Early Childhood Mathematics Education/Inch and centimeter

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A way to teach these concepts to pre-schoolers, even prior to understanding a ruler, is the bogie (short for Kraadtzenbogen, a stick (limit 11 inches for safety's sake) with notches to produce a horrific rattling noise when scraped (kratzed) across the corner of a piece of furniture, a rim of a cooky tin, or coathangerwires on a zooky (nasty violin-shaped instrument). See Essential Preschool Part I. (Diagrams are in preparation.)

Along one long edge of the stick, from the narrower end up to 3-4 inches short of the thicker end (if applicable), dig notches one inch apart by means of a file. Along another long edge dig notches one centimeter apart. (On a round stick the notches can be along opposite sides.) You can use a ruler to make sure these are exactly correct, but it doesn't matter that much.

When the youngster uses the bogie to kratz on something, the inch-apart notches will create a sparer, less rattly rattle noise than the centimeter-apart ones, thus the infant learns a synesthetic way of understanding the difference between inch and centimeter-- sound, feel (the vibrations) and sight (the visible difference between the two notch series).