This investigation could be introduced with the class gathered together on the floor. Tell a story about the city and the people who live there. Have cubes ready to illustrate it and then and build the houses together.
If you do not have enough cubes for the children to work in pairs then this will be the best way to continue.
Recording can be done easily on squared paper.
Some children will be finding pairs that make 7 etc while others ware racing ahead and discover the rule that there is always one less way of making houses than the number of cubes used. If they do not know if they have found all the ways of making a set of houses then get them to arrange their houses in order - 1 and 6, 2 and 5, 3 and 4 etc.
(If someone asks what happens when someone lives alone - they are not allowed to! They have to find someone to share a house with!)
This is a useful investigation in which children can learn to be
methodical. Questions such as the following could be used to guide and
extend:
What about families of 6, 5 and 4?
Can you guess how many ways there are of building houses for 8 people? Try
and see if you are right.
Have you found a pattern?
If you have, you could say how many ways there are of building houses of a
hundred rooms!