In this activity students will combine knots to see how they can be added together. They will manipulatively experience the concept of identity and explore some of the subtleties of the nature of mathematical truth. If students have already done the activity A Classroom Menagerie of Mathematical Knots , they will have plenty of knots to work with in this activity, and a familiarity with knots that will help them understand the concept of knot addition better. Materials Instructions Ideas for discussion Materials Knots that were made in the activity A Classroom Menagerie of Mathematical Knots or for each group of students, the knots in the top row of the collection of knot diagrams . Paper and pencil.
Instructions Draw the figure below on the chalk board.
Explain that knots are added together by doing a little bit of surgery. First, make a cut in each one of the knots that will be added. Do this carefully, without untying. Help the students to generate questions about adding knots. What happens if we add two knots together, then take the same two knots, flip one them over, and add them.