On a Desert Island with Unit Sticks, Continued Fractions and Lagrange

This lab style activity has students measure the length of an object (generally a tabletop) using an unmarked stick (a disposable chopstick being the most common choice). Students use the single stick as a fundamental unit of measure, then use remainders of the stick (and remainders of remainders) when measuring the total length to solve for the length in "sticks" using continued fractions, after Lagrange (1795). Students estimate error in their own measurements, but must grapple with what that really means, as they have no easy decimalized marks to choose as halfway points for error judgments. Excellent source of class discussion about fundamental concepts of units, error, and measurement. Applicable beyond the geosciences.