Students can make and evaluate mathematical conjectures and arguments.
Students can discuss mathemtaical ideas and make conjectures and convincing arguments. Students learn that new mathematics continues to be invented, and connections between different parts of mathematics continue to be found. As with other topics in topology, a fundamental problem is identifying what features in a knot are invariant. Mathematicians have distinguished 13,000 single-component knots with 13 or fewer crossings, not counting mirror objects. The following activities serve as an introduction to knot theory and will help students appreciate how a seemingly simple idea can lead to interesting and challenging problems.