Visitors to Some printable paper rulers have made observations like this:

"I discovered that many of my students do not really understand linear measurement. I found this out when I gave them rulers without numbers. Some of them were completely at sea. Previously they just read the numbers off the ruler with no concept that they are measuring a given distance. It turned out that few of the students (top academic classes) [could] do the measurements, they didn't know where to start, they didn't know that the ruler was metric, they didn't know that each centimeter had 10 divisions!!! Give them a broken ruler (one without a zero): boy! does that ever demonstrate weaknesses in understanding. This year I am going to START with the numberless rulers."

My approach is to make the ticks and/or numbers either missing, shifted, or strange looking. The rulers are all correct, simply unusual. Hopefully unusual in ways which will expose misunderstandings.

So, here are some "odd" rulers...

This pdf was derived from this handwritten PostScript source using ps2pdf.

Which mutants should get an entire sheet? "Without a zero". And what else? All of them?

Notes: Out of time for tonight. Didn't get a chance to fiddle with ticks. Doables: Fiddle with ticks. Numbers rotated; alignment odd or variable. What else? Walk mind process of using a ruler looking for failure modes to tickle. Very sparsely numbered ruler (opportunity to disregard numbers). Are the cyclic and up-and-down numbered mutants really still "correct"? History: 2003-Dec-06 Added rule with "more randomly" missing numbers. Thanks to a reader for the suggestion. 2003-Dec-05 Created.