One Formula, to Rule them All
Two-dimensional area starts and ends in pretty much the same place, with base and height. Kids in elementary school calculate space by counting grids. Calculus classrooms do the same thing (on a more complex level of course), but through the short cut of integration. Somewhere in the middle, with geometry and the like, it gets complicated and students lose the conceptual understanding.
Here’s what we did instead.
Start with a few applets:
Then we document our thoughts. Some people call this notes.:
Students watch in amazement as if this were a magical experience. Audible comments of “wow” and “that’s cool” are common.
So then we conclude that there really is just one way to calculate 2 dimensional straight line areas:
base times height (and sometimes half)