On the Edge
Why do this problem ?
This problem is a familar context involving perimeters and squares that requires careful analysis. There are opportunities to experiment but a need to think ahead.
Possible approach
Arrange nine large squares into a $3 \times 3$ array and colour the edges - counting from $1$ to $12$ this time.
Rearrange the nine squares in a haphazard way to enable you to colour the edges in a different colour (counting $1$ to $12$).
"Does this mean we cannot do it?"
or
When any pair is successful challenge them to repeat the task:
"Well done. Would you be able to do this again without making any "false moves"?"
"Can we use more colours when we have $16$ squares?"
"How about with $25$ squares...?"
Key questions
Can you anticipate where certain squares will have to go in future rounds?
Possible support
Lots of paper squares so students do not have to worry about making mistakes.
A $4 \times 4$ array is probably easier.
Possible extension
Can students do all three colourings without rearranging the squares?
Will it always be possible to add an extra colour as the squares get larger?
For a 3D version of this problem students could try Inside Out
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