In the 1952 movie, Hans Christian Anderson, starring Danny Kaye in the title role, to the oligatto of children singing their "addition tables", Danny sings the delightful Frank Loesser song:

			Inchworm. Inchworm.
			Measuring the marigolds.
			You and your arithmetic
			Will probably go far. [etc.]

Am inchworm is, of course, a small caterpillar, about an inch long that "inches along" a tree branch or whatever. It is also known as "a measureworm".

I chose the latter label to describe a MATHTIVITY in which kids learn about measuring instruments and measures by modeling them on their own physical properties.

I explain that this has historical precedent, since many units of measure were derived from the physical property of a king or some notable.

For example, the English unit of length, known as "the foot" derived from the length of a king's foot. The yard derived from the distance between another king's nose and the forefinger of his outstretched arm.

I guide each kid in

• selecting a unit of length equal to the distance from his/her nose to forefinger of outstretched arm -- cutting a cord to this length, then a wooden rod of equal length;

• using a homemade jeweler's balance, choose a unit of weight equal to "the butcher's thumb", using his/her thumb;

• cut a cord equal to the length-unit, attach a weight equal to the unit created above, and attach this to a "ceiling hook" as a pendulum, whose "natural vibration"becomes the kid's unit of time.

Now all of this, so far, is for fun and to connect with historical events. But this has a more important purpose: TO MOTIVATE KIDS IN LEARNING TO USE FRACTIONS AND RATIOS.

Let's say that Mary has created an l-mary unit of length, a w-mary unit of weight, inducing a t-mary unit of time. And Joe has his own respective STANDARDS: l-joe, w-joe, t-joe.

Now, let each kid proclaim a "state" with "custom officials for those carrying trade across a state boundary". If Joe crosses Mary's boundary and must pay customs, problems arise:

• how many l-joes equals an l-mary, that is, what is the ratio: l-joe/l-mary?

• And similarly for the other dimensional units.

Perhaps you can think of other motivations with this setup.