Why do this problem?
This is a good activity
for getting good language flowing when encouraging children to explain their thinking. Encouraging their curiosity may lead them to lots of further ideas of which there are many possibilities. See the note at the bottom about the whole aspect of curiosity.
It is probably best to start with the pupils sitting round in a circle with some blocks in the middle that represent the blocks of flats. Then, introduce the challenge and get some ideas, showing them physically where the fence could go with string or ribbon.
Then the pupils can have time for exploring the ideas on their own or in small groups.
How did you get this idea?
Are any of yours the same as any others?
How do you make sure that you have done the halving of the 16 blocks?
As suggested in the problem, some children will enjoy looking at other shapes and extending the number of blocks in either a square or rectangular shape.
Some blocks or something else for pupils to use individually to represent the blocks of flats will be useful.
You may be interested in the following talks given by Professor Susan Engels, which focus on encouraging curiosity and are available on YouTube:
The Rise and Fall of Curiosity
- the extract from 23.50 to 37.15 on adult encouragement and teacher behaviour is particularly worth viewing
The Hungry Mind: The Origins of Curiosity
- the extract from 8.22 to 12.29 on children asking questions is especially useful.