Enhancing Learning With a Graphics Calculator - CasioEd

Enhancing learning with a graphics calculator
beautifully illustrated on the screen, and it is clear how the left, right and midpoint
approximations are related. By choosing increasingly larger numbers of intervals, the gap
between these closes, of course, which is an important understanding for students to acquire.
If a large number of intervals is chosen, the area under the curve appears to be almost a solid
area in these various procedures, and the variation among the estimates reduces.
To illustrate, here is a simple example, using an elementary linear function (under which
students can easily calculate the area of 12 square units by finding the area of the polygonal
shape concerned).
We start by drawing the graph of y = x + 1 in the first quadrant:
To consider the area under the line from x = 0 to x = 4, start the program and enter the limits
of 0 and 4, pressing EXE after each:
To see the approximation process, start with a small number of intervals. In this case, we
chose 5. The calculator starts by drawing five rectangles from the left endpoints, and giving
their total area after EXE is pressed:
Clearly, the rectangles on the left intervals underestimate the area under the line, which is
seen to be larger than 10.4.
Press EXE to continue with the rightmost rectangles on the same five intervals. The sum of
13.6 is now clearly larger than the area sought:
The midpoint of the intervals is provided next, after EXE is pressed.
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