Author Notes

Hello Dr. Kahn,
I've corrected the mauscript according to the suggestions offered by the external reviewers. The title, while perhaps not "eye grabbing" has been retained because it accurately reflects the content of the lesson and in any case, the
words used in the title should also be explained by the teacher as a part of the lesson plan.

Since not all schools have access to balances having 0.1 mg precision, I reworked the examples using a much less expensive balance having 1 mg precision, with excellent results.

I have tried to show how areas calculated by the method could be rescaled so as to be useful in some real-world applications. The simple algebra should be well within the grasp of most students and introduces some mathematical terms.

Lastly, for completeness, I've included a Youtube reference that shows how Photoshop can be used to calculate areas. This approach uses photographs of shapes and rather expensive software. What is nice about the method is that it also uses proportions (essentially the same conceptual apparatus as in the lesson). My experiments with Photoshop using the figures in the text, while yielding results of comparable accuracy, required good control of surface illumination, so as to produce a shadowless, uniformly bright photographic image. Some finesse in handling the camera was also needed -I had to use a tripod to arrange the camera to look straight down.

I hope all is in good order with the manuscript.

Regards,
Philip Gabriel
Sunshine Kathryn grimes

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