Visitors to the "Beyond Numbers" exhibit encounter knot models, cultural string games, and even a model of "the place where a knot is not." to learn more about how mathematicians view knots.
 
 

 Mathematics as Reasoning:
Students can understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs. 
Students can make and evaluate mathematical conjectures and arguments.

 Mathematics as Communication:
Students can develop common understandings of mathemacial ideas, including the role of definitions. Students can discuss mathemtaical ideas and make conjectures and convincing arguments.

 The Nature of Mathematics, Patterns and Relationships:
Students learn that new mathematics continues to be invented, and connections between different parts of mathematics continue to be found.

 The Nature of Mathematics, Mathematics, Science, and Technology:
Students know that mathematics and science as enterprises share many values and features: belief in order, ideals of honesty and openness, the importance of criticism by colleagues, and the essential role played by imagination. 

 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.
 
 

 Activity 2 - Knot Tag 
Show the participants the ten pre-made knots and emphasize that they are not to be disconnected. Give every participating pair of students a completed knot and a plain length of rope. Challenge them to recreate the completed knot. You might suggest loosening the completed knot to see how the crossings are arranged.

 When the knot is completed, have the chaperon verify that the knot is correct and then use tape to tag the model knot with the team initials. Trade tagged knot models with another team. Continue until a team has tagged all of the models.