Explore the relationship between knot diagrams and physical
knots.
Become adept at making physical knots from diagrams so that they
can quickly and accurately produce knots that they want to
experiment with in other activities.
At the end of the activity, each student or small group of students will
have many knots to examine and work with. They can use these knots in
other activities.
Tape that will hold the end of the knots securely.
One large set of the knots that students will make for
reference and display. These can be the same knots that were
used in the activity Knot Observations
.
If this is the students' first experience with knots, give them
some background about the mathematical study of
knots.
Show how mathematical knots are closed loops
with the ends tied together.
Explain that each student or group will be making several knots.
By making knots yourself, you will be able to understand a lot of
things about the structure of knots. Then we will all have quite a
few knots to study and experiment with.
Have the students look at the knot in the upper left hand corner
of the collection of knot diagrams it is a trefoil knot
. Draw
this knot on the board and show students how the broken line in the diagram
means that the strand of rope goes under the other strand when the two
cross.
Using a large strand of rope, demonstrate to the students how to
form a trefoil knot according to the diagram. It is easiest to make
knots from diagrams on a flat surface, rather than holding them in
your hand where they can flop around. Use a slanted board to
demonstrate to the whole class, or form the knots on the table, the
floor, or other flat surface and have the students gather round and
watch. Show how you fasten the ends of the knot together with tape so
that the closure is secure and smooth.
Have the students make the trefoil knot
. Help them verify
that the knots have been made correctly. Be especially careful that the
students have not made the other trefoil knot --the one to the right
of it in the collection of knot diagrams--by mistake. Encourage students to help
one another, to explain the method or techniques that they used to
make the knot and to check that it was correct.
When students understand how to make knots from the diagrams,
tell them which other knots they should make. Choose four or five
knots that everyone will make. Then allow students make two or three
other knots of their own choosing from the collection of knot diagrams.
It is very important that the knots be produced exactly as they
are in the diagrams. (If the knots aren't exactly right now, this will
pose a problem later if the students do the activity Are they the Same or Knot . In that
activity, students combine their knot collections
and examine knots which are identical.) As the number of crossings
increases, it is easy to make mistakes. Have students pair up and
compare the knots that they have made to be sure they are indeed
identical. If the knots appear different, have them study the knots
and the diagram carefully to determine what the problem is. When one
group has completed a set of knots, they should ask members of another
group to verify that they have made the knots exactly as they are in
the diagrams.
When the knots are finished and verified for accuracy, have
students label them with their names. Also, be sure the knots are
strong, and not likely to pull apart, because they will receive a lot
of use in further activities.
Materials 
