an opportunity for children to sort and categorise, both of which are important mathematical processes. This open activity challenges children to find their own categories and then name them, which might mean it is a good way to introduce specific vocabulary.
You could begin by putting some numbers into a box on the board yourself and asking the children to describe the set. Encourage learners to find different ways of naming a particular group of numbers or introduce them to new vocabulary as appropriate. Pairs of children could come to the board to create their own set in a similar way.
Children could work in pairs, perhaps using digit cards/number cards, and pencil and paper. As they work, it is a great opportunity for you to listen to their justifications and how well they are able to use mathematical language.
As a plenary you could write several numbers on the board and ask pupils to say which one doesn't belong and why. Encourage creative responses to this - in fact any could be chosen if we give an appropriate reason.
What is the same about these two numbers?
Can we find others that could go with them?
What could we call this set?
Is there another way we could describe the set?
Encourage learners to increase the range of numbers from which they are selecting examples.
Some children might want to use just the numbers up to 20, for example, to start with. You could get them started by suggesting categories to make.