Each group of students (2-4 works well for this) will need three cans of play-doh (full-size cans). They can be the same color or different, it doesn't matter, but play-doh from the different cans will get mixed together.
The group begins by dividing the play-doh into 51 lumps/balls; that's 17 from each can. These do not need to be exactly the same size, and they do not need to be rolled into perfect balls. You will have some students who want to be very exact about it and it will frustrate them a bit (myself included); try to keep them moving so this doesn't become an all day activity.
After each group has their 51 lumps of play-doh, they will need to decide how to lump them back together so that they have two balls - one representing the Earth and the other the moon.
For example, they could smush 20 lumps together to make the moon and the other 31 together to make the Earth. Or 11 lumps to make the moon and 40 to make the Earth.
They need to work as a group to come up with some sort of consensus about how to divide their lumps. Once a consensus has been reached (some discussion will probably need to take place), they can go ahead and smush the play-doh together to create the Earth and moon.
Upon completion of this, time should be taken to go around the room and have each group share their Earth and moon and the number of lumps of play-doh found in each.
Then it's time for the big reveal... Using this model, the moon should be made of 1 lump of play-doh and the Earth made of 50 lumps of play-doh. The moon is approximately 1/50 of the Earth's volume.
If you wish to continue... the distance between the Earth and the moon is approximately 30 times the Earth's diameter. So, measure you Earth lump, multiply the number by 30 and move the moon that far away from the Earth.
Now, if you start thinking about how small the Earth is in comparison to the Sun, you get a feel for how tiny our moon is within the solar system.... but that's a discussion for another day...
Presented by Dr. Christine Anne Royce (Shippensburg University) at the 2007 New Jersey Science Convention.