Arranging the Tables
There are $44$ people coming to a dinner party. There are $15$ square tables that seat 4 people - one at each side - like this:
Or the tables can be joined together to make groups like this:
And so on...
Find a way to seat the $44$ people using all $15$ tables, with no empty places.
Why do this problem?
This is quite a fun activity
to do both numerically and practically using something like multilink to represent the tables. It gives an opportunity for pupils to explore a real situation and see the mathematics contained in it, and what can be investigated further.
Pupils should be encouraged to choose what practical bits and pieces might help them to find solutions. The solutions would probably be best recorded somehow. Again, pupils should be encouraged to find good ways of recording which suit them. Some might draw pictures, some may use sketches and some may just use numbers. (Some examples can be found on the sheet linked to the extension
In a plenary, as well as focusing on solutions, you could draw attention to the different ways children have used to record their work.
What do you see here?
How are you getting to your answer?
See this sheet
Using some resources to show the situations practically would help some pupils.