Tuesday, October 25, 2011

Week 7, Marlborough School

October 25th 2011

Scouting for land, learning about area and perimeter

The plan was to choose the acre and hopefully string up the borders.  To prepare for this: last week we saw what an acre looks like, I brought 800ft of twine.  We began class discussing a mistake I made.  An honest mistake, but one that lead the way to learn about the relationships between area, perimeter and the number of sides or points a shape has.  Last week we learned that a square acre has about 200ft per side.  I took this knowledge home with me and remembered that longer pieces of string are very easily tangled and the last two times I have been witness to the stringing up of an acre, we had to cut and tie the string in many places. I decided to section off our string, rather than provide one piece that is 800ft long (should be 836ft for a more accurate measure).  I considered making four 200ft pieces.... but even better would be to have eight 100ft pieces right?!?  I briefly explained this to the class, with the end goal being that we could split into small groups and each group place a piece of string, making sure all pieces get tied together.  Can anyone tell me my mistake?  I had drawn a circle, square, triangle, and octagon on the board.  No one was really sure.  I pointed out that all of the shapes on the board had 800ft perimeters (however, they were not drawn to accurately or to scale, which the students noticed immediately!).  We already know that the square has an area of about 43,000 square feet and a perimeter of 800ft (200ft per side).  What do we think will happen if we take that 800 foot piece of string and make an equilateral triangle with it?  Each side will be about 266ft long.  Will that give us more or less area than the square with the same perimeter?  The class did a bit of murmuring and decided that it would probably be smaller.  Any guesses as to how much smaller?  Some numbers were thrown out the closest was 28,000 square feet.  Very close!  The actual area is about 30,600 square feet.  So if we strung up and 800ft perimeter triangle we would loose about a third of the land we are entitled to claim for our village.  Next we looked at the circle.  Do we think the circle will be smaller or larger?  Larger!  How much?  Several guesses were blurted out, the nearest being 50,000 square feet. The actual circle would be nearly 51,000 square feet.  How about this octagon, bigger or smaller than the square?  Bigger!  Bigger or smaller than the circle?  This shape gave us some trouble, some said smaller and others were sure it was bigger.  Any guesses as to the area of the octagon?  The nearest was 47,000 square feet.  The actual size is about 48,000 square feet.  So if we string up our acre using the eight strings I provided and create an octagon we will be claiming about 5000 extra square feet!  Does anyone know how big 5000 square feet is?  Well we measured the gym once and found out how many square meters it was.  How many?  I don't remember.    We established that we would be claiming a LOT of extra land and left it at that.

Onto the outdoors...
We grouped up in front of the school.  Did anyone find any land last week that they want to share with the rest of the group?  I found some near the cross country track, with a river going through it.  Hey, why don't we just build where we built last year?  I suggested that we look at last years site as it was closer, led by those who played last year.  We explored a bit and regrouped out by the pavilion.  We discussed some pros and cons regarding the site in the woods.  We moved on to the other site near the stream.  The kids were getting cold and having a hard time focusing on discussion at site number two, so we moved back out to the pavilion to discuss pros and cons for the stream site.  We then compared the two sites to each other.  I then had everyone who wanted the stream site to stand on one side, everyone for the woods on the other and those undecided in the middle.  There were eleven for the stream, eight for the woods and three undecided.  Now what are we going to do?  It was suggested that we have two villages and a civil war.  It was suggested that there was a third site that had many similar pros to the first two sites and fewer cons.  We ventured off one more time to a very nice site and began a pros and cons discussion.  Unfortunately the  bell rang at that time so we all had to hustle back to the school for the next class.

Next week I intend to continue this topic and hopefully select land.

No comments:

Post a Comment