perimeter and area

the sets of shapes are intended to prompt students to ask their own questions

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?

students could create their own sequence of growing shapes and explore the growth of the perimeter

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 one from 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'