Building a Riemann Sum Spreadsheet

Reflections of a Second-career Math Teacher

With the second semester now underway, my AP Calculus AB students began their journey into integral calculus by exploring the Riemann Sum, named for the German mathematician Bernhard Riemann (1826-1866).  Herr Riemann formalized a specific application of the method of exhaustion pioneered by the Greeks, which itself evolved over time as Eudoxus improved upon Antiphon’s work from the 5th century B.C.E., which led to Archimedes applying the method using triangles to find the area under a paraboloid.  Riemann’s contribution used rectangles to estimate the area under any curve.  Three different approaches for computing the Riemann Sum estimate for a function, f(x), are shown below.

Left Right Midpoints

Technology 101

While leading my students in their journey, I discovered that our new calculus textbook includes a set of problems that need a program that runs on the TI-84 calculator; however, I did not receive the program with the textbook’s ancillary materials.  Without the calculator…

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About Dave aka Mr. Math Teacher

Secondary math teacher teaching math intervention, algebra 1, honors precalculus, and AP Calculus AB. I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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