Activity 1 provides an introduction to
mathematical knots. Students learn
about trefoil, figure-eight, and
pentafoil knots. Using string they
make knots and then transform them
to get visually different but equivalent
knots. Through this process, students
discover that equivalent knots can
look quite different.
In Activity 2, students
tackle the problem of differentiating
between knots. They are introduced
to the unknotting number and
tricolorability, two tools for determining
if two knots are equivalent. In
Activity 3, students are introduced to
links—knots that are intertwined.
They discover that linking numbers
can sometimes be used to determine
whether or not two links are equivalent.
Activity 4 discusses how knots
and links can be used to synthesize
molecules with special properties.
The activities in this pull-out address
Mathematical Practices #4 Model with
mathematics and #7 Look for and make
use of structure from the Common Core
State Standards for High School