I don’t know if the room dimensions shown on the sketch in my previous post are correct. I’ve never checked.
When I decided to start thinking about layout plan options I asked a couple of kids who had finished their classwork early to measure the room. I made a rough chalk sketch of the major features on the blackboard, handed them a variety of different measuring tapes and asked them to fill the sketch in with the lengths of each section of wall and the distances between opposite walls. This is a photo of the results:
You won’t be able to see much of the detail in this compressed image, but I still zoom in on the original file whenever I need to check something. Some of the measurements are hilarious.
When I first started teaching I discovered that even high school students today have no idea how to operate a ruler. At first I found this to be astonishing, but I’ve since observed that many of the “technologies” that were part of my life growing up are quickly becoming specialized crafts. Cursive handwriting is rarely taught any more, it’s gone. It freaks a child out if you ask them to write (print) more than about half a page without letting them use a computer. And even typing is starting to go away as voice recognition becomes increasingly accurate and useful.
At some point in every year of teaching math I apologize to students for the failure of my generation to complete the process Congress started back in the 60s and 70s to convert the US to the metric system. There is a solid two years of school math that would be unnecessary if we weren’t one of only three countries left in the world still reliant on the Imperial system (Burma and Liberia are the other two). But, I like teaching specialized crafts like the Imperial system of measurement. It’s cute.
It really frustrates them when I ask them to do calculations with Imperial units and conventions, especially when the task involves tools which make obvious the comparison with how intuitive and straightforward the same task would be with metric. They can see clearly that the underlying mathematical principles are often obscured by the Imperial system, if you see what I mean.
Anyway, one of the important concepts that measurement demands is “attending to accuracy.” That doesn’t mean always use the most sensitive micrometer that you can find, it means use a level of accuracy that is appropriate for the task at hand, and express your values so that the degree of accuracy is clear. One of the longer room dimensions on the blackboard is recorded as 27 feet 3 and 5/32 inches. Wow, that’s confidence!
I ask students to measure things a lot. I asked them to measure what scale speed the locomotive on the Inglenook was traveling (in scale miles per hour, natch). They needed to know what the scale of the model was (HO, technically 1:87.0857142 with the last five digits repeating, but I suggested that they just use 1:87), how many actual inches lay between two points, and how many seconds it took to transit that distance. Then they had to do all of the conversions to get from actual inches per second to scale miles per hour. Trivial, but for middle school students that’s a fairly boggling amount of measuring and calculating to do. But they did it, and I think most of them really understood what they were doing and felt proud of themselves for working it out.
They didn't care as much for the followup assignment to identify the possible sources of error in their measurements of time and distance and estimate the range of possible actual values that would result from the extremes of these small errors. If their first measurement came to 16 mph, did their tolerances with the ruler and stopwatch mean the actual value was somewhere between 14 and 18, or what?
Jeff
