Students examine and learn how to tie some practical knots that are used
for various purposes. This gives them further exposure to the structure of
knots and provides a new context in which to apply their skills of
observing and making conjectures about knots.
Remind the students that knots have been useful in the world for
years.
Review some of the purposes and uses of knots. Many books about
knot tying classify knots according to some scheme based on their
type and purpose (i.e., tying to a post, shortening a rope, etc.)
Have students examine and tie several knots and relate this
experience to their mathematical study of knots.
What are some of the differences between mathematical
knots and everyday knots that are tied for a variety of purposes?
How are they the same?
Knots can be classified by the ways in which they are used for
practical purposes. Do these classifications match the ways in which
you have classified knots mathematically?
Using several practical knots as a starting point, ask some of
the questions you have asked about mathematical knots. Are some knots
equivalent? Can they be
decomposed ? What happens when you
add them?
Materials 
