Why do this problem?
This fun activity
can be used as a short or long activity as part of both spacial awareness (transformations such as line symmetry and rotation symmetry) and number recognition.
If pupils are experienced in telling the time in a digital way then a brief introduction will enable them to choose what they are going to explore.
Tell me what's special about this time you've chosen.
Can you find any more like that?
Learners could look at the number of 'special times' that occur between certain times. More advanced pupils may find systems to allow them to know how many there will be without actually writing them down. You could set a 'simmering activity', for example invite children to find times in which the digits add to $10$, or where there is a horizontal line of symmetry. They could work on this
task whenever they had spare time, or at home and could contribute ideas to a designated area of the classroom wall.
It would help to have mirrors available for those that would like to use them.