Geometry Through Art

Norman Shapiro

A Lesson on Teaching Measurement

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Table of Contents
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Egyptian knotted string

Use plain kite string and bring geometry into your math program.

The ancient Egyptians used string. They knotted it and stretched it to do their measuring. A very young child can get the idea of making geometric measurements the same way. Children can begin to comprehend the rudiments of geometry with string by being measured themselves.

In kindergarten and first and second grade, a teacher can take children's measurements and use their respective heights as basic length-units for having them measure things in the immediate environs. That's what the Egyptians did. They called the surveyors "rope-stretchers." A string with knots carefully made at both ends becomes your basic line segment.

Children (with the aid of classmates) stretch these strings alongside things in school and at home, and the notions of size, scale, proportion, and even space itself become concrete and accessible.

Measuring is matching. I am this big. The length of my tricycle, parked, takes up this amount of space, less than my height.

This measured "me" as a length-unit should be arrived at with deliberate care for accuracy. An effort to do this will make your students conscious that the mark on the paper, or the string itself against the wall, is not something arbitrarily arrived at.

The head, being round, presents a problem: at what point on the wall is it "truly" in line with the very tiptop of the child's noggin? If such measuring is to be an ongoing project conducted at different times (with children taking over the chores) during this and subsequent years, the concepts of parallel and perpendicular will emerge in the process. Such basic words as vertical, horizontal, and diagonal come easily and should be among the first to be used.

The knotted string itself, tagged perhaps with name, class, and date, becomes more than a souvenir: one does not throw away a tool so useful for followup activities.

What intriguing and useful purposes can you as a teacher conjure up to make this string work in the teaching of fractions, devising homemade rulers, etc.?

The Egyptians learned to subdivide the string into knotted segments of equal length: whole, half, quarter, eighth, etc. Useful indeed is the concept of the simple mechanics of making fractional lengths geometrically. Easiest in exploring the making of rulers is folding paper. With a little practice, most eight-year-olds could make "Egyptian" knotted strings to perform surveying and make Pythagorean triangles and other polygons.

Pythagorean numbers are whole numbers that make up the sides of a right triangle; one such is 3, 4, 5 (9 + 16 + 25). Ancient geometers discovered such whole numbers and used them with knotted rope.

This 'answer sheet' shows learners that the squares on the two shorter sides of the triangle add up to the squares on the longer side. Children can see this and number the squares on the grid as they count.

Egyptian knotted string: an important device for bringing more geometry into your math program.

On to Classroom Supplies You Will Need

Copyright 1995 Norman Shapiro

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