Why do this problem?
is a very simple investigation which allows for many levels of participation. There are those youngsters who can use three different sized rings and just "play around" with them. This provides a wonderful basis for most useful discussion as to the positioning of each of the three rings and their physical
relationship to each other. Children who go about it more systematically seem to have great enjoyment in the systems that they use. These two groups have to deal with the fact that some arrangements may 'look' very different but in the context of this challenge are equivalent. This again leads to very worthwhile discussion.
I usually provide the children with just two different sized rings and have the third one as an imaginary one that they can alter the size of for their own use, each time.
How would you talk about this ring?
What is this ring doing?
The more advanced youngsters who have no problems with the "look" and can "see" equivalent situations are usually able to go through the activity fairly quickly and are soon asking "I wonder what would happen if ... they were squares . . . the rings were all the same size. . . ?"
Having an adult working with a small group so as to help the language to flow can sometimes be very effective.