Finding all the possibilities... in math

Check out the problem we started working on today in math:
Building a Town

You are an explorer in Alaska. With a team of sled dogs you have been able to visit areas that no one else has seen before. One night at your campsite you find a few pieces of broken pottery that you think may be from an unknown ancient civilization. This is a major discovery! You need to get other researchers, historians, and explorers to come to the area to help you investigate. There is no where for your research team to live, so you must design a small town for them to live in. You must have space for exactly 60 families. All the buildings have to be the same size. You have been asked to find all the possible designs for the town.

Use the multi-link cubes to help you find all the possible ways to create housing for the 60 research families that will be exploring this new ancient civilization. Only one family can fit in each cube. You may stack cubes on top of each other to make tall buildings. Remember, for each possible town design each building must be the same height. The design must hold exactly 60 families. How can you make sure that you have found all the possible ways? The Governor of Alaska wants a report of ALL the possible solutions at the next meeting. You should record each design in your notebook using words, pictures, and numbers.