Changing Areas, Changing Perimeters
This task is on the NRICH website. Pupils investigate the measure of area and perimeter, and how both of these change as a shape is altered. The aim is that learners realise that as area increases, perimeter does not necessarily increase at the same time.
While there can sometimes be an uneasy relationship between measuring and proving, there can be ways in which a more mutually-supportive relationship might be possible.