Measure an Acre

So Friday, yesterday, was the end of my first trimester at my new school.  The sixth grade commemorated the event by taking the second-to-last class period of the day, and going out on the fields for the “Measure an Acre” project.  It turns out that in many places in the world, a half-acre is the minimum amount of farmland that can feed a family; their job was measure out three acres of land.  It was the culmination of our Inventory of John Alden project, since Mr. Alden had owned about three acres at his death.

I say about, because it turns out to be incredibly difficult to measure an acre.  Especially if you’re in sixth grade.

I and two colleagues divided the sixth grade into three groups.  One group had the largest expanse of open field to work with on campus, and did it as a Greek geometry problem; measuring out one side and then calculating the two perpendiculars, and then finding the last right angle.

The second group used the 17th century measurement, the “Perch”. which was fixed by Alden’s time at 16 1/2 feet. They had a double-perch cord, which is simply a rope with three knots in it — one at each end, and one in the middle.  Using that, they were to measure out forty square perches.

The third group used a modern measuring wheel, with a clicker to count rotations, and simply measured off 208 feet on a side, and did some math to re-figure the area when they discovered that their field wasn’t actually 208 feet wide, and they couldn’t accurately make a square.

All three groups encountered problems.  The third group found it hard to generate right angles, until they hit on the idea of using a plywood board to create the right angle for them.  The second group accidentally derived the A^2+B^2=C^2 formula, and also found that their piece of ground was actually only twenty square perches, not forty.  So they had to estimate the area of the second half of their acre off into the woods and marshland — which they noted would be unusually suitable for growing the wrong kind of rye.

And the third group got yelled at by a woman walking her dog in her back yard. Their Greek geometry problem led them off the edge of school property into the neighbor’s yard, and she quite rightly yelled at them and got upset.  After all, this group was measuring her land.  Obviously, that’s what they were doing, calculating feet and inches, and swinging a cord around central points to draw arcs and circles, and calculate perpendiculars and whatnot.  In our debrief afterwards,  I was able to say this —

“In math class, you’re used to thinking of areas and squares and triangles as having arbitrary dimensions: feet in this problem, meters in that one, and yards in this other one over here.  But today you learned that the power to measure and estimate the size of an area of ground is the power to control — whether by taxation, assessment or invasion.  The ability to measure was a powerful technology for states, nations and empires: because it gave them the ability to tax, or to raise armies, or to feed those armies.”

And most of the kids got it, I think.  The less clear point, though, is that one acre of ground is not the same all places in the world. The right amount of water, the right amount of nutrients, the right amount of compost all have to be correct to make that ground usable and suitable.  It’s my hope that the science department’s garden can make that point a little better than my lesson… because it’s going to be a vital point in the coming years.

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