Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.
Work with this topic is most productive when the theme can be
given some time.
Because it is not traditional school mathematics it offers a
good opportunity for students to explore something new and
experience the emergence of structure for themselves.
Allow plenty of time for discussion :
How do we begin to talk about something which for most of us is
just a tangle of string or a tied knot we do so automatically, like
a shoe lace or a reef knot, that we hardly think about it ?
A knot collection might make a stimulating talking point for
students in a classroom.