09.24.07
Math fun - week two - Measuring distance
When the first class ended, I had no idea what the next class would entail. It was some point over the weekend before I finally figured out an idea.
Since we covered counting, we could look at measurement. I quickly settled on only focusing on measuring length.
As I worked out different activities, I quickly decided that this would be an outside class. (And believe me, I was watching the weather report for any chance of rain.)
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My classes ran in the same order, so I started with the pages. I started by asking them what we can measure and it was like pulling teeth to finally get one to respond with ‘a rock.’
Okay, ‘what can we measure about a rock?’ After some nudging and guiding we touched on mass, volume, and length.
Then I approached how we might start working on a common unit. I had them line themselves up by height and we talked about how comparison was fine, as long as everyone was together. From there we went into some history of units, ending on feet.
So, we first all lined up and counted out 10 heel/toe feet across the driveway to see how they all varied.
Our next activity was to trace and cut out everyone’s foot so they would each have a ‘foot ruler’ to measure with and we measured each other’s height and then the width of the driveway.
So we discussed the need for standardization and the fact that most towns would post how long a ‘foot’ was for their town. Which then expanded into national standardization and the stories about Henry I setting them.
Lastly, we talked about measuring longer lengths. I took an exercise from my college level survey class years ago and had them count paces between two stakes set 100 feet apart. We then roughly calculated their pace length and used that to measure the width of the driveway.
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My oldest class, the knights, was next.
We started by discussing the history of units used for measuring.
How the body was the basis of small units. The inch was the width of a thumb or between two joints on the pointer finger, and was set at 3 barleycorns (pre 1066 England). The foot was either a natural foot (shoe included), 36 barleycorns, or set by the Romans as 12 inches. And we touched on digits (width of a finger, .75 inches), palm (3 inches), hand (4 inches), shaftment ( a palm with the thumb at a right angle to the pointer finger, 6 inches), span (fingers outstretched, 9 inches), cubit, yard, and fathom.
That the mile was a 1000 paces of a Roman legion (which was 2 paces by our standards).
We then did the same pacing exercise as the first class, but used the result to measure the length of the driveway.
From there we discussed how we might measure longer distances and I introduced how surveying was done a generation ago using transits and poles. While I couldn’t borrow a transit from the local engineering college, I did find this fun little exercise for them to try.
From there we talked about chains and rods and how their length was set by the mile.
And I split them into 3 groups. Two groups each had a 9 foot chain. (a real chain is 66 ft., but I didn’t want them to have to deal with so much, let alone have to buy that much for the class), the other group had a modern chain, or measuring tape. 
I then gave each group a sketch of the property and asked them to measure distances. They spent the remaining time surveying the property.
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As before, my last group gets a blend of activities from the first two classes.
They started with the ‘What can we measure?’ question (with much better results) and we compared heights, made ‘foot rulers’ and measured the width of the driveway with them.
We discussed some of the history, hitting on points closer to the details of the older class, but not as complete.
They then did the pacing exercise and paced the length of the driveway. We followed with the thumb trick and discussed using chains.
Lastly, I split them into two groups and they used the chains to measure the length of the driveway.
