A computer dialog about area continues many of the arguments of the distance dialog. However, the definition of area, for arbitrary figures, is likely to be unknown to many students. So an important aspect of this dialog is to build with full input from the student an adequate operational concept of area to cover all situations involving closed planar curves.
This unit begins with intuitive notions of area, measuring the size of a lot. A student is shown an irregularly shaped area and a square that can grow or shrink under user control. The student is asked to make the area of the square, a figure whose area is likely to be better understood and appreciated, the ``same'' as the area of the other figure. This activity is carried out before any formal definition of area is developed, so it develops intuition. The role of intuition is important in many of the activities discussed.
The student then proceeds to construct a general definition of area, counting squares in a grid plane over an irregular figure, and then using finer and finer grids. The student is active in this process, doing the counting and making major decisions. Only closed figures in the plane are considered; the definition the student develops covers all those figures.
Later sections apply this definition to such familiar figures as rectangles and squares, deriving the standard formulae for area of these figures. Thus students draw on their previous knowledge.