I Think Knot : Modeling with Knots and Links

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 Mathematics.