Why do this problem?
gives pupils a challenge in both spatial and numerical problem solving. It is also quite a challenge for recording methods. It is probably best suited for a group of children who are confident problem solvers.
The activity also opens out the possibility of pupils asking “I wonder what would happen if . . .?” Pupils' curiosity may be easily aroused while finding solutions to the challenges.
It would be good to have a square grid background and then have coloured squares arranged for the tile surround.
This could be on card on the floor for the children to see, or represented on an interactive whiteboard.
Some time needs to be spent arranging ribbons/string/lines that obey the rules and produce a square so that learners can internalise the rules.
Give children time to explore for themselves and intersperse this with some 'mini plenaries' to exchange ideas.
It may be helpful for learners to have a printed copy
of the task.
How are you working out the area to show they are not the same?
How have you decided that this is the biggest/smallest?