Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Age 11 to 14 Challenge Level:
Alan Schoenfeld reports that:
Some people think that the room will go (almost) instantaneously
dark as the wheel first passes the window, that it will stay dark
for a short while and then go (almost) instantaneously light as the
Others think that the room will go (almost) instantaneously dark as
the wheel first passes the window, that it will stay dark for a
relatively long time and then go (almost) instantaneously light as
the wheel leaves.
Others think that the room darkens slowly, as though a large
curtain is being pulled, more or less horizontally (from left to
right), or diagonally (from the top left corner), or vertically
downwards, as in the sketches below:
The room then stays dark for a short /long period of time, after
which it lightens in a way that is complementary to the way it
What do you think?
Perhaps this interactivity can
You can make the wheel bigger and smaller by pressing the up
and down arrow keys and you can make it roll by using the other
arrow keys. You can also move the blue square around.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.