the 'families' in the vertical strips all have some commonality
questions could include:
- for a constant area, when is the perimeter greatest/least?
- why is the perimeter usually even and can it be odd?
- how come the perimeter stays the same when bites are taken out of a shape?
- how is the perimeter of a square related to the area?
finding and establishing why rules work
it can be helpful for students to actually measure (or estimate) the various lengths in order to find the perimeter
it is intended that the lengths are a whole number of cms.
this task is based on a John Mason session where he asked participants to draw a shape and then try to draw examples with a larger and a smaller perimeter but with the same area and then examples with the same perimeter but a larger or smaller area
it is also similar to the NRich task, 'changing areas, changing perimeters'