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I Think Knot : Modeling with Knots and Links

Marsha Davis and Mehdi Khorami

 Mathematics Topic:Various Application Areas:Knot Theory Prerequisites:Students have learned about equivalent fractions and equivalent algebraic expressions.

| ©2017 Consortium 112 | 17 pages |

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 linksâ€”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.