- Knot Observations By making observations about knots, students become acquainted with the idea of knots as a mathematical object.
- A Classroom Menagerie of Mathematical Knots Students explore the structure of knots by making them. Using diagrams as a guide, they learn how knots can be represented on paper.
- Seifert Surfaces Observing what happens when knots are turned into bubble-makers takes the study of knots in a surprising direction.
- Are They the Same--or Knot? Determining whether two knots are the same or different is one of the central issues in knot theory . Students make puzzles for one another that explore this.
- Knot Arithmetic Students experiment with ways that two or more knots can be combined to make a single one.
- Building Block Knots Can complex knots be described in terms of more simple ones? Students try to find ways to figure out how to do this.
- Knots in the World What is the relationship between mathematical knots and the knots that are used to tie and fasten things in the real world?
- Braids and Links Braided rope and knots that are fastened together like the links of a chain also find their way into the study of mathematical knots .