Knots have been studied extensively by
mathematicians for the last hundred
years. Recently the study of knots has proved to be of great interest to
theoretical physicists and molecular biologists. One of the most peculiar
things which emerges as you study knots is how a category of objects
as simple as a knot could be so rich in profound mathematical connections.

Here are a variety of activities for exploring
knots made from pieces of rope. Students can make and verify observations
about knots, classify them, combine them, and find ways to determine if two
knots are alike. The activities outlined here can be combined to form a
single lesson about mathematical knots, or a larger investigative unit
that extends over a longer period of time. The sequence in which the activities are
listed is roughly in order of increasing difficulty and
challenge,
but all of the earlier activities are not strict prerequisites
for the later ones.

Finding ways to make precise spoken or written statements about an
inherently spatial and manipulative experience is a meaningful and
interesting challenge for all students. Teachers can help students learn
to do this by helping them develop classroom conventions for naming knots,
parts of knots, groups of knots, or for labeling parts of knots to make
them easier to talk about.

Although presentations and discussions are appropriate as a whole-class
activity when studying knots, most of these activities will work best when
students work individually, in pairs and small groups. It is important for
each student to be able touch and twist the knots that they are thinking
about.