One of the great Manhattan Country School Thanksgiving traditions is the Fifth Floor Math Trail, which takes place on the Tuesday morning before the holiday break. In previous years, we have sojourned to City Hall Park to analyze the works of Sol LeWitt in subzero weather, measured the distance across the East River from the shores of Randall’s Island, made predictions and collected data about shopping in East Harlem and compared the geometry in Moorish and Gothic buildings.
This year’s Math Trail investigated the feasibility of transporting the contents of the MCS library by forming a book brigade connecting our current home on East 96th Street to our new building on West 85th Street. We began by splitting into seven groups, each of which walked a different route from East 96th to West 85th Street. Students calculated the length of their route in three different ways: first, they did a flash estimate by looking at the route and comparing it to a scale printed along the bottom of the map. These flash estimates were shared and averaged out to come up with a crowd-sourced estimate of the route length. Next, students used strings, rulers and tape measures to compute a more accurate length of the route proposed for their group. These routes went to the north and south of the Central Park reservoir, as well as followed paths along Fifth Avenue and Central Park West. The final step was to map the route using a smartphone app called Map My Walk, which used GPS data to calculate the distance to the nearest 10th of a mile.
For many students the walk to 85th Street was their first visit to our new home. They were relieved to discover that the new building not only has a beautiful facade, but also hosts a grand staircase from the first floor to the second, and, like our current home on East 96th, sports a large fire escape on the back side. They were also enthusiastic about our proximity to Central Park’s Great Lawn (and the swings for big kids nearby), neighborhood restaurants and an adjoining school building with basketball courts.
When we returned to 96th Street, students visited the MCS library to estimate the number of books that would have to be transported. They used various kinds of estimation techniques, including taking a sample count of a single shelf and multiplying that by the number of shelves. Some groups measured the number of books per foot, and then multiplied that by the number of feet of shelving in the library.
After all this data was collected, students calculated the number of people that would be needed to stand along the path to form the book brigade. To make this calculation, students needed to convert the length of the path to feet, then create an estimate of how far apart people would stand along the path. One group stood side-by-side and lifted their arms so that they could comfortably transfer a sample book from person to person. By measuring the length of five people standing this way, they could form a ratio: five people could transport a book 30 feet, so how many people would we need to move that book 6,100 feet? As the calculations were made, students were reminded to think about the level of precision necessary to get a good answer.
The final step was to calculate the length of time it would take the book brigade to transport a single book across the park, and then calculate the time for the entire library. What is tricky about this problem is that it is not simply a matter of taking the number of minutes for a single book and multiplying it by the number of volumes in the library: as one student pointed out, since the books will be coming one after another, the solution is to figure out how fast a new book can be added to the line, multiplying that by the number of books and adding the amount of time for the first book to get across the park.
Each group presented the results of their findings. After these were assembled into a Google spreadsheet, students wrote equations to instruct Excel to average their findings. The results of our morning investigation revealed that it would take a little more than 1,900 people nearly three hours to move the 6,550 books in the MCS library the 1.4 miles from their current home on 96th Street to our new library on 85th Street. Asked whether they thought that this was a reasonable idea, the seventh- and eighth-graders thought it sounded “doable.” After all, if each current MCS student recruited 10 people (parents, friends, alumni, teachers) we’d have more than enough.