Many of Year 5 think that shapes with the same perimeter must have the same area. On the board, the teacher opens a GeoGebra file made before the lesson: a rectangle on a centimetre grid whose perimeter is fixed at 20 cm, with a slider for its width and its area shown beside it. The rectangle starts at 1 cm by 9 cm, and children write on mini whiteboards whether the area will change as it gets wider. The teacher drags the slider slowly, stopping at 2 by 8, 3 by 7, 4 by 6 and 5 by 5, and the area climbs from 9 cm² through 16, 21 and 24 to 25 cm² while the perimeter stays at 20 cm. The teacher also stops between whole numbers, at 4.5 cm by 5.5 cm, where the area reads 24.75 cm², then sets the perimeter to 36 cm and asks which rectangle will have the largest area before dragging to the 9 cm square. Children record both tables in their books and write a sentence on which rectangle encloses the most space.
This page is one of a growing set of PICRAT examples by cell, subject and grade. Page maintained by Andy Perryer.