Preview of Article:
The Square Root of a Fair Share
School desks and dream homes
Illustrator: Michael Duffy
Man-o-man, were they crowded. When I asked my 8th-grade class how much personal space they got at school, their eyes rolled and — no surprise — they started talking to each other. They felt cramped in the hall, leaving class, and pressing against the door in the cold in the morning. And pity the poor souls who get a middle locker on the bottom tier. In-class conditions weren’t much better. At their desks, the bother was their stuff. Prepared students pack a binder, a planner, hopefully two pencils, a pen, a textbook, a notebook and a book for silent reading. Students soon learn that part of getting along in class means taking up as little space as possible. While 8th graders don’t usually make the connection, how much room they get is mathematics: it’s a matter of area.
After a few years of having my middle school students struggle to grasp square roots, I had decided to start with listening to how they experience area in order to connect squares and square roots to their everyday experience. I hoped that giving my students multiple opportunities to see that the side length of a square is the square root of its area, and conversely, that the area of a square is its side length squared, would help them understand this fascinating mathematical concept.
After my students’ ready response to my query about personal space, I decided they would compare the area of their desks to the area taken up by their supplies. From there, I would invite them to think critically about how and where people experience luxurious amounts of space or pressing closeness every day. The class would compare the size of the average newly built suburban house to houses built a generation ago and to dwellings in other parts of the world.
