Why do this problem?
can be a fun way of introducing pupils to the idea of considering a system/method/pattern when tackling some investigations.
If you are happy with a computer presentation package then a captivating way of introducing the problem would be for them to see a house gradually taking place.
I would suggest that recording is not made an issue here as it can be rather hard, although I have found that 9-10 year olds can usually invent quite good ways of recording each design. A simple example I've come across has been:-
and then various ways have been found for tackling the overhanging, balcony rooms.
Tell me about the ways that you are finding more and more house shapes.
Using extension activities such as asking how much paint would be used to paint the outside of the designs is a good activity to link with surface area work. If children are challenged to find designs which use less paint and try to explain why that is so, really good-quality maths talk happens.
As mentioned in the problem some isometric paper can be a help for those who want to record in that way, however using a digital camera can make it easier for the pupils.